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% \usetheme{Hannover} % ima naslov i sadrzaj sa leve strane
% \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{tikz}
\usetikzlibrary{calc}
\usepackage[export]{adjustbox}
\usepackage{array}
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%%%% HYPERREF HYPERREF HYPERREF HYPERREF HYPERREF
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\usepackage{hyperref}
\hypersetup{
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pdfpagemode={None}
% Commenting this out fixes Windows acrobat problem (?!)
colorlinks=true,
linkcolor=webblue,
citecolor=webblue,
urlcolor=webblue,
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% \usepackage[pdfauthor={Boris Jeremic},
% colorlinks=true,
% linkcolor=webblue,
% citecolor=webblue,
% urlcolor=webblue,
% linktocpage,
% pdftex]{hyperref}
\usepackage{pause}
% or whatever
%\usepackage{html}
%\usepackage{url}
\usepackage[latin1]{inputenc}
% 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]
{Computational Modeling and Simulation of \\
Earthquake Soil Structure Interaction \\
Behavior of Nuclear Installations}
% {A Modern Computational Framework for \\
% the Nonlinear Seismic Analysis of \\
% Nuclear Facilities and Systems}
%
% {Interface Between Earthquake Ground Motions and Structural
%Response: Numerical Modeling and Simulation of ESSI Behavior}
%\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}
%\pgfdeclareimage[height=0.15cm]{UCDlogo}{/home/jeremic/BG/amblemi/ucdavis_logo_blue_sm}
%\pgfdeclareimage[height=0.18cm]{LBNLlogo}{/home/jeremic/BG/amblemi/LBNL/BerkeleyLab_Masterbrand_logo}
% % \pgfdeclareimage[height=0.15cm]{ESSIClogo}{/home/jeremic/BG/amblemi/ESSI/ESSI_Consultants_gray_02}
% \pgfdeclareimage[height=0.17cm]{ESSIClogo}{/home/jeremic/BG/amblemi/ESSI/ESSI_Consultants_white_01}
% \pgfdeclareimage[height=0.20cm]{UCDlogo}{/home/jeremic/BG/amblemi/UCD/UCD_white_01}
% \pgfdeclareimage[height=0.20cm]{LBNLlogo}{/home/jeremic/BG/amblemi/LBNL/LBNL_white_01}
% % \pgfdeclareimage[height=0.15cm]{ESSIClogo}{/home/jeremic/BG/amblemi/ESSI/ESSI_Consultants_gray_02}
% \pgfdeclareimage[height=0.20cm]{ESSIClogo}{/home/jeremic/BG/amblemi/ESSI/ESSIC_white_01}
% \pgfdeclareimage[height=0.40cm]{Best_PSHANI_2018_logo}{/home/jeremic/tex/works/Conferences/2018/BestPSHANI/Presentation/Best_PSHANI_2018_logo}
%\author[Jeremi{\'c} et al. Best PSHANI] % (optional, use only with lots of authors)
\author[Jeremi{\'c} et al.] % (optional, use only with lots of authors)
%{Boris~Jeremi{\'c}}
{Boris Jeremi{\'c}}
%Feng, Yang, Wang, Wang, Behbehani, Sinha, Abell, Pisan{\'o}}
%Fangbo Wang, David McCallen}
%Floriana Petrone, Francis McKenna, David McCallen}
\institute[\pgfuseimage{universitylogo}\hspace*{0.1truecm}\pgfuseimage{lbnllogo}] % (optional, but mostly needed)
%\institute[Computational Geomechanics Group \hspace*{0.3truecm}
%\institute[] % (optional, but mostly needed)
%\institute[\pgfuseimage{UCDlogo}\hspace*{0.15truecm}\pgfuseimage{LBNLlogo}] % (optional, but mostly needed)
%\institute[\pgfuseimage{UCDlogo}\hspace*{0.15truecm}\pgfuseimage{LBNLlogo}\hspace*{0.15truecm}\pgfuseimage{ESSIClogo}] % (optional, but mostly needed)
%\institute[\pgfuseimage{UCDlogo}\mbox{;}\pgfuseimage{LBNLlogo}\mbox{;}\pgfuseimage{ESSIClogo}] % (optional, but mostly needed)
%{ Professor, University of California, Davis\\
% { University of California, Davis, CA, USA}
%{ UCD and LBNL}
{ University of California, Davis, CA\\
and\\
Lawrence Berkeley National Laboratory, Berkeley, CA}
% ESSI Consultants, Davis, 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 CNERDWG, ANL, Apr2019}
\subject{}
% This is only inserted into the PDF information catalog. Can be left
% out.
% If you have a file called "universitylogofilename.xxx", where xxx
% is a graphic format that can be processed by latex or pdflatex,
% resp., then you can add a logo as follows:
%\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}
\tableofcontents[currentsection,currentsubsection]
% \tableofcontents[currentsection]
\end{frame}
\end{scriptsize}
}
% If you wish to uncover everything in a stepwise fashion, uncomment
% the following command:
\begin{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\titlepage
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Motivation}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Motivation}
\begin{itemize}
%\vspace*{0.3cm}
\item Improve modeling and simulation for seismic behavior of Nuclear
Installations
% \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*{3mm}
\item Reduce modeling uncertainty
%\vspace*{1mm}
% \item[] Desired level
% of sophistication (high $\leftrightarrow$ low) analysis
\vspace*{3mm}
\item Follow the flow, input and dissipation, of seismic energy,
\vspace*{3mm}
\item Practical system for modeling and simulation of
Earthquakes, Soils, Structures and their Interaction (ESSI):
% RealESSI:
\\
\vspace*{3mm}
\hspace*{20mm}
\href{http://realessi.info/}{http://realessi.info/}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Predictive Capabilities}
% \frametitle{High Fidelity Modeling of SFS System:
% Verification, Validation and Prediction}
\begin{itemize}
\item { Prediction under Uncertainty}
% use of computational model
% to predict the state of SSI system under
% conditions for which the computational model has not been validated.
\vspace*{3mm}
\item {{ Verification:}
% provides
evidence that the model is solved
correctly.}
% Mathematics issue.
\vspace*{3mm}
\item {{ Validation:}
% provides
evidence that the correct model is
solved.}
% Physics issue.
\vspace*{3mm}
\item Modeling and parametric uncertainties are always present
% need to be
% addressed
% \vspace*{1mm}
% \item Predictive capabilities with {low Kolmogorov Complexity}
%
\vspace*{3mm}
\item Goal: Predict and Inform rather than (force) Fit
\vspace*{3mm}
\item Risk informed is not enough $\rightarrow$ full risk calculations for ESSI,
analytical/numerical, accurate
\end{itemize}
\end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Verification and Validation Details}
\begin{figure}[!ht]
%\vspace*{0.5cm}
%\hspace*{0.5cm}
\begin{center}
{\includegraphics[width=11cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Verification_and_Validation_Introduction/tex_works_Conferences_2005_OpenSeesWorkshopAugust_DeveloperSymposium_VerifValidFund01.pdf}}
\end{center}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Verification}
The process of determining that a model
implementation accurately represents the developer's conceptual description
and specification.
% Mathematics issue. {\it Verification provides evidence that the
% model is solved correctly.}
\begin{itemize}
\item Identify and remove errors in computer coding
\begin{itemize}
\item Numerical algorithm verification
\item Software quality assurance practice
\end{itemize}
\item Quantification of the numerical errors in computed solution
\end{itemize}
%
%\begin{figure}[!ht]
%\vspace*{3mm}
%%\hspace*{4.5cm}
%\begin{center}
%{\includegraphics[width=6cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Verification_and_Validation_Introduction/tex_works_Conferences_2005_OpenSeesWorkshopAugust_DeveloperSymposium_VerifValidFund02.pdf}}
%\end{center}
%\end{figure}
%
\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
%
% \vspace*{2mm}
% \item Still finding and resolving issues, using large scale modeling
%
%
%
% \end{itemize}
%
% \end{frame}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Validation}
The process of determining the degree to which a
model is accurate representation of the real world from the perspective of
the intended uses of the model.
% Physics issue. {\it Validation provides
% evidence that the correct model is solved.}
\begin{itemize}
\item Tactical goal: Identification and minimization of uncertainties
and errors in the computational model
\item Strategic goal: Increase confidence in the quantitative
predictive capability of the computational model
\end{itemize}
%\begin{figure}[!ht]
%\vspace*{4mm}
%%\hspace*{5.5cm}
%\begin{center}
%%\begin{flushright}
%{\includegraphics[width=5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Verification_and_Validation_Introduction/tex_works_Conferences_2005_OpenSeesWorkshopAugust_DeveloperSymposium_VerifValidFund03.pdf}}
%%\end{flushright}
%\end{center}
%\end{figure}
%
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Types of Physical Experiments}
\begin{itemize}
\vspace*{1mm}
\item {Traditional Experiments}
\begin{itemize}
\vspace*{1mm}
\item Improve the fundamental understanding of physics involved
\vspace*{1mm}
\item Improve the mathematical models for physical phenomena
\vspace*{1mm}
\item Assess component performance
\end{itemize}
\vspace*{3mm}
\item {Validation Experiments}
\begin{itemize}
\vspace*{1mm}
\item Model validation experiments
\vspace*{1mm}
\item Designed and executed to quantitatively estimate mathematical
model's ability to simulate well defined physical behavior
\vspace*{1mm}
\item The simulation tool, RealESSI, computational model,
computational solution, is the customer
\end{itemize}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Uncertainties}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Uncertainties}
\begin{itemize}
%\vspace*{1mm}
\vspace*{2mm}
\item \underline{Modeling Uncertainty}, from simplifying assumptions
\begin{itemize}
\vspace{2mm}
\item Low, medium, high sophistication modeling and simulation
\vspace{2mm}
\item Sophistication level for confidence in analysis 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 Propagation of uncertainty in $M$, $C$ and $K^{ep}$
\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 Simplified modeling: Features (important ?) are neglected (3C, 6C
ground motions, inelasticity)
\vspace*{4mm}
\item Modeling Uncertainty: unrealistic and unnecessary modeling
simplifications
\vspace*{4mm}
\item Modeling simplifications are justifiable if one or two level higher
sophistication model shows that features being simplified out are not
important
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
\vspace*{10mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{7mm}
\includegraphics[width=6.2truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01Ed.pdf}
% \hfill
\includegraphics[width=4.8truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/YoungModulus_Histogram_Normal_01Ed.pdf}
%
\end{center}
\end{figure}
%\vspace*{1.8cm}
%\hspace*{3.3cm}
\begin{flushright}
{\small
%Transformation of SPT $N$value:
%1D Young's modulus, $E$
cf. Phoon and Kulhawy (1999B)
~}
\end{flushright}
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Parametric Uncertainty: Material Strength}
%
%
% \begin{figure}[!hbpt]
% \begin{center}
% %
% \hspace*{7mm}
% \includegraphics[width=6.50truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/ShearStrength_RawData_and_MeanTrendMod.pdf}
% \hspace*{7mm}
% % \hfill
% \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/ShearStrength_Histogram_PearsonIVFineTunedMod.pdf}
% %
% \end{center}
% \end{figure}
%
% % \vspace*{1.8cm}
% % %\hspace*{3.3cm}
% % \begin{flushright}
% % {\tiny
% % Transformation of SPT $N$value: \\
% % 1D Young's modulus, $E$ \\
% % (cf. Phoon and Kulhawy (1999B))\\
% % ~}
% % \end{flushright}
% % %
%
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Parametric Uncertainty: Material Properties}
%
%
%
% \begin{figure}[!hbpt]
% \begin{center}
% % %
% \hspace*{3mm}
% \includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiPdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiCdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldSuPdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=3.0truecm]{/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*{45mm}
% \hspace*{3mm}
% \includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiPdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiCdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuPdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=3.0truecm]{/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}
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\section{Modeling and Simulation }
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{RealESSI Simulator System}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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*{2mm}
% \item \underline{Design:} linear elastic, load combinations, dimensioning
%
%
% \vspace*{2mm}
% \item \underline{Assessment:} nonlinear/inelastic, DBE/BDBE, 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, ILEE,
% % etc.
% %
%
%
% \end{itemize}
%
% \end{frame}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{RealESSI Modeling Features}
%
% \begin{itemize}
%
%
%
% %\vspace*{2mm}
% \item Solid elements, dry, saturated, elastic, inelastic
%
% \vspace*{1mm}
% \item Structural elements, beams, shells, elastic, inelastic
%
% \vspace*{1mm}
% \item Contact elements, dry, coupled/saturated, hard, soft
%
% \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, material, viscous, algorithmic
%
% \vspace*{1mm}
% \item Solid/Structure  Fluid interaction, full coupling
%
% % \vspace*{1mm}
% % \item Features listed at
% % \hspace*{5mm}
% % % \hspace*{5mm}
% % % \href{http://realessi.info/}{http://realessi.info/}
% %
%
% \end{itemize}
%
% \end{frame}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{RealESSI Simulation Features}
%
% \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 Features listed at
% % \hspace*{5mm}
% % % \hspace*{5mm}
% % % \href{http://realessi.info/}{http://realessi.info/}
%
%
%
% \end{itemize}
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{RealESSI Model Development}
%
% \begin{itemize}
%
% \item PreProcessing, gmsh/gmESSI, translation (SASSI...)
%
%
% \vspace*{2mm}
% \item Choose level of sophistication, reduce modeling uncertainty
%
%
% %\vspace*{1mm}
% % \item Verify code, solutions, methods, elements, material models
%
%
%
% \vspace*{2mm}
% \item Model developed in phases
%
% \vspace*{2mm}
% \item Verify model components
%
%
% \vspace*{2mm}
% \item Build confidence in inelastic modeling
%
%
% %%\vspace*{2mm}
% %% \item Use such developed models to predict and inform, rather than force fit
%
%
%
% \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 Training and Education}
%
% \begin{itemize}
%
%
% \item Short Courses:
% \begin{itemize}
% %\vspace*{1mm}
% \item In person short course last year
% %\vspace*{1mm}
% \item Online short course this winter
% %\vspace*{1mm}
% \item Professional practice
% % %\vspace*{1mm}
% % \item Developers
% %\vspace*{1mm}
% \item Examples available in lecture notes, and documentation
% %\vspace*{1mm}
% \item RealESSI system, with examples on Amazon Web Services
%
% \end{itemize}
%
% %\vspace{1mm}
% % \item Documentation, extensive
%
% \vspace{2mm}
% \item Full documentation / lecture notes (2600+ pages) available online at
% \\
% \vspace*{2mm}
% \hspace*{5mm}
% \href{http://realessi.info/}{http://realessi.info/}
%
%
% \end{itemize}
%
% \end{frame}
%
% % OVDE OVDE OVDE
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{RealESSI Core Functionality}
%
% \begin{itemize}
%
%
%
% % %\vspace*{2mm}
% % \item Introduction to inelastic/nonlinear analysis for practicing engineers
%
%
% % \vspace*{3mm}
% \item 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
% %
% %
% %
% % %\vspace*{1mm}
% % % \item[] Directing, in space and time, seismic energy flow in the
% % % soil structure system
% %
%
%
% \end{itemize}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
%
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \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)
%
% \vspace*{2mm}
% \item Restart: Logic tree of load cases
%
% \vspace*{2mm}
% \item Simulation: Explicit (noequilibrium), Implicit (equilibrium),
%
% \vspace*{2mm}
% \item Core Functionality Application programs: APPs
% %
%
%
% \end{itemize}
%
%
% \end{frame}
%
%
%
%
%
%
%
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%
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\subsection{Modeling and Simulation Examples}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Energy Input and Dissipation}
\begin{itemize}
\vspace*{1mm}
\item[] Energy input, static and 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)
%\vspace*{4mm}
\item[] Numerical energy dissipation/production
\end{itemize}
%
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %
% % \frametitle{Incremental Plastic Work:
% % \makebox[0pt][l]{\hspace*{2mm}\raisebox{0.60ex}{\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Conferences/2018/GeoMEast2018/Short_Course/present/GeoMEast_presentation_EQ03.png}}}%
% % %$d W_p = \sigma_{ij} \, d\epsilon_{ij}^{pl}$
% % }
% %
% % \begin{itemize}
% % \item Negative incremental energy dissipation
% % %\item Plastic work is NOT plastic dissipation
% % \end{itemize}
% %
% % \begin{figure}[!H]
% % \begin{center}
% % \includegraphics[height=5.5cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Negative_Dissipation_Problem.png}
% % \end{center}
% % \end{figure}
% %
% % \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %
% % \frametitle{Energy Dissipation on Material Level}
% %
% %
% % \vspace*{2mm}
% %
% % Single elasticplastic element under cyclic shear loading
% %
% % \begin{itemize}
% % \item[] Difference between plastic work and dissipation
% % \item[] Plastic work can decrease, dissipation always increases
% % \end{itemize}
% %
% % \vspace*{7mm}
% % \begin{figure}[!hbpt]
% % \begin{center}
% % \hspace*{5mm}
% % \includegraphics[width=12.0truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Dissipation_Material.png}
% % \end{center}
% % \end{figure}
% %
% % \end{frame}
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %
% % \frametitle{Plastic Free Energy}
% %
% % \begin{itemize}
% % % \item Direct violation of the second law of thermodynamics
% % % % \item Where is the problem?
% % % \item Missing is the plastic free energy
% %
% %
% % \item Multiscale effect of particle interlocking/rearrangement
% % \item Strain energy on particle level
% % \end{itemize}
% %
% % \begin{figure}[!h]
% % \begin{center}
% % \includegraphics[width=7truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Plastic_Free_Energy.png}
% % \end{center}
% % \end{figure}
% %
% % \end{frame}
% % %%%%%%%%%%%%%%%%%%%%%%%%f%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %
% % \frametitle{Energy Transformation in ElasticPlastic Material}
% %
% % \begin{figure}[!H]
% % \begin{center}
% % \includegraphics[height=6cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Energy_Transformation.png}
% % \end{center}
% % \end{figure}
% %
% % \end{frame}
% % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
% %
% %
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Inelastic Modeling for NPP Soil Structure System}
%
% \begin{itemize}
%
% %\vspace*{1mm}
% \item Soil 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, Normal (hard and soft, gap open/close),
% Friction (nonlinear)
% \item Fully saturated, suction and excess pressure (buoyant force)
% \end{itemize}
%
%
% %\vspace*{1mm}
% \item Structural inelasticity/damage
% \begin{itemize}
% \item Nonlinear/inelastic fiber beams
% \item Nonlinear/inelastic reinforced concrete walls. plates, shells
% \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}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \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}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Simulation Result}
%
% \begin{figure}[!h]
% \begin{center}
% \subfigure[Selected Locations
% \label{Specific_Locations}]{\includegraphics[width=0.45\textwidth]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/NPP_Selected_Location_For_Study.pdf}}
% \subfigure[Total Displacement
% \label{Total_Displacement}]{\includegraphics[width=0.40\textwidth]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Total_Displacement_Z.pdf}}
% \end{center}
% \caption{\label{Fig:NPP_Selected_Location_For_Study} Locations selected to study nonlinear effects and plot of total displacement at center of model}
% \end{figure}
%
%
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Acc. Response, Top of Containment Building}
%
% \begin{figure}[!h]
% \begin{center}
% \hspace*{8mm}
% \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/D_Acceleration_X.pdf}
% \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/D_Acceleration_Y.pdf}
% \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/D_Acceleration_Z.pdf}
% \\
% \hspace*{8mm}
% \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/FFT_D_Acceleration_X.pdf}
% \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/FFT_D_Acceleration_Y.pdf}
% \includegraphics[width=4cm]{/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}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Acceleration Traces, Elastic vs Inelastic }
% \begin{figure}[!h]
% \vspace*{2mm}
% \begin{center}
% \hspace*{15mm}
% \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Acceleration_Elastic_Without_Contact_SMIRT_2017.pdf}
% \hspace*{20mm}
% \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Acceleration_Inelastic_With_Contact_SMIRT_2017.pdf}
% \hspace*{7mm}
% \end{center}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
\frametitle{Energy Dissipation in NPP 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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Wall, Regular and ASR Concrete}
%
% \vspace{5mm}
%
% \begin{figure}[!h]
% \begin{center}
% \includegraphics[width=2truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Rebar_Plan.pdf}
% \includegraphics[width=4truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/3D_mesh.pdf}
% \includegraphics[width=3truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Reg_A_Force_Displacement.pdf}
% \includegraphics[width=3truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/ASR_A1_Force_Displacement.pdf}
% \end{center}
% \end{figure}
%
%
% \vspace{2mm}
% \begin{figure}[!htbp]
% \begin{center}
% \includegraphics[width=10.0truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_Natural_Hazartd_Oct2018/Present/OECD_wall_damage_3_stages.jpg}
% \end{center}
% \end{figure}
%
%
%
% % \vspace{20mm}
% % \begin{figure}[!htbp]
% % \hspace*{10mm}
% % \begin{center}
% % \includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Damage_3000.pdf}
% % \hspace*{5mm}
% % \includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Damage_5000.pdf}
% % \hspace*{5mm}
% % \includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Damage_10000.pdf}
% % \end{center}
% % \end{figure}
% %
% %
% % \vspace*{5mm}
% % \hspace*{12mm}
% % \begin{footnotesize}
% % $u_y$ = 1.4 mm
% % \hspace{12mm}
% % $u_y$ = 1.8 mm
% % \hspace{12mm}
% % $u_y$ = 3.0 mm
% % \end{footnotesize}
%
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Solid/Structure  Fluid Interaction}
%
%
% %OVDE dodaj link na online...
%
% %\vspace*{5mm}
% \begin{center}
% % \hspace*{15mm}
% \movie[label=show3,width=8cm,poster,autostart,showcontrols]
% {\includegraphics[width=8.5cm]
% {/home/jeremic/tex/works/Conferences/2017/DOE_Project_Review_Meeting_LBNL_09June2017/Present/SolidFluidInteraction.jpg}}
% {/home/jeremic/tex/works/Thesis/HexiangWang/Files_06June2017/pic/Solid_Fluid_Interaction.mp4}
% \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}
% %
%
%
%
%
% \end{frame}
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% \begin{frame}
%
% \frametitle{Energy Dissipation for an 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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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
\frametitle{Seismic Motions}
%\vspace*{10mm}
\begin{itemize}
\item Variation in inclination, frequency, energy, duration...
\item Deterministic and Probabilistic
\item Stress test the soilstructure system
\end{itemize}
%\vspace*{4mm}
\begin{figure}[!htb]
\begin{flushleft}
\hspace*{5mm}
\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Conferences/2018/BestPSHANI/Presentation/stress_test_Best_SHANI_May2018.jpg}
\end{flushleft}
\end{figure}
%
% \vspace*{45mm}
% \begin{figure}[!htb]
% \begin{flushright}
% \includegraphics[width=4cm]{/home/jeremic/tex/works/Conferences/2015/CNSC_July/Present/Stress_test_NPP_idea.jpg}
% \hspace*{5mm}
% \end{flushright}
% \end{figure}
\vspace*{35mm}
\begin{figure}[!htb]
\begin{flushright}
\includegraphics[width=5cm]{/home/jeremic/tex/works/consulting/2017/IAEA/TECDOC/Version_14Mar2017/1Dvs3x1Dvs3D_waves.pdf}
\hspace*{5mm}
\end{flushright}
\end{figure}
\end{frame}
%
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\begin{frame}
\frametitle{Free Field, Variation in Input Frequency, $\theta = 60^{o}$}
% 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]
\movie[label=show3,width=10cm,poster,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/Free_Field_variation_in_wave_frequency.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/free_field_frequency.mp4}
\end{center}
% online
\vspace*{12mm}
\begin{flushleft}
\hspace*{4mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/free_field_frequency.mp4}
{\tiny (MP4)}
\end{flushleft}
% online
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
\frametitle{SMR ESSI, Variation in Input Frequency, $\theta = 60^{o}$}
% 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]
\movie[label=show3,width=10cm,poster,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/ESSI_SMR_variation_in_wave_frequency.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/SMR_frequency.mp4}
\end{center}
% online
\vspace*{12mm}
\begin{flushleft}
\hspace*{4mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/SMR_frequency.mp4}
{\tiny (MP4)}
\end{flushleft}
% online
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% %\frametitle{SMR ESSI, Variation in Input Frequency, $\theta = 60^{o}$}
% \frametitle{SMR ESSI, Variation in Input Frequency, REAL TIME}
%
% % 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]
% \movie[label=show3,width=10cm,poster,showcontrols]
% {\includegraphics[width=10cm]
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/ESSI_SMR_variation_in_wave_frequency.jpg}}
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMRESSI_real_time_four_freq.mp4}
% \end{center}
%
% % online
% \vspace*{12mm}
% \begin{flushleft}
% \hspace*{4mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMRESSI_real_time_four_freq.mp4}
% {\tiny (MP4)}
% \end{flushleft}
% % online
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\begin{frame}
%\frametitle{SMR ESSI, Variation in Input Frequency, $\theta = 60^{o}$}
\frametitle{SMR ESSI, 3C vs 3$\times$1C}
% 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]
\movie[label=show3,width=11cm,poster,showcontrols]
{\includegraphics[width=11cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/3Dvs1D_deconvolution.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/3Dvs1D_deconvolution.ogv}
\end{center}
% online
\vspace*{12mm}
\begin{flushleft}
\hspace*{4mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/3Dvs1D_deconvolution.ogv}
{\tiny (OGV)}
\end{flushleft}
% online
\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)
% \tiny X direction
% \end{textblock*}
% \begin{textblock*}{2cm}(0.2cm,6.3cm) % {block width} (coords)
% \tiny Z direction
% \end{textblock*}
% \begin{textblock*}{3cm}(2.4cm,7.6cm) % {block width} (coords)
% \tiny (a) $f=1Hz \ \ \theta=60^{o}$
% \end{textblock*}
% \begin{textblock*}{3cm}(5.6cm,7.6cm) % {block width} (coords)
% \tiny (b) $f=5Hz \ \ \theta=60^{o}$
% \end{textblock*}
% \begin{textblock*}{3cm}(8.8cm,7.6cm) % {block width} (coords)
% \tiny (c) $f=10Hz \ \ \theta=60^{o}$
% \end{textblock*}
%
% \vspace*{30mm}
% \begin{figure}[!H]
% \centering
% % \begin{flushleft}
% \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/1Hz_center_ax.pdf}
% \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/5Hz_center_ax.pdf}
% \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/10Hz_center_ax.pdf}
% \\
% \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/1Hz_center_az.pdf}
% \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/5Hz_center_az.pdf}
% \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/10Hz_center_az.pdf}
% % \end{flushleft}
% \end{figure}
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% \begin{figure}[!H]
% \begin{flushright}
% \hspace*{30mm}
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/Points_configuration.pdf}
% \hspace*{10mm}
% \end{flushright}
% \end{figure}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
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% %
%
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% \begin{frame}
%
% \frametitle{NPP 3C vs 3$\times$1C Motions}
%
% % Elastoplastic soil with contact elements
% %% Both solid and contact elements dissipate energy
%
%
% % \vspace*{5mm}
% \begin{flushleft}
% \hspace*{7mm}
% %\movie[label=show3,width=54mm,poster,autostart,showcontrols]
% \movie[label=show3,width=54mm,poster,showcontrols]
% {\includegraphics[width=54mm]
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_June2018/Displacement_Inclined_Wave_3C.jpg}
% }
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_June2018/Displacement_Inclined_Wave_3C.mp4}
% \end{flushleft}
% % online
% %\vspace*{12mm}
% \begin{flushleft}
% %\hspace*{10mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_June2018/Displacement_Inclined_Wave_3C.mp4}
% {\tiny (MP4)}
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% % online
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% \movie[label=show3,width=54mm,poster,showcontrols]
% {\includegraphics[width=54mm]
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_June2018/Displacement_Inclined_Wave_3_times_1C.jpg}
% }
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_June2018/Displacement_Inclined_Wave_3_times_1C.mp4}
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% % online
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% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_June2018/Displacement_Inclined_Wave_3_times_1C.mp4}
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% % 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}}
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% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animation/NPP_Plastic_Dissipation.mp4}
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\subsection{Probabilistic Inelastic Modeling}
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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{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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% \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}
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% \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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% \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}
%
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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}
{PEP_Animation.mp4}
\end{center}
%
% \includegraphics[width = 12cm]{./img/figure_PEP_25.pdf}
\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}
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\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}
{SEPFEM_Animation_Elastic.mp4}
\end{center}
% \includegraphics[width = 12cm]{./img/figure_elastic_900.pdf}
\end{frame}
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\section{Summary}
%\subsection*{Summary}
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\subsection{\ }
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\begin{frame}
\frametitle{Summary}
\begin{itemize}
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% \item Numerical modeling to predict and inform, rather than fit
\item Numerical modeling to predict, rather than fit
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% \item Inelastic/nonlinear analysis done in phases
\vspace*{4mm}
\item Education and Training is the key!
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\item RealESSI Simulator System: \\
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\url{http://realessi.info/} \\
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% \url{http://realessi.info/}
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% \item Challenges in project funding management
% \vspace*{2mm}
% \item Collaboration and financial support from the USDOE, USNRC,
% USNSF, Caltrans, CNSCCCSN, UNIAEA, Shimizu, Basler\&Hofmann, ILEE,
% etc.
\end{itemize}
\end{frame}
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\end{document}
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