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% \usetheme{Singapore} % ima sadrzaj i tackice gore
% \usetheme{Antibes} % ima sadrzaj gore i kao graf ...
% \usetheme{Berkeley} % ima sadrzaj desno
% \usetheme{Berlin} % ima sadrzaj gore i tackice
% \usetheme{Goettingen} % ima sadrzxaj za desne strane
% \usetheme{Montpellier} % ima graf sadrzaj gore
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% \usepackage[pdfauthor={Boris Jeremic},
% colorlinks=true,
% linkcolor=webblue,
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% linktocpage,
% pdftex]{hyperref}
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% or whatever
\usepackage{times}
\usepackage[T1]{fontenc}
% Or whatever. Note that the encoding and the font should match. If T1
% does not look nice, try deleting the line with the fontenc.
% Site Specific Dynamics of Structures:
%From Seismic Source to
%the Safety of Occupants and Content
\title[RealESSI]
{ Modeling and Simulation of \\
Earthquake Soil Structure Interaction}
%\subtitle
%{Include Only If Paper Has a Subtitle}
%\author[Author, Another] % (optional, use only with lots of authors)
%{F.~Author\inst{1} \and S.~Another\inst{2}}
%  Give the names in the same order as the appear in the paper.
%  Use the \inst{?} command only if the authors have different
% affiliation.
\pgfdeclareimage[height=0.2cm]{universitylogo}{/home/jeremic/BG/amblemi/ucdavis_logo_blue_sm}
\pgfdeclareimage[height=0.7cm]{lbnllogo}{/home/jeremic/BG/amblemi/lbnllogo}
\author[Jeremi{\'c} et al.] % (optional, use only with lots of authors)
%{Boris~Jeremi{\'c}}
{Boris Jeremi{\'c}
}
%\institute[Computational Geomechanics Group \hspace*{0.3truecm}
\institute[\pgfuseimage{universitylogo}\hspace*{0.1truecm}\pgfuseimage{lbnllogo}] % (optional, but mostly needed)
%{ Professor, University of California, Davis\\
{ University of California, Davis, CA\\
% and\\
% Faculty Scientist, Lawrence Berkeley National Laboratory, Berkeley }
Lawrence Berkeley National Laboratory, Berkeley, CA}
%  Use the \inst command only if there are several affiliations.
%  Keep it simple, no one is interested in your street address.
\date[] % (optional, should be abbreviation of conference name)
{\small Shijiazhuang Tiedao University \\
Shijiazhuang, July 2019}
\subject{}
% This is only inserted into the PDF information catalog. Can be left
% out.
% If you have a file called "universitylogofilename.xxx", where xxx
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%\pgfdeclareimage[height=0.2cm]{universitylogo}{/home/jeremic/BG/amblemi/ucdavis_logo_gold_lrg}
%\logo{\pgfuseimage{universitylogo}}
% \pgfdeclareimage[height=0.5cm]{universitylogo}{universitylogofilename}
% \logo{\pgfuseimage{universitylogo}}
% Delete this, if you do not want the table of contents to pop up at
% the beginning of each subsection:
% \AtBeginSubsection[]
\setcounter{tocdepth}{3}
\AtBeginSubsection[]
% \AtBeginSection[]
{
\begin{scriptsize}
\begin{frame}
\frametitle{Outline}
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\begin{document}
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\begin{frame}
\titlepage
\end{frame}
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\begin{frame}
\frametitle{Outline}
\begin{scriptsize}
\tableofcontents
% You might wish to add the option [pausesections]
\end{scriptsize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Structuring a talk is a difficult task and the following structure
% may not be suitable. Here are some rules that apply for this
% solution:
%  Exactly two or three sections (other than the summary).
%  At *most* three subsections per section.
%  Talk about 30s to 2min per frame. So there should be between about
% 15 and 30 frames, all told.
%  A conference audience is likely to know very little of what you
% are going to talk about. So *simplify*!
%  In a 20min talk, getting the main ideas across is hard
% enough. Leave out details, even if it means being less precise than
% you think necessary.
%  If you omit details that are vital to the proof/implementation,
% just say so once. Everybody will be happy with that.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Motivation}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Motivation}
\begin{itemize}
%\vspace*{0.3cm}
\item[] Improve modeling and simulation for infrastructure objects
% \vspace*{2mm}
% \item[] Expert numerical modeling and simulation tool
%
% \vspace*{1mm}
% \item[] Use of numerical models to
% analyze statics and dynamics of soil/rockstructure systems
%
\vspace*{1mm}
\item[] Reduction of modeling uncertainty
\vspace*{1mm}
\item[] Choice of analysis level of sophistication
\vspace*{1mm}
\item[] Goal: Predict and Inform rather than fit
\vspace*{1mm}
\item[] Engineer needs to know!
%
%
%
% \vspace*{1mm}
% \item[] Follow the flow, input and dissipation, of seismic energy,
\vspace*{1mm}
\item[] System for modeling and simulation of
Earthquakes and/or Soils and/or Structures and their Interaction:\\
RealESSI,
\raisebox{1.2mm}{\includegraphics[height=5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/Real_ESSI_in_different_langauges/Real_ESSI_Chinese.jpeg}}
% \\
% \vspace*{1mm}
% % % \hspace*{25mm}
% % \url{http://realessi.info/} \\
% % % \hspace*{25mm}
% \url{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
% % \href{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}{{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
% % % \url{http://msessi.info/}
% %
%
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Prediction under Uncertainty}
\begin{itemize}
%\vspace*{1mm}
\item \underline{Modeling Uncertainty}, Simplifying assumptions
\begin{itemize}
\vspace*{2mm}
\item[] Low, medium, high sophistication modeling and simulation
\vspace*{2mm}
\item[] Choice of sophistication level for confidence in results
\end{itemize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\vspace*{4mm}
\item \underline{Parametric Uncertainty}, ${M} \ddot{u_i} + {C} \dot{u_i} + {K}^{ep} {u_i} = {F(t)}$,
\begin{itemize}
\vspace*{2mm}
\item[] Uncertain mass $M$, viscous damping $C$ and stiffness $K^{ep}$
\vspace*{2mm}
\item[] Propagation of uncertainty in loads, $F(t)$
\vspace*{2mm}
\item[] Results are PDFs and CDFs for $\sigma_{ij}$, $\epsilon_{ij}$, $u_i$, $\dot{u}_i$, $\ddot{u}_i$
\end{itemize}
\end{itemize}
%
%
% %Le doute n'est pas un {\'e}tat bien agr{\'e}able,\\
% mais l'assurance est un {\'e}tat ridicule. (Fran{\c c}oisMarie Arouet, Voltaire)
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Modeling Uncertainty}
\begin{itemize}
\item[] Important (?!) features are simplified, 1C vs 3C, inelasticity
%\vspace*{4mm}
% \item Unrealistic and unnecessary modeling simplifications
\vspace*{1mm}
\item[] Modeling simplifications are justifiable if one or two
level higher sophistication model demonstrates that features being
simplified out are not important
\end{itemize}
% local
%\vspace*{2mm}
\begin{center}
\hspace*{7mm}
%\movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
\movie[label=show3,width=5.5cm,poster,autostart, showcontrols]
{\includegraphics[width=50mm]
{/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_2_npps_mp4_icon.jpeg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_2_npps.mp4}
%
%\hfill
\hspace*{5mm}
%
\movie[label=show3,width=6.0cm,poster,autostart,showcontrols]
{\includegraphics[width=50mm]
{/home/jeremic/tex/works/Conferences/2017/SMiRT_24/present/3D_Nonlinear_Modeling_and_it_Effects/NPP_Plastic_Dissipation_grab.jpg}}
{/home/jeremic/tex/works/Thesis/HanYang/Files_10Aug2017/NPP_Plastic_Dissipation.mp4}
\hspace*{7mm}
%\end{flushleft}
%%
\end{center}
% local
% % \vspace*{5mm}
% \begin{center}
% %\begin{flushleft}
% % \hspace*{15mm}
% \movie[label=show3,width=5cm,poster,autostart,showcontrols]
% {\includegraphics[width=5cm]
% {/home/jeremic/tex/works/Conferences/2017/SMiRT_24/present/3D_Nonlinear_Modeling_and_it_Effects/NPP_Plastic_Dissipation_grab.jpg}}
% {/home/jeremic/tex/works/Thesis/HanYang/Files_10Aug2017/NPP_Plastic_Dissipation.mp4}
% %\end{flushleft}
% %%
% \hfill
% %%
% %\begin{flushright}
% % \hspace*{15mm}
% \movie[label=show3,width=5cm,poster,autostart,showcontrols]
% {\includegraphics[width=5cm]
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation_screen_grab.jpg}}
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mp4}
% %\end{flushright}
% \end{center}
%
\end{frame}
%OVDE
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Modeling Uncertainty, 6C vs 1C Motions}
%
%
% % local
% \vspace*{2mm}
% \begin{center}
% \hspace*{7mm}
% %\movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
% \movie[label=show3,width=8.8cm,poster, showcontrols]
% {\includegraphics[width=92mm]
% {/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_2_npps_mp4_icon.jpeg}}
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_2_npps.mp4}
% \end{center}
% % local
% % \vspace*{2mm}
% % \begin{center}
% % \hspace*{7mm}
% % \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
% % {\includegraphics[width=90mm]{movie_2_npps_mp4_icon.jpeg}}{movie_2_npps.mp4}
% % \end{center}
%
%
% % online
% \vspace*{12mm}
% \begin{flushleft}
% %\vspace*{15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_2_npps.mp4}
% {\tiny (MP4)}
% \end{flushleft}
% % online
%
%
%
%
%
% \end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Parametric Uncertainty: Soil Stiffness and Strength}
\vspace*{2mm}
%\vspace*{3mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{7mm}
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01Ed.pdf}
\hspace*{3mm}
% \hfill
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/YoungModulus_Histogram_Normal_01Ed.pdf}
%
\end{center}
\end{figure}
\vspace*{5mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{7mm}
\includegraphics[width=5.00truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/ShearStrength_RawData_and_MeanTrendMod.pdf}
\hspace*{3mm}
% \hfill
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/ShearStrength_Histogram_PearsonIVFineTunedMod.pdf}
%
\end{center}
\end{figure}
%\vspace*{5mm}
%\vspace*{1.8cm}
%\hspace*{3.3cm}
\begin{flushright}
{\tiny
(cf. Phoon and Kulhawy (1999B))\\
~}
\end{flushright}
%
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Parametric Uncertainty: Material Properties}
%
%
%
% \vspace*{5mm}
% \begin{figure}[!hbpt]
% \begin{center}
% % %
% \hspace*{3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiPdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiCdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldSuPdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldSuCdf.pdf}
% \\
% %\vspace*{2mm}
% \hspace*{2.5cm} \mbox{\tiny Field $\phi$} \hspace*{3.5cm} \mbox{\tiny Field $c_u$}
% \\
% \vspace*{10mm}
% \hspace*{3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiPdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiCdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuPdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuCdf.pdf}
% \\
% %\vspace*{8mm}
% \hspace*{2.5cm} \mbox{\tiny Lab $\phi$} \hspace*{3.5cm} \mbox{\tiny Lab $c_u$}
% \end{center}
% \end{figure}
%
%
%
% \end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{ESSI: Energy Input and Dissipation}
\begin{itemize}
\vspace*{1mm}
\item[] Energy input, dynamic forcing
\vspace*{4mm}
\item[] Energy dissipation outside SSI domain:
\begin{itemize}
\item[] SSI system oscillation radiation
\item[] Reflected wave radiation
\end{itemize}
\vspace*{1mm}
\item[] Energy dissipation/conversion inside SSI domain:
\begin{itemize}
\item[] Inelasticity of soil, contact/interface zone, structure, foundation, dissipators
\item[] Viscous coupling with pore fluids, and external fluids
% % \item[] potential and kinetic energy
% \item[] potential $\leftarrow \! \! \! \! \! \! \rightarrow$ kinetic energy
\end{itemize}
\vspace*{1mm}
% \item[] Numerical energy dissipation (numerical damping/production and period errors)
% \item[] Numerical energy dissipation (damping/production)
\item[] Numerical, algorithmic energy dissipation/production
\end{itemize}
%
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Fully Coupled Formulation, upU}
%
%
\begin{small}
\begin{eqnarray}
\hspace*{13mm}
\left[ \begin{array}{ccc}
(M_s)_{KijL} & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & (M_f)_{KijL}
\end{array} \right]
\left[ \begin{array}{c}
\ddot{\overline{u}}_{Lj} \\
\ddot{\overline{p}}_N \\
\ddot{\overline{U}}_{Lj}
\end{array} \right]
+
\left[ \begin{array}{ccc}
(C_1)_{KijL} & 0 & (C_2)_{KijL} \\
0 & 0 & 0 \\
(C_2)_{LjiK} & 0 & (C_3)_{KijL} \\
\end{array} \right]
\left[ \begin{array}{c}
\dot{\overline{u}}_{Lj} \\
\dot{\overline{p}}_N \\
\dot{\overline{U}}_{Lj}
\end{array} \right]
\nonumber
\\
+
\left[ \begin{array}{ccc}
(K^{EP})_{KijL} & (G_1)_{KiM} & 0 \\
(G_1)_{LjM} & P_{MN} & (G_2)_{LjM} \\
0 & (G_2)_{KiL} & 0
\end{array} \right]
\left[ \begin{array}{c}
\overline{u}_{Lj} \\
\overline{p}_M \\
\overline{U}_{Lj}
\end{array} \right]
=
\left[ \begin{array}{c}
\overline{f}_{Ki}^{solid} \\
0 \\
\overline{f}_{Ki}^{fluid}
\end{array} \right] \nonumber
%\\
%\label{68}
\end{eqnarray}
\end{small}
%
%
%
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Fully Coupled Formulation, upU}
%
%
%
%
%
\begin{eqnarray}
\hspace*{10mm} (M_s)_{KijL}&=&\int_{\Omega} H_K^u (1n) \rho_s \delta_{ij} H_L^u d\Omega
\hspace*{5mm} (M_f)_{KijL}=\int_{\Omega} H_K^U n \rho_f \delta_{ij} H_L^U d\Omega \nonumber\\
\hspace*{10mm} (C_1)_{KijL}&=&\int_{\Omega} H_K^u n^2 k_{ij}^{1} H_L^u d\Omega
\hspace*{5mm} (C_2)_{KijL}=\int_{\Omega} H_K^u n^2 k_{ij}^{1} H_L^U d\Omega \nonumber\\
\hspace*{10mm} (C_3)_{KijL}&=&\int_{\Omega} H_K^U n^2 k_{ij}^{1} H_L^U d\Omega
\hspace*{5mm} (K^{EP})_{KijL}=\int_{\Omega} H_{K,m}^u D_{imjn} H_{L,n}^u d\Omega \nonumber\\
\hspace*{10mm} (G_1)_{KiM}&=&\int_{\Omega} H_{K,i}^u (\alphan) H_M^p d\Omega
\hspace*{5mm} (G_2)_{KiM}=\int_{\Omega} n H_{K,i}^U H_M^p d\Omega \nonumber\\
\hspace*{10mm} P_{NM}&=&\int_{\Omega} H_N^p \frac{1}{Q} H_M^p d\Omega \nonumber
\end{eqnarray}
%
%
%
%
%\newpage
% \begin{eqnarray}
% \overline{f}_{Ki}^{solid}&=&(f_1^u)_{Ki}(f_4^u)_{Ki}+(f_5^u)_{Ki} \nonumber\\
% \overline{f}_{Ki}^{fluid}&=&(f_1^U)_{Ki}+(f_2^U)_{Ki} \nonumber\\
% (f_1^u)_{Ki}&=&\int_{\Gamma_t} H_K^u n_j \sigma_{ij}^{''} d\Gamma \nonumber\\
% (f_4^u)_{Ki}&=&\int_{\Gamma_p} H_K^u (\alphan) n_i p d\Gamma \nonumber\\
% (f_5^u)_{Ki}&=&\int_{\Omega} H_K^u (1n) \rho_s b_i d\Omega \nonumber\\
% (f_1^U)_{Ki}&=&\int_{\Gamma_p} n H_K^U n_i p d\Gamma \nonumber\\
% (f_2^U)_{Ki}&=&\int_{\Omega} n H_K^U \rho_f b_i d\Omega
% \label{69}
% \end{eqnarray}
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\begin{figure}[!H]
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\includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_g.pdf}
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%
% Single elasticplastic element under cyclic shear loading
%
% \begin{itemize}
% \item[] Difference between plastic work and plastic dissipation
% \item[] Plastic work can decrease
% \item[] Plastic dissipation always increases
% \end{itemize}
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% \includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSISite_Response_Analysis/Liquefaction_01.jpg}
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% \includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSISite_Response_Analysis/Liquefaction_03.jpg}
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% \begin{figure}[!H]
% \hspace*{10mm}
% \includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/upU_element_type_annotation.pdf}
% \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/bouyant_displacement.pdf}
% \end{figure}
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% %  % \begin{tikzpicture}[remember picture,overlay]
% %  % \node[anchor=south west,inner sep=0pt] at ($(current page.south west)+(7.5cm,2.5cm)$) {
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% %  % \end{tikzpicture}
% % 
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% % \begin{itemize}
% % \item \scriptsize Upward structural displacement under buoyant force
% % \end{itemize}
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% \movie[label=show3,width=9cm,poster,autostart,showcontrols]
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% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Fluid_Solid_interaction/Solid_Fluid_Interaction_NEW.mpeg}
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% \begin{flushleft}
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% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Fluid_Solid_interaction/Solid_Fluid_Interaction.mp4}
% % \href{./homo_50mmesh_45degree_Ormsby.mp4}
% {\tiny (MP4)}
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\section{RealESSI Simulator System}
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%\subsection*{RealESSI Simulator System}
\subsection{Real ESSI Components}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{RealESSI Simulator System}
The RealESSI,
{\underline {\bf Real}}istic
%{\underline {\bf M}}odeling and
%{\underline {\bf S}}imulation of
{M}odeling and
{S}imulation of
{\underline {\bf E}}arthquakes,
{\underline {\bf S}}oils,
{\underline {\bf S}}tructures and their
{\underline {\bf I}}nteraction. Simulator is a software, hardware and
documentation system for time domain,
linear and nonlinear, inelastic, deterministic or probabilistic, 3D, finite
element modeling and simulation of:
\begin{itemize}
%\vspace*{1mm}
\item[] statics and dynamics of soil,
%\vspace*{1mm}
\item[] statics and dynamics of rock,
%\vspace*{1mm}
\item[] statics and dynamics of structures,
%\vspace*{1mm}
\item[] statics of soilstructure systems, and
%\vspace*{1mm}
\item[] dynamics of earthquakesoilstructure system interaction
\end{itemize}
Used for:
\begin{itemize}
%\vspace*{1mm}
\item[] Design, linear elastic, load combinations, dimensioning
%\vspace*{1mm}
\item[] Assessment, nonlinear/inelastic, safety margins
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{RealESSI Simulator System}
\begin{itemize}
\item RealESSI System Components
\begin{itemize}
\item[] RealESSI Preprocessor (gmsh/gmESSI, X2ESSI)
\item[] RealESSI Program (local, remote, cloud)
\item[] RealESSI PostProcessor (Paraview/pvESSI, Python)
\end{itemize}
\vspace*{1mm}
\item RealESSI System availability:
\begin{itemize}
%\vspace*{1mm}
\item[] Educational Institutions: AWS, Linux Image, free
\item[] Government Agencies, National Labs: AWS GovCloud
\item[] Professional Practice: AWS, commercial
%\vspace*{1mm}
%%\vspace*{1mm}
% \item Sources available to collaborators
\end{itemize}
\vspace*{1mm}
\item RealESSI Short Courses, online, worldwide
\vspace*{1mm}
\item
% System description and documentation at
\url{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
%
%\url{http://realessi.info/}
%
% \vspace*{2mm}
% \item
%
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Quality Assurance}
\begin{itemize}
\item Full verification suit for each element, model, algorithm
\vspace*{5mm}
\item Certification process
\begin{itemize}
\vspace*{2mm}
\item[] ASME NQA1
\vspace*{2mm}
\item[] ISO900032014
\end{itemize}
%\vspace*{3mm}
%\item[] Verification examples given below
\end{itemize}
\end{frame}
% %
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{RealESSI}
%
% \begin{itemize}
%
%
%
% %\vspace*{2mm}
% \item A system for time domain, nonlinear/inelastic, deterministic or
% probabilistic, modeling and simulation of
%
% \begin{itemize}
% \item statics and dynamics of soil,
% \item statics and dynamics of rock,
% \item statics and dynamics of structures,
% \item statics of soilstructure systems, and
% \item dynamics of earthquakesoilstructure system interaction.
% \end{itemize}
%
%
% \vspace*{1mm}
% \item Design, linear elastic, load combinations, dimensioning
%
%
% \vspace*{1mm}
% \item Assessment, nonlinear/inelastic, safety margins
%
%
%
% %\vspace*{1mm}
% % \item Develops methods and models that inform and predict rather than (force) fit.
%
% \vspace*{1mm}
% \item Collaboration and financial support from the USDOE, USNRC,
% USNSF, Caltrans, CNSCCCSN, UNIAEA, Shimizu, Basler\&Hofmann, etc.
%
%
%
% \end{itemize}
%
% \end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{RealESSI Modeling Features}
\begin{itemize}
%\vspace*{2mm}
\item[] Solid elements, dry, (un)saturated, elastic, inelastic
\vspace*{1mm}
\item[] Structural elements, beams, shells, elastic, inelastic
\vspace*{1mm}
\item[] Contact elements, dry, coupled/saturated,
\vspace*{1mm}
\item[] Super element, stiffness and mass matrices
\vspace*{1mm}
\item[] Material models, soil, concrete, steel...
\vspace*{1mm}
\item[] Seismic input, 1C and 3C, deterministic or probabilistic
\vspace*{1mm}
\item[] Energy dissipation calculations
\vspace*{1mm}
\item[] Solid/Structure  Fluid interaction, full coupling
\vspace*{1mm}
\item[] Intrusive probabilistic inelastic modeling
%
%\vspace*{1mm}
% \item Modeling features listed at
% \hspace*{5mm}
% \href{http://realessi.info/}{http://realessi.info/}
%% \hspace*{5mm}
%% and
%% \hspace*{5mm}
%% \href{http://realessi.info/}{http://realessi.info/}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{RealESSI Simulation Features}
%\vspace*{10mm}
\begin{itemize}
\item[] Static loading stages
\vspace*{2mm}
\item[] Dynamic loading stages
\vspace*{2mm}
\item[] Restart, simulation tree
\vspace*{2mm}
\item[] Solution advancement methods/algorithms, \\
on global and constitutive levels, \\
with and without enforcing equilibrium
%\vspace*{1mm}
% \item Load combinations, elastic, for design
\vspace*{2mm}
\item[] High Performance Computing
% clusters, cloud, supercomputers
\begin{itemize}
\vspace*{1mm}
\item[.] Fine grained, template mataprograms, small matrix library
\vspace*{1mm}
\item[.] Coarse grained, distributed memory parallel
\end{itemize}
% \vspace*{1mm}
% \item All Simulation Features are listed at
% \hspace*{5mm}
% \href{http://realessi.info/}{http://realessi.info/}
% % \hspace*{5mm}
% % and
% % \hspace*{5mm}
% % \href{http://realessi.info/}{http://realessi.info/}
\end{itemize}
\vspace*{60mm}
%\begin{figure}[!hbpt]
\begin{flushright}
\includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Theory_Introduction/tex_works_psfigures_loading_stageincrementsiterations.pdf}
\end{flushright}
%\vspace*{0.5cm}
%\end{figure}
%
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{RealESSI Model Development}
\begin{itemize}
\item[] PreProcessing, model development gmsh/gmESSI
\vspace*{1mm}
\item[] Existing model translation, SASSI$\rightarrow$RealESSI
\vspace*{1mm}
\item[] Self documenting input language
\vspace*{1mm}
\item[] Units required for all input variables
\vspace*{1mm}
\item[] All variables and constants need to be defined by user
\vspace*{1mm}
\item[] Choose level of sophistication
\vspace*{1mm}
\item[] Reduce modeling uncertainty
\vspace*{1mm}
\item[] Model developed in phases
\vspace*{1mm}
\item[] Verify model components
\vspace*{1mm}
\item[] Build confidence in inelastic modeling
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{RealESSI Modeling Phases}
\begin{figure}[htbp]
\begin{center}
\includegraphics[width = 2.3cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figurefiles/nonlinear_analysis_steps/soilstructure/overview.png}
\vspace*{1mm}
\\
\includegraphics[width = 0.35cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figurefiles/nonlinear_analysis_steps/free_field_1D/DRM_1D_motion_3D_just_column.jpg}
\hspace*{5mm}
% \includegraphics[width = 0.1cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figurefiles/nonlinear_analysis_steps/free_field_1D/DRM1D_Motion3D.png}
\includegraphics[width = 2.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figurefiles/nonlinear_analysis_steps/free_field_3D/motion3D_DRM3D_free_field.png}
\hspace*{5mm}
% \includegraphics[width = 1cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figurefiles/nonlinear_analysis_steps/soilfoundation/soil_foundation.png}
% \includegraphics[width = 3cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figurefiles/nonlinear_analysis_steps/soilfoundation/slice.png}
\includegraphics[width = 2.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figurefiles/nonlinear_analysis_steps/soilfoundation/foundation_results.png}
% \includegraphics[width = 3cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figurefiles/nonlinear_analysis_steps/soilstructure/overview.png}
\\
\vspace*{3mm}
\includegraphics[width = 1.0cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figurefiles/nonlinear_analysis_steps/structure/eigen/structureonly.png}
\hfill
\includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figurefiles/nonlinear_analysis_steps/structure/eigen/eigen1.png}
\hfill
\includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figurefiles/nonlinear_analysis_steps/structure/eigen/eigen2.png}
\hfill
\includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figurefiles/nonlinear_analysis_steps/structure/eigen/eigen3.png}
\hfill
\includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figurefiles/nonlinear_analysis_steps/structure/eigen/eigen4.png}
\hfill
\includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figurefiles/nonlinear_analysis_steps/structure/eigen/eigen5.png}
\hfill
\includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figurefiles/nonlinear_analysis_steps/structure/eigen/eigen6.png}
\hfill
% \includegraphics[width = 1.0cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figurefiles/nonlinear_analysis_steps/structure/imposed_motion/structureonly.png}
%\hfill
\includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figurefiles/nonlinear_analysis_steps/structure/imposed_motion/imposed_motion_results.png}
% \includegraphics[width = 0.1cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figurefiles/nonlinear_analysis_steps/soilstructure/overview.png}
\\
\vspace*{1mm}
\includegraphics[width = 6cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figurefiles/nonlinear_analysis_steps/soilstructure/DRM3D_motion3D_structure.png}
\end{center}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{RealESSI Results Post Processing}
\begin{itemize}
\item All output is saved (stress, strain, displacements, energy...)
\vspace*{5mm}
\item Time histories, scripts to plot or extract in preferred format
\vspace*{5mm}
\item 3D visualization, Paraview with pvESSI plugin
% OVDE dodaj primere vizualizacije
\end{itemize}
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{RealESSI Verification}
%
% \begin{itemize}
%
%
% \item Implementation verification
%
% \vspace*{2mm}
% \item Solution verification for each component
% \begin{itemize}
% \item Finite elements
% \item Constitutive algorithms
% \item Solution advancement, static and dynamic
%
% \end{itemize}
%
%
% \vspace*{2mm}
% \item Error quantification for ranges of modeling parameters
%
% \vspace*{2mm}
% \item Automatic verification, a 13 hour process on multiple CPUs
%
%
%
% \end{itemize}
%
% \end{frame}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{RealESSI Validation}
%
% %OVDE
% \begin{itemize}
%
% \item Validation partially done, need for high quality data
%
% \vspace*{1mm}
% \item Validation, UNR soil box tests in the near future
% \begin{itemize}
%
% %\vspace*{1mm}
% \item Soil testing, range of strains, confinements, stress paths
%
% %\vspace*{1mm}
% \item Contact testing, axial, shear, soilconcrete, formed, poured
%
% %\vspace*{1mm}
% \item Wave propagation through soil, equivalent elastic and inelastic,
% 1C and 2C, dilatancy influence
%
% %\vspace*{1mm}
% \item Inelastic structural behavior for beams, walls, plates, shells, use of
% already published high quality test data
%
% %\vspace*{1mm}
% \item ESSI tests for a complete simplified SSI systems
%
% \end{itemize}
%
%
% \end{itemize}
%
%
% \begin{figure}[!htbp]
% \begin{flushleft}
% \includegraphics[width=2cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/soilbox_model_gmsh.png}
% \hspace*{1mm}
% \includegraphics[width=1.2cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mesh_detail.pdf}
% \end{flushleft}
% \end{figure}
%
%
%
% \vspace*{30mm}
% \begin{figure}[!htbp]
% \begin{flushright}
% \includegraphics[width=1.6cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode1_side.pdf}
% \includegraphics[width=1.6cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode2_side.pdf}
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% % \includegraphics[width=1cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode12_side.pdf}
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\begin{frame}
\frametitle{RealESSI Training and Education}
\begin{itemize}
\item Short Courses:
\begin{itemize}
\vspace*{1mm}
\item[] Online short course, Fall 2019
%\vspace*{1mm}
% \item[] Professional practice
% % \vspace*{1mm}
% \item Developers
\vspace*{1mm}
\item[] Examples available in lecture notes, and documentation
%\vspace*{1mm}
% \item[] RealESSI Simulator system, with examples on Amazon Web Services
% (AWS)
\end{itemize}
%\vspace{1mm}
% \item Documentation, extensive
\vspace{2mm}
\item Full lecture notes (2600+ pages) available online
\url{http://sokocalo.engr.ucdavis.edu/~jeremic/}
%\vspace{2mm}
% \item Up to date information on RealESSI at:
% \\ \vspace*{2mm}
% \hspace*{5mm}
% \url{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
%%
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%%\href{http://realessi.info/}{http://realessi.info/}
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\end{itemize}
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% OVDE OVDE OVDE
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\begin{frame}
\frametitle{RealESSI Core Functionality}
\begin{itemize}
%\vspace*{2mm}
\item [] Introduction to inelastic, nonlinear analysis for practicing engineers
%
% % \vspace*{3mm}
% \item Usable models for professional practice
%
% %\vspace*{2mm}
% \item Core functionality needed for nonlinear modeling in professional
% practice
% %
%
% %\vspace*{0.3cm}
% %\vspace*{2mm}
% \item Hierarchy of modeling capabilities,
%
% \begin{itemize}
%
% %\vspace*{1mm}
% \item Linear elastic models, elastic constants, viscous damping
%
% %\vspace*{1mm}
% \item Nonlinear models, core functionality, does not require much
% material data however, sensitivity study is advised
%
% %\vspace*{1mm}
% \item High sophistication nonlinear models, require material data
%
%
% \end{itemize}
%
\vspace*{2mm}
\item[] Use of prescribed, required (low, medium, high) fidelity numerical
models to analyze ESSI behavior
\vspace*{2mm}
\item[] Set of suggested modeling and simulation parameters
\vspace*{2mm}
\item[] Investigate sensitivity of response to model sophistication
\vspace*{2mm}
\item[] Investigate sensitivity of response to model parameters
%
% \vspace*{1mm}
% \item[] Accurately follow the flow of seismic energy in a
% soil structure system
%
% \vspace*{1mm}
% \item[] The goal is to create methodology and numerical tool that is used to
% predict and inform and not to fit
%
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% %\vspace*{1mm}
% % \item[] Directing, in space and time, seismic energy flow in the
% % soil structure system
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\end{itemize}
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\frametitle{RealESSI Core Functionality Components}
\begin{itemize}
\item[] Structural elements: Truss, Beam, Shell, SuperElement
\vspace*{2mm}
\item[] Soil, solids: elastic, $G/G_{max}$
\vspace*{2mm}
\item[] Contacts: Bonded, Frictional, Gap open/close
\vspace*{2mm}
\item[] Loads: Static, Dynamic (earthquake, 1C or 3$\times$1C), Restart
\vspace*{2mm}
\item[] Simulation: Explicit noequilibrium, Implicit equilibrium
\vspace*{2mm}
\item[] Core Functionality Application programs: APPs
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% \frametitle{NPP, Inelastic Response, Energy Dissipation}
%
% % Elastoplastic soil with contact elements
% %% Both solid and contact elements dissipate energy
%
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% % \vspace*{5mm}
% \begin{center}
% % \hspace*{15mm}
% \movie[label=show3,width=10cm,poster,autostart,showcontrols]
% {\includegraphics[width=10cm]
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/NPP_Plastic_Dissipation_grab.jpg}}
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/NPP_Plastic_Dissipation.mp4}
% \end{center}
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%
% \begin{flushleft}
% \vspace*{15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animation/NPP_Plastic_Dissipation.mp4}
% % \href{./homo_50mmesh_45degree_Ormsby.mp4}
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\subsection{Stochastic Modeling}
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Uncertainties are inevitable in predicting behaviors of structures during future earthquakes}
%\vspace{0.5cm}
%
% \begin{tabular}{c c}
% \begin{minipage}{0.45\textwidth}
% %
% \hspace{1cm} {\color{blue} Soils are spatially nonuniform}
% \begin{itemize}
%
% \footnotesize
% \item Spatial nonuniformity is a function of soil formation process.
% \vspace*{0.1cm}
% \item Spatial nonuniformity is usually 'uncertain', due to limited data!
% \vspace*{0.1cm}
% \item Soil parameters are ideally described as nonGaussian random fields
% \end{itemize}
%
% \end{minipage} &
% %
% \hspace*{0.75truecm}
% \begin{minipage}{0.50\textwidth}
%
% \begin{figure}
% \includegraphics[height=5.45cm]{Fangbo_figs/TypicalSoilVariability.jpg}
% \end{figure}
% \vspace*{0.5truecm}
% \centering
% \scriptsize Schematic profile of a soil deposit \\
% \hspace*{0.1cm} {\tiny(Terzaghi, Peck and Mesri, 1996)}
% \end{minipage}
% \end{tabular}
%
% \end{frame}
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% \begin{frame}
% \frametitle{Uncertainties are inevitable in predicting behaviors of structures during future earthquakes}
%
% \begin{columns}
%
% \column{0.5\textwidth}
%
% {\color{blue} Bedrock motion is also uncertain}
% \begin{itemize}
% \small
% \item Factors lead to uncertainty:
% \begin{itemize}
% \item Mechanism of source
% \item Source parameters
% \item Earthquake propagation path
% \item ...
% \end{itemize}
%
% \item Bedrock motion is ideally described as a nonstationary random process
% \end{itemize}
% \vspace{0.5cm}
%
%
% \column{0.5\textwidth}
% \includegraphics[scale=0.2]{Fangbo_figs/Three_stages_of_ground_mtion_Jie_Li.pdf} \\
% \vspace{0.6cm}
% \begin{flushright}
% \scriptsize{Three stages explicitly indicate the nonstationarity of seismic wave}
% \end{flushright}
% \centering
% \vspace{0.3cm}
% \hspace{0.5cm} \tiny(Li and Chen, 2009)
%
%
% \end{columns}
%
% \end{frame}
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%
% \begin{frame}
% \frametitle{Uncertainties are inevitable in predicting behaviors of structures during future earthquakes}
% \vspace{0.2cm}
% {\color{blue}{Design frameworks can account for uncertainties:}}
% \footnotesize
% \begin{itemize}
% \item ASD $\rightarrow$ a single factor of safety
% \item LRFD $\rightarrow$ load and resistance factors
% \item Performancebased design (PBD):
% \end{itemize}
%
% \vspace{0.4cm}
% \begin{figure}
% \includegraphics[scale=0.3]{Fangbo_figs/Performance_design_framework.jpg}
% \vspace{0.3cm}
% \caption{ \scriptsize{Schematic of PBD framework} {\tiny(Moehle and Deierlein, 2004)} }
% \end{figure}
%
% \end{frame}
%
%
% \begin{frame}[t]
% \frametitle{Uncertainties are inevitable in predicting behaviors of structures during future earthquakes}
%
% {\footnotesize \color{blue}{However, numerical simulations  which are used to feed design framework  still remain exclusively deterministic:}}
% \vspace{0.2cm}
% \begin{columns}
% \column{0.5\textwidth}
% \minipage[c][0.6\textheight][s]{\columnwidth}
% \begin{figure}
% \includegraphics[width=0.8\textwidth, angle=90]{Fangbo_figs/SSI_model_deterministic}
% \tiny{\linespread{1.0} Schematic of a SoilFoundationStructure system subjected to earthquake}
% \end{figure}
%
% \endminipage
%
% \column{0.5\textwidth}
% \footnotesize
%
% \begin{itemize}
% \item Although highfidelity models that reduce modeling uncertainty are increasingly being used
% \item Uncertainties in model parameters are ignored:
% \begin{itemize}
% \scriptsize
% \item Material parameters
% \item Forcing function
% \end{itemize}
% \item Resulting in negation of the effects of nonlinear stochastic dynamics
% \end{itemize}
%
% \end{columns}
%
% \end{frame}
%
%
%
%
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%
%
% \begin{frame}{Effects of nonlinear stochastic dynamics must be captured for accurate prediction}
%
% \begin{columns}
%
% \column{0.4\textwidth}
% \scriptsize
%
% %\begin{center}
% %traditional SSI model \\
% %+ \\
% %uncertain soil deposit \\
% %+ \\
% %uncertain bedrock motion \\
% %$\Downarrow$ \\
% %stochastic SSI model
% %\end{center}
% Dynamic interaction of:
% \vspace{0.3cm}
% \begin{itemize}
% \item NonGaussian characteristics and spatial correlation of material parameters
% \item Temporal correlation of the forcing function
% \item Probabilistic evolution of material parameters as materials plastify
% \end{itemize}
%
% \column{0.60\textwidth}
% \vspace{1cm}
% % \hspace{0.9cm}
% \begin{figure}
% \begin{flushleft}
% \includegraphics[width=0.7\textwidth, angle=90]{Fangbo_figs/SSI_model_stochastic}
% \end{flushleft}
% \caption{\scriptsize Schematic illustration of a stochastic soilfoundationstructure system.}
% \end{figure}
%
% \end{columns}
%
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %\begin{frame}{Governing equations of solid mechanics}
% %\footnotesize
% %{
% %\begin{itemize}
% % \item Equilibrium equation:
% % \begin{flushleft}
% % \begin{equation*}
% % \frac{\partial \sigma_{ij}}{\partial x_j}+ {\color{blue}{b_j}} = \rho u_i
% % \end{equation*}
% % \end{flushleft}
% % \item Strain compatibility equation:
% % \begin{equation*}
% % \epsilon_{ij} = \frac{1}{2} \left( \frac{\partial u_{i}}{\partial x_j}+ \frac{\partial u_{j}}{\partial x_i} \right)
% % \end{equation*}
% % \item Constitutive equation:
% % \begin{equation*}
% % \dot{\sigma}_{ij} = {\color{blue}{D_{ijkl}}} \dot{\epsilon}_{kl}
% % \end{equation*}
% %\end{itemize}
% %}
% %\vspace{0.5cm}
% %\centering Input uncertainties (${\color{blue}{D_{ijkl}}}$, ${\color{blue}{b_j}}$) $\rightarrow$ stochastic PDE
% %\end{frame}
%
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\begin{frame}{Existing Simulation Methods for Stochastic PDEs}
\begin{itemize}
\item Analytical, stochastic differential equation approach: difficult to solve with complex random coefficients
\vspace*{3mm}
\item Monte Carlo method : Computationally expensive
\vspace*{3mm}
\item Perturbation approach: Small variation with respect to mean, closure problem
\vspace*{3mm}
\item Stochastic collocation method: Global error minimization
\vspace*{3mm}
\item Stochastic Galerkin method: Local error minimization
% \begin{itemize}
% \item \color{blue}{ \footnotesize Previous studies$\rightarrow$ Uncertain static loading, linear elastic material.}
% \item \color{blue}{ \footnotesize My research$\rightarrow$ Uncertain dynamic loading, nonlinear material.}
% \end{itemize}
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{Uncertainty Propagation through
Inelastic System}
%
\begin{itemize}
\item Incremental elpl constitutive equation
%
\begin{eqnarray}
\nonumber
\Delta \sigma_{ij}
=
% E^{EP}_{ijkl}
E^{EP}_{ijkl} \; \Delta \epsilon_{kl}
=
\left[
E^{el}_{ijkl}

\frac{\displaystyle E^{el}_{ijmn} m_{mn} n_{pq} E^{el}_{pqkl}}
{\displaystyle n_{rs} E^{el}_{rstu} m_{tu}  \xi_* h_*}
\right]
\Delta \epsilon_{kl}
\end{eqnarray}
\vspace*{2mm}
\item Dynamic Finite Elements
%
\begin{equation}
{ M} \ddot{ u_i} +
{ C} \dot{ u_i} +
{ K}^{ep} { u_i} =
{ F(t)}
\nonumber
\end{equation}
\vspace*{2mm}
\item Material and load parameters are uncertain
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{Probabilistic ElasticPlastic Response}
\begin{figure}[!hbpt]
\begin{center}
%\includegraphics[width=8cm]{/home/jeremic/tex/works/Papers/2007/ProbabilisticYielding/figures/vonMises_G_and_cu_very_uncertain/Contour_PDFedited.pdf}
\includegraphics[width=8cm]{/home/jeremic/tex/works/Conferences/2012/DOELLNLworkshop2728Feb2012/ProbabilisticYielding_vonMises_G_and_cu_very_uncertain_Contour_PDFedited.pdf}
\end{center}
\end{figure}
\end{frame}
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\begin{frame}
\frametitle{Probabilistic ElasticPlastic Modeling}
% % \vspace*{5mm}
% \begin{center}
% % \hspace*{15mm}
% \movie[label=show3,width=7cm,poster,autostart,showcontrols]
% {\includegraphics[width=7cm]
% {/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/NPP_Plastic_Dissipation_Density.png}}
% %{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/NPP_without_Contact_vonMises.mp4}
% {NPP_without_Contact_vonMises.mp4}
% \end{center}
%\vspace*{5mm}
\begin{center}
% \hspace*{15mm}
\movie[label=show3,width=9cm,poster,autostart,showcontrols]
{\includegraphics[width=9cm]
{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.png}}
% /home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.pdf
%{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Animations/PEP_Animation.mp4}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Probabilistic_Elasto_Plasticity_and_Stochastic_Elastic_Plastic_Finite_Element_Method/PEP_Animation.mp4}
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% \includegraphics[width = 12cm]{./img/figure_PEP_25.pdf}
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% \begin{frame}
%
% \frametitle{Previous Work}
%
%
%
% \begin{itemize}
%
% \item
% Linear algebraic or differential equations:
%
% \begin{itemize}
% \item Variable Transf. Method (Montgomery and Runger 2003)
% \item Cumulant Expansion Method (Gardiner 2004)
% \end{itemize}
%
% \item
% Nonlinear differential equations:
%
% \begin{itemize}
%
% \item Monte Carlo Simulation (Schueller 1997, De Lima et al 2001, Mellah
% et al. 2000, Griffiths et al. 2005...) \\ $\rightarrow$ can be accurate, very costly
%
% \item Perturbation Method (Anders and Hori 2000, Kleiber and Hien 1992,
% Matthies et al. 1997) \\ $\rightarrow$ first and second order Taylor series
% expansion about mean  limited to problems with small C.O.V. and inherits
% "closure problem"
%
% \item SFEM (Matthies et al, 2004, 2005, 2014...)
%
%
% \end{itemize}
%
% %
% % \item
% % Monte Carlo method: accurate, very costly
% %
% % \item
% % Perturbation method:
%
% \end{itemize}
%
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% \begin{frame} \frametitle{{3D FPK Equation}}
%
% \begin{footnotesize}
%
% \begin{eqnarray}
% \nonumber
% \lefteqn{\displaystyle \frac{\partial P(\sigma_{ij}(x_t,t), t)}{\partial t} = \displaystyle \frac{\partial}{\partial \sigma_{mn}}
% \left[ \left\{\left< \vphantom{\int_{0}^{t}} \eta_{mn}(\sigma_{mn}(x_t,t), D_{mnrs}(x_t), \epsilon_{rs}(x_t,t))\right> \right. \right.} \\
% \nonumber
% &+& \left. \left. \int_{0}^{t} d\tau Cov_0 \left[\displaystyle \frac{\partial \eta_{mn}(\sigma_{mn}(x_t,t), D_{mnrs}(x_t),
% \epsilon_{rs}(x_t,t))} {\partial \sigma_{ab}}; \right. \right. \right. \\
% \nonumber
% & & \left. \left. \left. \eta_{ab} (\sigma_{ab}(x_{t\tau}, t\tau), D_{abcd}(x_{t\tau}), \epsilon_{cd}(x_{t\tau}, t\tau)
% \vphantom{\int_{0}^{t}} \right] \right \} P(\sigma_{ij}(x_t,t),t) \right] \\
% \nonumber
% &+& \displaystyle \frac{\partial^2}{\partial \sigma_{mn} \partial \sigma_{ab}} \left[ \left\{ \int_{0}^{t} d\tau Cov_0 \left[
% \vphantom{\int_{0}^{t}} \eta_{mn}(\sigma_{mn}(x_t,t), D_{mnrs}(x_t), \epsilon_{rs}(x_t,t)); \right. \right. \right. \\
% \nonumber
% & & \left. \left. \left. \eta_{ab} (\sigma_{ab}(x_{t\tau}, t\tau), D_{abcd}(x_{t\tau}), \epsilon_{cd}(x_{t\tau}, t\tau))
% \vphantom{\int_{0}^{t}} \right] \vphantom{\int_{0}^{t}} \right\} P(\sigma_{ij}(x_t,t),t) \right]
% \end{eqnarray}
%
%
% \end{footnotesize}
%
%
%
% % \begin{itemize}
% %
% %
% %
% % \item 6 equations
% %
% % \item Complete description of 3D probabilistic stressstrain response
% %
% % \end{itemize}
% %
% %
%
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% \end{frame}
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% \begin{frame}
%
% \frametitle{FPK Equation}
%
%
%
% \begin{itemize}
%
% \item Advectiondiffusion equation
% %
% \begin{equation}
% \nonumber
% \frac{\partial P(\sigma,t)}{\partial t} = \frac{\partial}{\partial \sigma}\left[N_{(1)}P(\sigma,t)\frac{\partial}{\partial \sigma}
% \left\{N_{(2)} P(\sigma,t)\right\} \right]
% \end{equation}
%
% %
%
% \item Complete probabilistic description of response
%
%
% \item Solution PDF is secondorder exact to covariance of time (exact mean and variance)
%
%
% \item It is deterministic equation in probability density space
%
% \item It is linear PDE in probability density space
% $\rightarrow$ simplifies the numerical solution process
%
% %\vspace*{0.2truecm}
%
% \end{itemize}
%
% %
% % \vspace*{0.5cm}
% % {%
% % \begin{beamercolorbox}{section in head/foot}
% % \usebeamerfont{framesubtitle}\tiny{B. Jeremi\'{c}, K. Sett, and M. L. Kavvas, "Probabilistic
% % ElastoPlasticity: Formulation in 1D", \textit{Acta Geotechnica}, Vol. 2, No. 3, 2007, In press (published
% % online in the \textit{Online First} section)}
% % %\vskip2pt\insertnavigation{\paperwidth}\vskip2pt
% % \end{beamercolorbox}%
% % }
%
%
%
% \end{frame}
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
%
%
% \frametitle{Template Solution of FPK Equation}
%
%
%
% \begin{itemize}
%
%
%
%
% \item FPK diffusionadvection equation is applicable to any material model $\rightarrow$
% only the coefficients $N_{(1)}$ and $N_{(2)}$ are different for different material models
% % %
% % %
% % %
% % %\begin{normalsize}
% % \begin{equation}
% % \nonumber
% % \frac{\partial P(\sigma,t)}{\partial t} = \frac{\partial}{\partial \sigma}\left[N_{(1)}P(\sigma,t)\frac{\partial}{\partial \sigma}
% % \left\{N_{(2)} P(\sigma,t)\right\} \right]
% % %\nonumber
% % = \frac{\partial \zeta}{\partial \sigma}
% % \end{equation}
% % %\end{normalsize}
%
% %
%
% \item Initial condition
%
% \begin{itemize}
%
% \item Deterministic $\rightarrow$ Dirac delta function $\rightarrow$ $ P(\sigma,0)=\delta(\sigma) $
%
% \item Random $\rightarrow$ Any given distribution
%
% \end{itemize}
%
% \item Boundary condition: Reflecting BC $\rightarrow$ conserves probability mass
% $\zeta(\sigma,t)_{At \ Boundaries}=0$
%
% \item Solve using finite differences and/or finite elements
%
%
% \item However (!!) it is a stress solution and probabilistic stiffness is an
% approximation!
%
% \end{itemize}
%
%
% \end{frame}
%
%
%
%
%
%
%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Direct Solution for Probabilistic Stiffness and Stress in 1D}
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%% BEGGINING PEP %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
% \begin{frame}{Direct Probabilistic Constitutive Modeling in 1D}
%
%
% % \begin{itemize}
% %
% % \vspace{0.5cm}
% %
% % \item<1> Probabilistic constitutive modeling : \vspace{0.5cm}
%
% \begin{itemize}
%
%
% \item Zero elastic region elastoplasticity with stochastic ArmstrongFrederick
% kinematic hardening
%
% $ \Delta\sigma =\ H_a \Delta \epsilon  c_r \sigma \Delta \epsilon ;
% \hspace{0.5cm}
% E_t = {d\sigma}/{d\epsilon} = H_a \pm c_r \sigma $
%
% \vspace*{2mm}
% \item Uncertain:
% init. stiff. $H_a$,
% shear strength $H_a/c_r$,
% strain $\Delta \epsilon$:
%
% $ H_a = \Sigma h_i \Phi_i; \;\;\;
% C_r = \Sigma c_i \Phi_i; \;\;\;
% \Delta\epsilon = \Sigma \Delta\epsilon_i \Phi_i $
%
%
%
% \vspace*{2mm}
% \item Resulting stress and stiffness are also uncertain
%
% % 
% %  $ \sum_{l=1}^{P_{\sigma}} \Delta\sigma_i \Phi_i = \sum_{i=1}^{P_h} \sum_{k=1}^{P_e}\ h_i \Delta \epsilon_k \Phi_i \Phi_k  \sum_{j=1}^{P_g} \sum_{k=1}^{P_e}\sum_{l=1}^{P_{\sigma}} \ c_i \Delta \epsilon_k \sigma_l \Phi_j \Phi_k \Phi_l$
% % 
% %  $ \sum_{l=1}^{P_{E_t}} \Delta E_{t_i} \Phi_i = \sum_{i=1}^{P_h} h_i \Phi_i \pm \sum_{i=1}^{P_c} \sum_{l=1}^{P_{\sigma}} \ c_i \sigma_l \Phi_i \Phi_l$
% % 
%
%
% \end{itemize}
%
%
% % \vspace{0.5cm}
%
%
%
% % \vspace{1cm}
%
% %\item<1> Time integration is done via Newmark algorithm
%
% %
% % \end{itemize}
% %
% \end{frame}
%
%
% % % % % % % % % % % % % % % % %
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}{Probabilistic Stiffness Solution}
%
% \begin{itemize}
%
%
% \item Analytic product for all the components,
%
% $ E^{EP}_{ijkl}
% =
% \left[
% E^{el}_{ijkl}
% 
% \frac{\displaystyle E^{el}_{ijmn} m_{mn} n_{pq} E^{el}_{pqkl}}
% {\displaystyle n_{rs} E^{el}_{rstu} m_{tu}  \xi_* h_*}
% \right]
% $
%
%
%
%
% \item Stiffness: each Polynomial Chaos component is updated incrementally
% % at each Gauss Point via stochastic Galerkin projection
%
%
%
% \small{$E_{t_1}^{n+1} = \frac{1}{<\Phi_1\Phi_1> }\{\sum_{i=1}^{P_h} \ h_i <\Phi_i \Phi_1> \pm \sum_{j=1}^{P_c} \sum_{l=1}^{P_{\sigma}} \ c_j \sigma_l^{n+1} <\Phi_j \Phi_l \Phi_1>\}$}
%
% $\large{\vdots}$
%
% \small{$E_{t_P}^{n+1} = \frac{1}{<\Phi_1\Phi_P> }\{\sum_{i=1}^{P_h} \ h_i <\Phi_i \Phi_P> \pm \sum_{j=1}^{P_c} \sum_{l=1}^{P_{\sigma}} \ c_j \sigma_l^{n+1} <\Phi_j \Phi_l \Phi_P>\}$}
%
%
% \item Total stiffness is :
%
% $ E_{t}^{n+1} = \sum_{l=1}^{P_{E}} E_{t_i}^{n+1} \Phi_i $
%
%
%
%
% \end{itemize}
%
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}{Probabilistic Stress Solution}
%
% \begin{itemize}
%
%
%
% \item Analytic product, for each stress component,
%
% $ \Delta \sigma_{ij} = E^{EP}_{ijkl} \; \Delta \epsilon_{kl} $
% % =
% % \left[
% % E^{el}_{ijkl}
% % 
% % \frac{\displaystyle E^{el}_{ijmn} m_{mn} n_{pq} E^{el}_{pqkl}}
% % {\displaystyle n_{rs} E^{el}_{rstu} m_{tu}  \xi_* h_*}
% % \right]
% % \Delta \epsilon_{kl}
% %
%
%
% \vspace*{1mm}
% \item Incremental stress: each Polynomial Chaos component is updated
% incrementally
% % via stochastic Galerkin projection
%
%
%
%
% {$\Delta\sigma_1^{n+1} = \frac{1}{<\Phi_1\Phi_1> }\{\sum_{i=1}^{P_h} \sum_{k=1}^{P_e}\ h_i \Delta \epsilon_k^n <\Phi_i \Phi_k \Phi_1> \sum_{j=1}^{P_g} \sum_{k=1}^{P_e}\sum_{l=1}^{P_{\sigma}} \ c_j \Delta \epsilon_k^n \sigma_l^n <\Phi_j \Phi_k \Phi_l \Phi_1>\}$}
%
% ${\vdots}$
%
% {$\Delta\sigma_P^{n+1} = \frac{1}{<\Phi_P\Phi_P> }\{\sum_{i=1}^{P_h} \sum_{k=1}^{P_e}\ h_i \Delta \epsilon_k^n <\Phi_i \Phi_k \Phi_P> \sum_{j=1}^{P_g} \sum_{k=1}^{P_e}\sum_{l=1}^{P_{\sigma}} \ c_j \Delta \epsilon_k^n \sigma_l^n <\Phi_j \Phi_k \Phi_l \Phi_P>\}$}
%
%
% \vspace*{1mm}
% \item Stress update:
%
% $ \sum_{l=1}^{P_{\sigma}} \sigma_i^{n+1} \Phi_i = \sum_{l=1}^{P_{\sigma}} \sigma_i^{n} \Phi_i + \sum_{l=1}^{P_{\sigma}} \Delta\sigma_i^{n+1} \Phi_i$
%
%
%
% \end{itemize}
%
% \end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section[Formulation]{Stochastic Dynamic Finite Element Formulation}
%\subsection[Time domain stochastic Galerkin method]{Time domain stochastic Galerkin method}
%\frame{\tableofcontents[currentsubsection,sectionstyle=show/shaded]}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Time Domain Stochastic Galerkin Method}
\begin{itemize}
\item Input random field/process{\normalsize{(nonGaussian, heterogeneous/ nonstationary)}}
\begin{itemize}
\item[] Multidimensional Hermite Polynomial Chaos (PC) with {known coefficients}
\end{itemize}
\vspace{0.05in}
\item Output response process
\begin{itemize}
\item[] Multidimensional Hermite PC with {unknown coefficients}
\end{itemize}
\vspace{0.05in}
\item Galerkin projection: minimize the error to compute unknown coefficients of response process
\vspace{0.05in}
\item Time integration using Newmark's method
\begin{itemize}
\item[] Update coefficients following an elasticplastic constitutive law at each time step
\end{itemize}
\end{itemize}
%\scriptsize
%Note: PC = Polynomial Chaos
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \begin{frame}{Discretization of Input Random Process/Field $\beta(x,\theta)$}
% \begin{center}
% \includegraphics[scale=0.35]{/home/jeremic/tex/works/Thesis/FangboWang/slides_13Mar2019/Fangbo_slides/figs/PC_KL_explanation.PNG} \\
% \end{center}
%
%
% \footnotesize{Note: $\beta(x,\theta)$ is an input random process with any
% marginal distribution, \\ \hspace{21mm} with any covariance structure;} \\
% \footnotesize{\hspace{8mm} $\gamma(x,\theta)$ is a zeromean unitvariance Gaussian random process.} \\
%
% \end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Polynomial Chaos Representation}
%\scriptsize{
Material random field:
%\vspace{0.3cm}
%\begin{equation*}
$D(x, \theta)= \sum_{i=1}^{P1} a_i(x) \Psi_i(\left\{\xi_r(\theta)\right\})$
%\end{equation*}
\vspace{3mm}
Motion random process:
%\vspace{0.3cm}
%\begin{equation*}
$f_m(t, \theta)=\sum_{j=1}^{P_2} f_{mj}(t) \Psi_j(\{\xi_k(\theta)\})$
%\end{equation*}
\vspace{3mm}
Displacement response:
%\vspace{0.3cm}
%\begin{equation*}
$u_n(t, \theta)=\sum_{k=1}^{P_3} d_{nk}(t) \Psi_k(\{\xi_l(\theta)\})$
%\end{equation*}
\vspace{3mm}
%Acceleration response:
%%\vspace{0.3cm}
%%\begin{equation*}
%$\ddot u_n(t, \theta)=\sum_{k=1}^{P_3} \ddot d_{nk}(t) \Psi_k(\{\xi_l(\theta)\})$
%%\end{equation*}
\vspace{3mm}
\vspace{3mm}
where $a_i(x), f_{mj}(t)$ are {known PC coefficients}, while $d_{nk}(t)$
are {unknown PC coefficients}.
%}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Stochastic ElasticPlastic Finite Element Method}
\begin{itemize}
\item Material uncertainty expanded into stochastic shape funcs.
%$E(x,t,\theta) = \sum_{i=0}^{P_d} r_i(x,t) * \Phi_i[\{\xi_1, ..., \xi_m\}]$
\vspace*{1mm}
\item Loading uncertainty expanded into stochastic shape funcs.
%$f(x,t,\theta) = \sum_{i=0}^{P_f} f_i(x,t) * \zeta_i[\{\xi_{m+1}, ..., \xi_f]$
\vspace*{1mm}
\item Displacement expanded into stochastic shape funcs.
%$u(x,t,\theta) = \sum_{i=0}^{P_u} u_i(x,t) * \Psi_i[\{\xi_1, ..., \xi_m, \xi_{m+1}, ..., \xi_f\}]$
%\item
%Stochastic system of equation resulting from Galerkin approach (static example):
%
%\item Time domain integration using Newmark and/or HHT, in probabilistic spaces
\end{itemize}
\begin{tiny}
\[
%$
\begin{bmatrix}
\sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_0> K^{(k)} & \dots & \sum_{k=0}^{P_d} <\Phi_k \Psi_P \Psi_0> K^{(k)}\\
\sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_1> K^{(k)} & \dots & \sum_{k=0}^{P_d} <\Phi_k \Psi_P \Psi_1> K^{(k)}\\ \\
\vdots & \vdots & \vdots & \vdots\\
\sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_P> K^{(k)} & \dots & \sum_{k=0}^{M} <\Phi_k \Psi_P \Psi_P> K^{(k)}
\end{bmatrix}
\begin{bmatrix}
\Delta u_{10} \\
\vdots \\
\Delta u_{N0}\\
\vdots \\
\Delta u_{1P_u}\\
\vdots \\
\Delta u_{NP_u}
\end{bmatrix}
=
%\]
%\[
\begin{bmatrix}
\sum_{i=0}^{P_f} f_i <\Psi_0\zeta_i> \\
\sum_{i=0}^{P_f} f_i <\Psi_1\zeta_i> \\
\sum_{i=0}^{P_f} f_i <\Psi_2\zeta_i> \\
\vdots \\
\sum_{i=0}^{P_f} f_i <\Psi_{P_u}\zeta_i>\\
\end{bmatrix}
%$
\]
\end{tiny}
\end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \begin{frame}
% \frametitle{SEPFEM: System Size}
%
% \begin{itemize}
%
% \item SEPFEM offers a complete solution (single step)
%
% \item It is NOT based on Monte Carlo approach
%
% \item System of equations does grow (!)
%
% \end{itemize}
%
%
% % \normalsize{Typical number of terms required for a SEPFEM problem} \vspace{1cm}\\
% \scalebox{0.7}{
% \begin{tabular}{ c c c c}
% \# KL terms material & \# KL terms load & PC order displacement& Total \# terms per DoF\\ \hline
% 4 & 4 & 10 & 43758 \\
% 4 & 4 & 20 & 3 108 105 \\
% 4 & 4 & 30 & 48 903 492 \\
% 6 & 6 & 10 & 646 646 \\
% 6 & 6 & 20 & 225 792 840 \\
% 6 & 6 & 30 & 1.1058 $10^{10}$ \\
% 8 & 8 & 10 & 5 311 735 \\
% 8 & 8 & 20 & 7.3079 $10^{9}$ \\
% 8 & 8 & 30 & 9.9149 $10^{11}$\\
%
% ... & ... & ... & ...\\
% % \hline
% \end{tabular}}
%
%
% \end{frame}
%
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{SEPFEM: Example in 1D}
\vspace*{2mm}
\begin{center}
% \hspace*{15mm}
\movie[label=show3,width=9cm,poster,autostart,showcontrols]
{\includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_elastic_900.png}}
% /home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.pdf
%{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Animations/SEPFEM_Animation_Elastic.mp4}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Probabilistic_Elasto_Plasticity_and_Stochastic_Elastic_Plastic_Finite_Element_Method/SEPFEM_Animation_Elastic.mp4}
\end{center}
% \includegraphics[width = 12cm]{./img/figure_elastic_900.pdf}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{High Performance Computing}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Course and Fine Grained HPC}
\begin{itemize}
\vspace*{2mm}
\item Hardware Aware Plastic Domain Decomposition (HAPDD) Method
\vspace*{2mm}
\item Small Tensor Library
\end{itemize}
\begin{figure}[!Htbp]
\begin{center}
\hspace*{5mm}
\includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Exit_Seminar_slides/img_slides_yuan_exit_seminar/1_speedup_analysis.jpg}
\end{center}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{HAPDD}
\begin{figure}[!Htbp]
\begin{center}
\hspace*{5mm}
\includegraphics[width=12cm]{/home/jeremic/tex/works/Conferences/2019/Hori_and_Watanabe_visit_LBNL_1415Mar2019/present/HAPDD01.jpg}
\end{center}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{HAPDD}
\begin{figure}[!Htbp]
\begin{center}
\hspace*{5mm}
\includegraphics[width=12cm]{/home/jeremic/tex/works/Conferences/2019/Hori_and_Watanabe_visit_LBNL_1415Mar2019/present/HAPDD02.jpg}
\end{center}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Small Tensor Library}
\begin{figure}[!Htbp]
\begin{center}
\hspace*{5mm}
\includegraphics[width=12cm]{/home/jeremic/tex/works/Conferences/2019/Hori_and_Watanabe_visit_LBNL_1415Mar2019/present/Small_tensor_lib_01.jpg}
\end{center}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Modeling and Simulation Examples}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Seismic Motions}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{ESSI: 6C or 1C Seismic Motions}
%
%
% \begin{itemize}
%
%
% \item Assume that a full 6C (3C) motions at the surface are only recorded in one
% horizontal direction
%
%
% \item From such recorded motions one can develop a vertically propagating shear
% wave (1C) in 1D
%
% \item Apply such vertically propagating shear wave to same soilstructure
% system
%
% \end{itemize}
%
% \vspace*{3mm}
% \begin{figure}[!H]
% \begin{center}
% \includegraphics[width=6.5cm]{/home/jeremic/tex/works/Conferences/2015/CompDyn/Present/6D_to_1D_01.jpg}
% \end{center}
% \end{figure}
%
%
%
% \end{frame}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \begin{frame}
% \frametitle{6C Free Field Motions (closeup)}
%
%
%
% %\vspace*{2mm}
% \begin{center}
% \movie[label=show3,width=80mm,poster,showcontrols]
% {\includegraphics[width=80mm]{/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_input_closeup_mp4_icon.jpeg}}
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_closeup.mp4}
% \end{center}
%
% \begin{flushleft}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_closeup.mp4}
% {\tiny (MP4)}
% \end{flushleft}
% % local
% % local
% %
%
%
% % out
% % out
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% % out \begin{center}
% % out \hspace*{7mm}
% % out \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
% % out {\includegraphics[width=70mm]{BJicon.png}}{movie_input_closeup.mp4}
% % out \end{center}
% % out
% % out \begin{flushleft}
% % out \vspace*{15mm}
% % out \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_01AApr2015/movie_input_closeup.mp4}
% % out % \href{./homo_50mmesh_45degree_Ormsby.mp4}
% % out {\tiny (MP4)}
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% % out %
% % out
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%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{1C vs 6C Free Field Motions}
%
%
%
%
% \begin{itemize}
%
% \item One component of motions (1D) from 3D
% % or 3$\times$1D (it is done all the time!)
%
% \item Excellent fit
% % (goal is to predict and inform and not (force) fit)
%
%
% \end{itemize}
%
%
%
%
% % local
% %\vspace*{2mm}
% \begin{center}
% \hspace*{16mm}
% %\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
% \movie[label=show3,width=61mm,poster, showcontrols]
% {\includegraphics[width=60mm]{/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_ff_3d_mp4_icon.jpeg}}
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_ff_3d.mp4}
% %\hspace*{2mm}
% %\hfill
% %\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
% \movie[label=show3,width=61mm,poster, showcontrols]
% {\includegraphics[width=60mm]
% {/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_ff_1d_mp4_icon.jpeg}}
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_ff_1d.mp4}
% \hspace*{16mm}
% \end{center}
% % local
%
%
% % online
% \begin{center}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_3d.mp4}
% {\tiny (MP4)}
% %
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_1d.mp4}
% {\tiny (MP4)}
% \end{center}
% % online
%
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% % out
% % out % local
% % out %\vspace*{2mm}
% % out \begin{center}
% % out \hspace*{16mm}
% % out %\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
% % out \movie[label=show3,width=61mm,poster, showcontrols]
% % out {\includegraphics[width=60mm]{movie_ff_3d_mp4_icon.jpeg}}{movie_ff_3d.mp4}
% % out % \hspace*{16mm}
% % out % \end{center}
% % out % %
% % out % %
% % out % %
% % out % \begin{center}
% % out % \hspace*{16mm}
% % out \movie[label=show3,width=61mm,poster, showcontrols]
% % out {\includegraphics[width=60mm]{movie_ff_1d_mp4_icon.jpeg}}{movie_ff_1d.mp4}
% % out \hspace*{16mm}
% % out \end{center}
% % out %
% % out
% % out \begin{flushleft}
% % out %\vspace*{15mm}
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\frametitle{Seismic Motions}
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\item Variation in inclination, frequency, energy, duration...
\item Deterministic and Probabilistic
\item Stress test the soilstructure system
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\frametitle{SMR ESSI, Variation in Input Frequency, $\theta = 60^{o}$}
% Elastoplastic soil with contact elements
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{\includegraphics[width=10cm]
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%\frametitle{SMR ESSI, Variation in Input Frequency, $\theta = 60^{o}$}
\frametitle{SMR ESSI, Variation in Input Frequency, REAL TIME}
% Elastoplastic soil with contact elements
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% \vspace*{5mm}
\begin{center}
% \hspace*{15mm}
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{\includegraphics[width=10cm]
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%\frametitle{SMR ESSI, Variation in Input Frequency, $\theta = 60^{o}$}
\frametitle{SMR ESSI, 3C vs 3$\times$1C}
% Elastoplastic soil with contact elements
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% \vspace*{5mm}
\begin{center}
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{\includegraphics[width=10cm]
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\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/3Dvs1D_deconvolution.ogv}
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\frametitle{3C, 6C Seismic Motions}
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\begin{itemize}
\item All (most) measured motions are full 3C, 6C
\item One example of an almost 2C motion (LSST07, LSST12)
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\begin{figure}[!hbpt]
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%
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\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Lotung_LSST07_FA25.jpeg}
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Lotung_LSST12_FA25.jpeg}
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% \item 1D (?): M 6.9 San Pablo, Guatemala EQ, 14Jun2017
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% \item Knowledge of geology (deep and shallow) needed
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% \item Collaboration with LLNL: Dr.~Rodgers, Dr.~Pitarka and Dr.~Petersson
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% % \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
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% % \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
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% % \includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/Vs_at_top.jpg}
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% % % \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
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\begin{frame}
\frametitle{ESSI: 6C or 1C Seismic Motions}
\begin{itemize}
\item Assume that a full 6C (3C) motions at the surface are only recorded in one
horizontal direction
\item From such recorded motions one can develop a vertically propagating shear
wave (1C) in 1D
\item Apply such vertically propagating shear wave to same soilstructure
system
\end{itemize}
\vspace*{3mm}
\begin{figure}[!H]
\begin{center}
\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Conferences/2015/CompDyn/Present/6D_to_1D_01.jpg}
\end{center}
\end{figure}
\end{frame}
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\begin{frame}
\frametitle{6C Free Field Motions (closeup)}
%\vspace*{2mm}
\begin{center}
\movie[label=show3,width=80mm,poster,showcontrols]
{\includegraphics[width=80mm]{/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_input_closeup_mp4_icon.jpeg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_closeup.mp4}
\end{center}
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\begin{frame}
\frametitle{1C vs 6C Free Field Motions}
\begin{itemize}
\item One component of motions, 1C from 6C
% or 3$\times$1D (it is done all the time!)
\item Excellent fit
% (goal is to predict and inform and not (force) fit)
\end{itemize}
% local
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{\includegraphics[width=60mm]{/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_ff_3d_mp4_icon.jpeg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_ff_3d.mp4}
%\hspace*{2mm}
%\hfill
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\movie[label=show3,width=61mm,poster, showcontrols]
{\includegraphics[width=60mm]
{/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_ff_1d_mp4_icon.jpeg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_ff_1d.mp4}
\hspace*{16mm}
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% \frametitle{1D vs 3$\times$1C vs 3C Seismic Motions}
%
%
% \begin{itemize}
%
% \vspace{2mm}
% \item 1D is required by the code
%
% \vspace{4mm}
% \item 3$\times$1D can be used depending on frequency/wave length of interest,
%
% \vspace{4mm}
% \item 3C is more realistic, however it is challenging to define motions in full 3C
%
% \end{itemize}
% \end{frame}
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% \frametitle{When to use 3C and/or 3$\times$1C}
%
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% \begin{center}
% %
% %\includegraphics[width=4.5truecm]{/home/jeremic/tex/works/Papers/2016/3D_vs_3_x_1D_motions/version_04Jan2017/NearFieldESSINPPs/results/3d_vs_1d_6/node_733_acce.pdf}
% %\includegraphics[width=4.5truecm]{/home/jeremic/tex/works/Papers/2016/3D_vs_3_x_1D_motions/version_04Jan2017/NearFieldESSINPPs/results/6/node_733_acce.pdf}
% % %
% % \\
% % \includegraphics[width=9.5truecm]{/home/jeremic/tex/works/Papers/2016/3D_vs_3_x_1D_motions/version_04Jan2017/NearFieldESSINPPs/results/3d_vs_1d_6/node_733_fft.pdf}
% % \\
% \includegraphics[width=11truecm]{/home/jeremic/tex/works/consulting/2017/IAEA/TECDOC/Version_14Mar2017/1Dvs3x1Dvs3D_waves.pdf}
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\begin{frame}
\frametitle{6C vs 1C NPP ESSI Response Comparison}
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\vspace*{2mm}
\begin{center}
\hspace*{7mm}
%\movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
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{\includegraphics[width=92mm]
{/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_2_npps_mp4_icon.jpeg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_2_npps.mp4}
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\begin{frame}
\frametitle{Stress Testing SSI Systems}
\begin{itemize}
\item Excite SSI system with a suite of seismic motions
\item Waves: P, SV, SH, Surface (Rayleigh, Love, etc.)
\item Variation in inclination, frequency, energy and duration
\item Try to "break" the system, shakeout strong and weak links
\end{itemize}
\vspace*{4mm}
\begin{figure}[!htb]
\begin{center}
\hspace*{5mm}
\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Conferences/2018/BestPSHANI/Presentation/stress_test_Best_SHANI_May2018.jpg}
\end{center}
\end{figure}
\vspace*{5mm}
\begin{figure}[!htb]
\begin{center}
\hspace*{5mm}
%\includegraphics[width=4cm]{/home/jeremic/tex/works/consulting/2017/IAEA/TECDOC/Version_14Mar2017/1Dvs3x1Dvs3D_waves_02.pdf}
\includegraphics[width=7.5cm]{/home/jeremic/tex/works/Conferences/2018/WCCM2018/Present/1Dvs3x1Dvs3D_waves_03.pdf}
\hspace*{4mm}
\includegraphics[width=3.6cm]{/home/jeremic/tex/works/Conferences/2018/WCCM2018/Present/1Dvs3x1Dvs3D_waves_02.pdf}
\hspace*{5mm}
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\end{figure}
\end{frame}
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\begin{frame}
\frametitle{Stress Test Source Signals}
\begin{itemize}
% \item Gauss
% \begin{figure}[!hbpt]
% \begin{flushright}
% \vspace*{0.5cm}
% \includegraphics[width=7.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/gauss.png}
% \end{flushright}
% \end{figure}
\item Ricker
\begin{figure}[!hbpt]
\begin{flushright}
\vspace*{1cm}
\includegraphics[width=4.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ricker2nd.pdf}
\includegraphics[width=4.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ricker2nd_FFT.pdf}
\hspace*{0.7cm}
\end{flushright}
\end{figure}
\item Ormsby
\begin{figure}[!hbpt]
\begin{flushright}
\vspace*{1cm}
\includegraphics[width=4.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ormsby.pdf}
\includegraphics[width=4.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ormsby_FFT.pdf}
\hspace*{0.7cm}
\end{flushright}
\end{figure}
\end{itemize}
% \begin{figure}[!hbpt]
% \begin{center}
% %
% \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/gauss.png}
% %
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ricker2nd.pdf}
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ricker2nd_FFT.pdf}
% %
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ormsby.pdf}
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ormsby_FFT.pdf}
% %
% \end{center}
% \end{figure}
\end{frame}
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% \begin{frame}
%
% \frametitle{Free Field vs ESSI  Different Frequencies}
%
%
% \begin{textblock*}{8cm}(1.0cm,2.5cm) % {block width} (coords)
% \scriptsize Acceleration response  Surface center point A
% \end{textblock*}
% \begin{textblock*}{2cm}(0.2cm,4cm) % {block width} (coords)
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% \end{textblock*}
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% \tiny Z direction
% \end{textblock*}
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% \tiny (a) $f=1Hz \ \ \theta=60^{o}$
% \end{textblock*}
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% \end{textblock*}
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% \tiny (c) $f=10Hz \ \ \theta=60^{o}$
% \end{textblock*}
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% \centering
% % \begin{flushleft}
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% \\
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\subsection{Plastic Energy Dissipation}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Energy Input and Dissipation}
\begin{itemize}
\vspace*{1mm}
\item[] Energy input, dynamic forcing
\vspace*{4mm}
\item[] Energy dissipation outside SSI domain:
\begin{itemize}
\item[] SSI system oscillation radiation
\item[] Reflected wave radiation
\end{itemize}
%\vspace*{1mm}
\item[] Energy dissipation/conversion inside SSI domain:
\begin{itemize}
\item[] Inelasticity of soil, contact zone, structure, foundation, dissipators
\item[] Viscous coupling with internal/pore fluids, and external fluids
% % \item[] potential and kinetic energy
% \item[] potential $\leftarrow \! \! \! \! \! \! \rightarrow$ kinetic energy
\end{itemize}
%\vspace*{1mm}
% \item[] Numerical energy dissipation (numerical damping/production and period errors)
% \item[] Numerical energy dissipation (damping/production)
\item[] Numerical energy dissipation/production
\end{itemize}
%
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Plastic Energy Dissipation}
\vspace*{2mm}
Single elasticplastic element under cyclic shear loading
\begin{itemize}
\item[] Difference between plastic work and plastic dissipation
\item[] Plastic work can decrease
\item[] Plastic dissipation always increases
\end{itemize}
%\vspace*{7mm}
\begin{figure}[!hbpt]
\begin{center}
\hspace*{5mm}
\includegraphics[width=11.0truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Dissipation_Material.png}
\end{center}
\end{figure}
\end{frame}
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% \begin{frame}
%
% \frametitle{Energy Dissipation Control Mechanisms}
%
% \begin{figure}[!H]
% %\hspace*{10mm}
% \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_plasticity.pdf}
% \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_Rayleigh.pdf}
% \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_Newmark.pdf}
% \end{figure}
%
%
% % \hspace*{10mm} Numerical \hspace*{20mm} Viscous \hspace*{20mm} Plasticity
% \hspace*{10mm} Plasticity \hspace*{20mm} Viscous \hspace*{20mm} Numerical
%
%
%
% \end{frame}
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\begin{frame}
\frametitle{Energy Dissipation Control}
\begin{figure}[!H]
%\hspace*{10mm}
% \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_a.pdf}
% \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_b.pdf}
\includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_g.pdf}
% \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_e.pdf}
\end{figure}
\end{frame}
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\begin{frame}
\frametitle{Inelastic Modeling of Soil Structure Systems}
\begin{itemize}
%\vspace*{1mm}
\item Soil, inelastic, elasticplastic
\begin{itemize}
\item[] Dry, single phase
\item[] Unsaturated, partially saturated
\item[] Fully saturated
\end{itemize}
%\vspace*{1mm}
\item Contact, inelastic, soil/rock  foundation
\begin{itemize}
\item[] Dry, single phase,
\begin{itemize}
\item[] Normal, hard and soft, gap open/close
\item[] Friction, nonlinear
\end{itemize}
\item[] Fully saturated, suction, excess pressure, buoyant force
\end{itemize}
%\vspace*{1mm}
\item Structure, inelastic, damage, cracks
\begin{itemize}
\item[] Nonlinear/inelastic 1D reinforced concrete fiber beam
\item[] Nonlinear/inelastic 3D reinforced concrete solid element
\item[] Alcali Silica Reaction concrete modeling
\end{itemize}
%%\vspace*{1mm}
% \item FluidSolid interaction (open surface)
\end{itemize}
%
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{NPP Model }
%
% \begin{figure}[!h]
% \begin{center}
% \includegraphics[width=8.5cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/NPP_With_Shallow_Foundation.pdf}
% \end{center}
% % \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
% \end{figure}
%
%
% % \begin{tikzpicture}[remember picture,overlay]
% % \node[xshift=3.5cm,yshift=0.6cm] at (current page.center) {\includegraphics[width=0.5\textwidth]{images/Contact_In_Industry}};
% % \end{tikzpicture}
%
% \end{frame}
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% \begin{frame}
%
% \frametitle{Structure Model}
%
% The nuclear power plant structure comprise of
% \begin{itemize}
% \item Auxiliary building, $f^{aux}_{1}= 8Hz$
% \item Containment/Shield building, $f^{cont}_{1}= 4Hz$
% \item Concrete raft foundation: $3.5m$ thick
% \end{itemize}
% \begin{figure}[!h]
% \begin{center}
% \includegraphics[width=0.8\textwidth]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/NPP_Model_Auxiliary_And_Containment_Building.pdf}
% \end{center}
% \caption{\label{Fig:NPP_Structure_Model_In_Real_ESSI} Auxiliary and Containment Building }
% \end{figure}
%
% \end{frame}
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\begin{frame}
\frametitle{Inelastic Soil and Inelastic Contact}
\begin{itemize}
\item Shear velocity of soil $V_s=500m/s$
\item Undrained shear strength (Dickenson 1994) $V_s [m/s] = 23 (S_u [kPa])^{0.475}$
\item For $V_s=500m/s$ Undrained Strength $S_u=650kPa$ and Young's Modulus of $E=1.3GPa$
\item von Mises, Armstrong Frederick kinematic hardening
($S_u=650kPa$ at $\gamma=0.01\%$; $h_a = 30MPa$, $c_r = 25$)
\item Soft contact (concretesoil), gaping and nonlinear shear
\end{itemize}
\begin{figure}[!h]
\begin{center}
\includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Von_Mies_non_Linear_Hardening.pdf}
\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/SoftContact.pdf}
\end{center}
\end{figure}
\end{frame}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Acc. Response, Top of Containment Building}
%
% \begin{figure}[!h]
% \begin{center}
% \hspace*{8mm}
% \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/D_Acceleration_X.pdf}
% \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/D_Acceleration_Y.pdf}
% \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/D_Acceleration_Z.pdf}
% \\
% \hspace*{8mm}
% \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/FFT_D_Acceleration_X.pdf}
% \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/FFT_D_Acceleration_Y.pdf}
% \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/FFT_D_Acceleration_Z.pdf}
% % \caption{\label{Fig:Response_of_Top_of_Containment_Building} Seismic Response at Top of Containment Building}
% \end{center}
% \end{figure}
% \end{frame}
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\begin{frame}
\frametitle{Acceleration Traces, Elastic vs Inelastic }
\hspace*{35mm}
\begin{figure}[!h]
\vspace*{2mm}
\begin{center}
\hspace*{15mm}
\includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Acceleration_Elastic_Without_Contact_SMIRT_2017.pdf}
\hspace*{20mm}
\includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Acceleration_Inelastic_With_Contact_SMIRT_2017.pdf}
\hspace*{25mm}
\end{center}
\end{figure}
\hspace*{35mm}
\hspace*{10mm} Elastic \hspace*{40mm} Inelastic \hspace*{40mm}
\end{frame}
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\begin{frame}
\frametitle{Displacement Traces, Elastic vs Inelastic}
\hspace*{35mm}
\begin{figure}[!h]
\vspace*{2mm}
\begin{center}
\hspace*{15mm}
\includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Elastic_Without_Contact_SMIRT_2017.pdf}
\hspace*{20mm}
\includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Inelastic_With_Contact_SMIRT_2017.pdf}
\hspace*{25mm}
\end{center}
\end{figure}
\hspace*{35mm}
\hspace*{10mm} Elastic \hspace*{40mm} Inelastic \hspace*{40mm}
\end{frame}
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\begin{frame}
\frametitle{Elastic and Inelastic Response: Differences}
% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy
% \vspace*{5mm}
\begin{center}
% \hspace*{15mm}
\movie[label=show3,width=10cm,poster,autostart,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_13Aug2017/NPP_Non_Linear_Effects_Sumeet.jpg}}
{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_13Aug2017/NPP_Non_Linear_Effects_Sumeet.mp4}
\end{center}
\begin{flushleft}
\vspace*{15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_August2017/NPP_Non_Linear_Effects_Sumeet.mp4}
% \href{./homo_50mmesh_45degree_Ormsby.mp4}
{\tiny (MP4)}
\end{flushleft}
%
\end{frame}
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\begin{frame}
\frametitle{Energy Dissipation in a LargeScale Model}
% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy
% \vspace*{5mm}
\begin{center}
% \hspace*{15mm}
\movie[label=show3,width=10cm,poster,autostart,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/tex/works/Conferences/2017/SMiRT_24/present/3D_Nonlinear_Modeling_and_it_Effects/NPP_Plastic_Dissipation_grab.jpg}}
{/home/jeremic/tex/works/Thesis/HanYang/Files_10Aug2017/NPP_Plastic_Dissipation.mp4}
\end{center}
\begin{flushleft}
\vspace*{15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/NPP_Plastic_Dissipation.mp4}
% \href{./homo_50mmesh_45degree_Ormsby.mp4}
{\tiny (MP4)}
\end{flushleft}
%
\end{frame}
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\begin{frame}
\frametitle{Energy Dissipation for an SMR Model}
% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy
% \vspace*{5mm}
\begin{center}
% \hspace*{15mm}
\movie[label=show3,width=10cm,poster,autostart,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation_screen_grab.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mp4}
\end{center}
\begin{flushleft}
\vspace*{15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mp4}
% \href{./homo_50mmesh_45degree_Ormsby.mp4}
{\tiny (MP4)}
\end{flushleft}
%
% \vspace*{5mm}
\end{frame}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Energy Dissipation for a SMR}
%
% % Elastoplastic soil with contact elements
% %% Both solid and contact elements dissipate energy
%
%
% % \vspace*{5mm}
% \begin{center}
% % \hspace*{15mm}
% %\movie[label=show3,width=9cm,poster,autostart,showcontrols]
% \movie[label=show3,width=10cm,poster,showcontrols]
% {\includegraphics[width=10cm]
% {/home/jeremic/tex/works/Conferences/2017/SMiRT_24/present/Nonlinear_Analysis_of_ESSI_for_SMR/SMR_Energy_Dissipation_screen_grab.jpg}}
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mpg}
% %{/home/jeremic/tex/works/Thesis/HanYang/Files_16Aug2017/SMR_Energy_Dissipation.mp4}
% \end{center}
%
%
% \begin{flushleft}
% \vspace*{15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mp4}
% % \href{./homo_50mmesh_45degree_Ormsby.mp4}
% {\tiny (MP4)}
% \end{flushleft}
% %
%
%
%
%
% \end{frame}
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% \begin{frame}
% \frametitle{Liquefaction as Base Isolation, Model}
%
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=4.5truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSISite_Response_Analysis/Liquefaction_04.jpg}
% \end{center}
% \end{figure}
%
% \end{frame}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Liquefaction, Wave Propagation}
%
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSISite_Response_Analysis/Liquefaction_01.jpg}
% \end{center}
% \end{figure}
%
% \hspace*{40mm} Dry \hspace*{10mm} Liquefied \hspace*{40mm}
%
% \end{frame}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Liquefaction, StressStrain Response}
%
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSISite_Response_Analysis/Liquefaction_03.jpg}
% \end{center}
% \end{figure}
%
% \hspace*{40mm} Dry \hspace*{10mm} Liquefied \hspace*{40mm}
%
% \end{frame}
%
%
%
%
%
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\begin{frame}
\frametitle{Energy Dissipation for Design}
\begin{figure}[!hbpt]
\begin{center}
\includegraphics[width=10.0truecm]{/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/2D_Frame_Model.pdf}
\end{center}
\end{figure}
\end{frame}
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\begin{frame}
\frametitle{Design Alternatives}
% local
%\vspace*{2mm}
\begin{center}
\hspace*{16mm}
%\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
\movie[label=show3,width=61mm,poster, showcontrols]
{\includegraphics[width=60mm]{/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/Individual_Foundation_screen_grab.jpg}}
{/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/Individual_Foundation.mp4}
%\hspace*{2mm}
%\hfill
%\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
\movie[label=show3,width=61mm,poster, showcontrols]
{\includegraphics[width=61mm]{/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/Continuous_Foundation_screen_grab.jpg}}
{/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/Continuous_Foundation.mp4}
\hspace*{16mm}
\end{center}
% local
% online % online
% online \begin{center}
% online \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_3d.mp4}
% online {\tiny (MP4)}
% online %
% online \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_1d.mp4}
% online {\tiny (MP4)}
% online \end{center}
% online % online
\end{frame}
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\begin{frame}
\frametitle{Solid, StructureFluid Interaction, Example}
%\vspace*{5mm}
\begin{center}
% \hspace*{15mm}
\movie[label=show3,width=9cm,poster,autostart,showcontrols]
{\includegraphics[width=8.5cm]
{/home/jeremic/tex/works/Conferences/2017/DOE_Project_Review_Meeting_LBNL_09June2017/Present/SolidFluidInteraction.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Fluid_Solid_interaction/Solid_Fluid_Interaction_NEW.mpeg}
\end{center}
\begin{flushleft}
\vspace*{15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Fluid_Solid_interaction/Solid_Fluid_Interaction.mp4}
% \href{./homo_50mmesh_45degree_Ormsby.mp4}
{\tiny (MP4)}
\end{flushleft}
%
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\subsection{Uncertain Inelasticity}
%\section[1D stochastic structural dynamic analysis]{1D stochastic structural dynamic analysis}
%\frame{\tableofcontents[currentsubsection,sectionstyle=show/shaded]}
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\begin{frame}
\frametitle{Uncertain Model Description}
\begin{textblock}{15}(0.3, 3.4)
\includegraphics[width=0.70\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/example_illustration.png}
\end{textblock}
\begin{textblock}{15}(1.2, 11.6)
\scriptsize
\begin{itemize}
\item Fault 1: San Gregorio fault
\item Fault 2: Calaveras fault
\item Uncertainty: Segmentation, \\ slip rate, rupture geometry, etc.
\end{itemize}
\end{textblock}
\begin{textblock}{15}(7.2, 11.7)
\scriptsize
\begin{itemize}
\item $Vs_{30}=620m/s$
\item $m=100kips/g$
\item $\overline{k} = 168kip/in$
\end{itemize}
\end{textblock}
\begin{textblock}{15}(9.7, 6.5)
\scriptsize
\[Cov_k =
\begin{bmatrix}
1.0 & 0.6 & 0.3 & 0.2\\
0.6 & 1.0 & 0.5 & 0.2\\
0.3 & 0.5 & 1.0 & 0.7\\
0.2 & 0.2 & 0.7 & 1.0
\end{bmatrix}
\]
\end{textblock}
\end{frame}
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\begin{frame}
\frametitle{Seismic Source Characterization}
\begin{textblock}{15}(0.3, 3.4)
\includegraphics[width=0.65\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/SSC_legend.pdf}
\end{textblock}
\begin{textblock}{15}(6.5, 12.1)
\scriptsize
\begin{itemize}
\item 371 total seismic scenarios
\item $M \ 5 \sim 5.5$ and $6.5 \sim 7.0$
\item $R_{jb} \ 20km \sim 40km$
\end{itemize}
\end{textblock}
\begin{textblock}{15}(11.7, 3.3)
\includegraphics[width=0.22\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/Acc_time_series100.pdf}\\
\includegraphics[width=0.22\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/Acc_time_series343.pdf}\\
\includegraphics[width=0.22\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/Acc_time_series439.pdf}
\end{textblock}
\end{frame}
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\begin{frame}
\frametitle{Stochastic Ground Representation}
{\begin{textblock}{15}(0.1, 3.62)
\scriptsize
\includegraphics[width=0.3\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/KL_mean_acc_from_acc.pdf}
\quad \quad Acc. marginal mean
\end{textblock}
\begin{textblock}{15}(3.7, 3.62)
\scriptsize
\includegraphics[width=0.3\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/KL_var_acc_from_acc.pdf}
\quad \quad Acc. marginal S.D.
\end{textblock}
\begin{textblock}{15}(7.6, 3.8)
\scriptsize
\includegraphics[width=0.3\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/KL_exact_acc_correlation_from_acc.pdf}
\quad \quad \quad Acc. realization Cov.
\end{textblock}
\begin{textblock}{15}(11.8, 3.9)
\scriptsize
\includegraphics[width=0.3\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/KL_simulated_acc_correlation_from_acc.pdf}
\quad \quad Acc. synthesized Cov.
\end{textblock}}
\begin{textblock}{15}(0.1, 9.3)
\scriptsize
\includegraphics[width=0.31\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/KL_mean_dis_from_dis.pdf}
\end{textblock}
\begin{textblock}{15}(0.9, 13.75)
\scriptsize
Dis. marginal mean
\end{textblock}
\begin{textblock}{15}(4.2, 9.4)
\scriptsize
\includegraphics[width=0.3\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/KL_var_dis_from_dis.pdf}
\end{textblock}
\begin{textblock}{15}(5.1, 13.75)
\scriptsize
Dis. marginal S.D.
\end{textblock}
\begin{textblock}{15}(8.2, 9.5)
\scriptsize
\includegraphics[width=0.27\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/KL_exact_dis_correlation_from_dis.pdf}
\quad \quad Dis. realization Cov.
\end{textblock}
\begin{textblock}{15}(12.2, 9.6)
\scriptsize
\includegraphics[width=0.27\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/KL_simulated_dis_correlation_from_dis.pdf}
\quad Dis. synthesized Cov.
\end{textblock}
\end{frame}
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\begin{frame}
\frametitle{Probabilistic Dynamic Response}
\begin{textblock}{15}(2.9, 4)
\scriptsize
\includegraphics[width=0.65\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/Probabilistic_Response_Node_1_new.pdf}
\end{textblock}
\begin{textblock}{15}(4.8, 3.8)
\scriptsize Probabilistic response of top floor from SFEM
\end{textblock}
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% \scriptsize
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\frametitle{Maximum Interstory Drift Ratio (MIDR)}
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\vspace*{5mm}
\begin{figure}[htb]
\begin{center}
\includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/MIDR_distribution.pdf}
\end{center}
\end{figure}
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\begin{frame}
\frametitle{Seismic Risk Analysis}
\begin{textblock}{15}(0.7, 4.8)
\scriptsize
\includegraphics[width=0.45\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/combined_risk_curve.pdf}
\end{textblock}
\begin{textblock}{15}(7.9, 4.8)
\scriptsize
\includegraphics[width=0.48\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/risk_deaggregation_MIDR1.pdf}
\end{textblock}
\begin{textblock}{15}(0.9, 11.9)
\begin{itemize}
\item[] \scriptsize $\lambda(MIDR >1 \%) = 9.7 \times 10^{3}$
\item[] \scriptsize $\lambda(MIDR >2 \%) = 1.7 \times 10^{3}$
\item[] \scriptsize $\lambda(MIDR >4 \%) = 5.9 \times 10^{5}$
\end{itemize}
\end{textblock}
\begin{textblock}{15}(9.3, 12.5)
\scriptsize Risk deaggregation for $\lambda(MIDR >1 \%)$
\end{textblock}
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% \frametitle{Sensitivity Study}
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% \scriptsize
% \includegraphics[width=0.42\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/risk_curve_different_kappa.pdf}
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% \scriptsize
% \includegraphics[width=0.42\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/median_FAS_stressdrop_comparison.pdf}
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% \scriptsize
% \includegraphics[width=0.42\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/median_FAS_kappa_comparison1.pdf}
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% \scriptsize Site $\kappa_0$:
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% \scriptsize Source $\Delta \sigma$:
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% \frametitle{Sensitivity Study}
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% Fundamental frequency $f$ increases from 1.6Hz to 8Hz:
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% \scriptsize
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\begin{frame}
\frametitle{Seismic Risk, Uncertain Material}
\begin{figure}[htb]
\begin{center}
\includegraphics[width=8cm]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/seismic_risk_compare.pdf}
\end{center}
\end{figure}
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\section{Conclusion}
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\subsection{RealESSI Simulator System}
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\begin{frame}
\frametitle{RealESSI Simulator System}
The RealESSI, Realistic
{\underline {\bf M}}odeling and
{\underline {\bf S}}imulation of
{\underline {\bf E}}arthquakes,
{\underline {\bf S}}oils,
{\underline {\bf S}}tructures and their
{\underline {\bf I}}nteraction. Simulator is a software, hardware and
documentation system for high fidelity, high performance, time domain,
nonlinear/inelastic, deterministic or probabilistic, 3D, finite element modeling
and simulation of:
\begin{itemize}
%\vspace*{1mm}
\item statics and dynamics of soil,
\vspace*{1mm}
\item statics and dynamics of rock,
\vspace*{1mm}
\item statics and dynamics of structures,
\vspace*{1mm}
\item statics of soilstructure systems, and
\vspace*{1mm}
\item dynamics of earthquakesoilstructure system interaction
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{RealESSI Simulator System}
\begin{itemize}
\item RealESSI System Components
\begin{itemize}
\item RealESSI Preprocessor (gmsh/gmESSI, X2ESSI)
\item RealESSI Program (local, remote, cloud)
\item RealESSI PostProcessor (Paraview/pvESSI, Python, Matlab)
\end{itemize}
\vspace*{1mm}
\item RealESSI System availability:
\begin{itemize}
%\vspace*{1mm}
\item Educational Institutions: Amazon Web Services (AWS), free
\item Government Agencies, National Labs: AWS GovCloud
\item Professional Practice: AWS, commercial
%\vspace*{1mm}
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% \item Sources available to collaborators
\end{itemize}
%\vspace*{1mm}
%\item Quality Management System, ASMENQA1, ISO90032018, Certification in progress
\vspace*{1mm}
\item RealESSI Short Courses (online, this Fall)
\vspace*{1mm}
\item System description and documentation at
\url{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
%
%\url{http://realessi.info/}
%
% \vspace*{2mm}
% \item
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\end{itemize}
\end{frame}
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%\subsection*{Summary}
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\begin{frame}
\frametitle{Science Quotes}
\begin{itemize}
\item Max Planck:
"A new scientific truth does not triumph by convincing its opponents and
making them see the light, but rather because its opponents eventually die, and
a new generation grows up that is familiar with it." (Science advances one
funeral at a time)
\vspace*{3mm}
\item Fran{\c c}oisMarie Arouet, Voltaire:
"Le doute n'est pas une condition agr{\'e}able, mais la certitude est absurde."
\vspace*{3mm}
\item Niklaus Wirth:
"Software is getting slower more rapidly than hardware becomes faster."
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{Summary}
\begin{itemize}
% \item Importance of using proper models correctly (verification,
% validation, level of sophistication)
%
% \item Reduction of modeling uncertainty
%
\vspace*{1mm}
\item Numerical modeling to predict and inform, rather than fit
%\vspace*{1mm}
% \item Change of demand due to inelastic effects
%\vspace*{1mm}
% \begin{itemize}
% \item Reduction of dynamic motions
% \item Increase in deformations
% \end{itemize}
\vspace*{1mm}
\item Sophisticated inelastic/nonlinear modeling and simulations need to be
done carefully and in phases
\vspace*{1mm}
\item Education and Training is the key!
\vspace*{1mm}
\item Collaborators: Feng, Yang, Behbehani, Sinha, Wang, Wang,
Pisan{\'o}, Abell, Tafazzoli, Jie, Preisig, Tasiopoulou, Watanabe, Luo,
Cheng, Yang...
\vspace*{1mm}
\item Funding from and collaboration with the USDOE, USNRC, USNSF,
CNSCCCSN, UNIAEA, and Shimizu Corp. is greatly appreciated,
\vspace*{1mm}
\item
\url{http://sokocalo.engr.ucdavis.edu/~jeremic}
\end{itemize}
\end{frame}
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