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% %% Jose Antonio Abell Mena provided this for DSL descriptions
% % (used in a file _Chapter_SoftwareHardware_Domain_Specific_Language_English.tex
% % This is added for listing FEI DSL
% % since he customized it, it needs to be changed (linked to
% % /usr/share/texmf/tex/latex/misc)
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% for inclusion of other PDF pages, in this case Frank's presentation
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%from http://mailman.mit.edu/pipermail/macpartners/2005January/000780.html
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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{hyperref}
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pdfmenubar=true,
pdftoolbar=true,
pdfpagemode={None}
colorlinks=true,
linkcolor=webblue,
citecolor=webblue,
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% \usepackage[pdfauthor={Boris Jeremic},
% colorlinks=true,
% linkcolor=webblue,
% citecolor=webblue,
% urlcolor=webblue,
% linktocpage,
% pdftex]{hyperref}
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\usepackage{times}
\usepackage[T1]{fontenc}
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% 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[Real ESSI Simulator]
{The Real ESSI Simulator System \\
Status Report}
%\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.
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\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 LBNL, 14Mar2019}
\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[]
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{
\begin{scriptsize}
\begin{frame}
\frametitle{Outline}
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% 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}
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\subsection{Motivation}
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\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 soilstructure systems
\vspace*{1mm}
\item Reduction of modeling uncertainty
\vspace*{1mm}
\item Desired level
of sophistication (high $\leftrightarrow$ low) analysis
\vspace*{1mm}
\item Follow and direct the flow of seismic energy,
\vspace*{1mm}
\item Practical system for modeling and simulation of
Earthquakes, Soils, Structures and their Interaction,
% RealESSI:
\\
% \vspace*{3mm}
% \hspace*{1mm}
% \hspace*{15mm}
\vspace*{2mm}
{\href{http://realessi.info/}{http://realessi.info/}}
% \\
% \small{\href{http://sokocalo.engr.ucdavis.edu/\~{}jeremic/Real\_ESSI\_Simulator/}{http://sokocalo.engr.ucdavis.edu/\~{}jeremic/Real\_ESSI\_Simulator/}}
\end{itemize}
\end{frame}
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% \begin{frame}
% \frametitle{Motivation: Modeling Uncertainty}
%
% \begin{itemize}
%
%
%
% \item Simplified modeling: Features (important ?) are neglected,
% simplified out (6C ground motions, inelasticity)
%
% \vspace*{3mm}
% \item Modeling Uncertainty: unrealistic (unnecessary?) modeling
% simplifications
%
% %\vspace*{3mm}
% % \item Modeling simplifications are justifiable if one or two level higher
% % sophistication model shows that features being simplified out are not
% % important
%
%
% %\vspace*{3mm}
% % \item Chief Engineer in my old company: "I would really love to know what
% % would a realistic response this object be"
%
%
% \end{itemize}
% \end{frame}
%
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\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*{1mm}
\item {{ Verification} provides evidence that the model is solved
correctly.} Mathematics issue.
\vspace*{1mm}
\item {{ Validation} provides evidence that the correct model is
solved.} Physics issue.
\vspace*{1mm}
\item Modeling and parametric uncertainties are always present, need to be
addressed
% \vspace*{1mm}
% \item Predictive capabilities with {low Kolmogorov Complexity}
%
\vspace*{1mm}
\item Goal: Predict and Inform rather than (force) Fit
\end{itemize}
\end{frame}
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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, 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}
%%\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://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*{4mm}
\item Certification process in progress for NQA1 and ISO900032014
%\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}
\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}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{RealESSI Model Development}
\begin{itemize}
\item PreProcessing, model development gmsh/gmESSI
\vspace*{2mm}
\item Existing model translation, SASSI$\rightarrow$RealESSI
\vspace*{2mm}
\item Choose level of sophistication
\vspace*{2mm}
\item Reduce modeling uncertainty
\vspace*{2mm}
\item Model developed in phases
\vspace*{2mm}
\item Verify model components
\vspace*{2mm}
\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}
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% \begin{figure}[!htbp]
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% \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}
% \includegraphics[width=1.6cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode3_side.pdf}
% \includegraphics[width=1.6cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode4_side.pdf}
% \\
% \includegraphics[width=1.6cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode5_side.pdf}
% \includegraphics[width=1.6cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode6_side.pdf}
% \includegraphics[width=1.6cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode7_side.pdf}
% \includegraphics[width=1.6cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode8_side.pdf}
% % \includegraphics[width=1cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode9_side.pdf}
% % \includegraphics[width=1cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode10_side.pdf}
% % \includegraphics[width=1cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode11_side.pdf}
% % \includegraphics[width=1cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode12_side.pdf}
% \end{flushright}
% \end{figure}
%
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% \end{frame}
%
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\begin{frame}
\frametitle{RealESSI Training and Education}
\begin{itemize}
\item Short Courses:
\begin{itemize}
\vspace*{1mm}
\item Online short course, soon
\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
\vspace{2mm}
\item Up to date information on RealESSI 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 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
%
%
%
% %\vspace*{1mm}
% % \item[] Directing, in space and time, seismic energy flow in the
% % soil structure system
%
\end{itemize}
\end{frame}
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\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), Restart
\vspace*{2mm}
\item Simulation: Explicit noequilibrium, Implicit equilibrium
\vspace*{2mm}
\item Core Functionality Application programs: APPs
%
\end{itemize}
\end{frame}
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%
% \frametitle{NPP, Inelastic Response, Energy Dissipation}
%
% % 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/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}
%
%
% \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}
% {\tiny (MP4)}
% \end{flushleft}
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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}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \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}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Existing Simulation Methods for Stochastic PDEs}
\begin{itemize}
\item Analytical, stochastic differential equation approach: difficult to solve with complex random coefficients
\vspace*{2mm}
\item Monte Carlo method : Computationally expensive
\vspace*{2mm}
\item Perturbation approach: Small variation with respect to mean, closure problem
\vspace*{2mm}
\item Stochastic collocation method: Global error minimization
\vspace*{2mm}
\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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\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]{Fangbo_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}{FEM and Stochastic ElasticPlastic FEM, SEPFEM}
%\vspace{4mm}
\vspace{2mm}
\small
{
%FEM:
\begin{eqnarray*}
\sum_{e} [ \int_{D_e} N_m(x)\rho(x)N_n(x)d\Omega \; {\color{blue}{\ddot{u}_n(t)}} +
\\
\int_{D_e}\nabla N_m(x) {\color{blue}{E(x)}} \nabla N_n(x)d\Omega \; {\color{blue}{u_n(t)}}  {\color{blue}{f_m(t)}} ]=0
\end{eqnarray*}
%SEPFEM:
\begin{eqnarray*}
&&\lefteqn{\sum_{n=1}^N \sum_{k=1}^{P_3} \langle \Psi_k \Psi_l \rangle \int_{D_e}N_m(x)\rho(x)N_n(x)d\Omega \; \; \ddot{d}_{nk}(t) \; \; +}
\\
&&\sum_{n=1}^N \sum_{k=1}^{P_3} \sum_{i=1}^{P_1} \langle \Psi_i \Psi_k \Psi_l \rangle
\int_{D_e}B_m(x) {\color{blue}{a_i(x,t)}} B_n(x)d\Omega \; \; d_{nk}(t)
=
\\
&&\sum_{j=1}^{P_2} \langle \Psi_j \Psi_l \rangle f_{mj}(t) \\
\end{eqnarray*}
}
\vspace{0.3cm}
%\scriptsize{Note: update \textcolor{blue}{$a_i(x,t)$} for elasticplastic material}
\vspace{0.4cm}
%\begin{beamercolorbox}{section in head/foot}
%\usebeamerfont{framesubtitle}\tiny{Wang, F. and Sett, K., "TimeDomain Stochastic Finite Element Simulation of Uncertain Seismic Wave Propagation through Uncertain Heterogeneous Solids", \textit{Soil Dynamics and Earthquake Engineering}, 88:369385, 2016.}
%\end{beamercolorbox}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{SEPFEM}
Matrix form:
\begin{equation*}
\bm{M} \ddot{\bm{d}} + \bm{K} \bm{d} = \bm{f}
\end{equation*}
For damped systems:
\begin{equation*}
\label{eqno_19}
\bm{M} \ddot{\bm{d}} + \bm{C} \dot{\bm{d}} + \bm{K} \bm{d} = \bm{f}
\end{equation*}
\hspace{5cm} {\huge $\Downarrow$ } \\
\hspace{2.2cm} Newmark's method to solve in time domain \\
\vspace{1cm}
\scriptsize{
\noindent where $\bm{M}$, $\bm{C}$ and $\bm{K}$ are generalized mass, damping and stiffness matrices,\\
\hspace{0.9cm} $\bm{f}$, $\bm{d}$, and $\ddot {\bm{d}}$ are generalized force, displacement, and acceleration vectors.
}
\end{frame}
%\begin{frame}{Physical significance of stochastic DOFs} \label{matrix_form}
%
%{\scriptsize Finite element system of equation  \only<1> {deterministic} \only<2> {stochastic}}
%\vspace{0.5cm}
%
%\begin{equation}
%\nonumber
%\tiny
%\left[ \begin{array}{ccccc}
%\uncover<2> {\displaystyle \sum_{i=1}^{P_1} C_{i11}} \only<1> {K_1} \only<2> {K_i} & \uncover<2> {\displaystyle \sum_{i=1}^{P_1} C_{i12} K_i} & \uncover<2> \dots & \uncover<2> \dots & \uncover<2> {\displaystyle \sum_{i=1}^{P_1} C_{i 1 P_{\scaleto{3}{3pt}}} K_i} \\
%\uncover<2> {\displaystyle \sum_{i=1}^{P_1} C_{i21} K_i} & \uncover<2> {\displaystyle \sum_{i=1}^{P_1} C_{i22} K_i} & \uncover<2> \dots & \uncover<2> \dots & \uncover<2> \vdots \\
%\uncover<2> \vdots & \uncover<2> \vdots & \uncover<2> \ddots & & \uncover<2> \vdots \\
%\uncover<2> \vdots & \uncover<2> \vdots & & \uncover<2> \ddots & \uncover<2> \vdots \\
%\uncover<2> {\displaystyle \sum_{i=1}^{P_1} C_{i P_{\scaleto{3}{3pt}} 1} K_i} & \uncover<2> {\dots} & \uncover<2>{\dots} & \uncover<2> {\dots} & \uncover<2> {\displaystyle \sum_{i=1}^{P_1} C_{i P_{\scaleto{3}{3pt}} P_{\scaleto{3}{3pt}}} K_i}
%\end{array} \right]
%%
%\left[ \begin{array}{c}
%\vec{d}_1 \\
%\\
%\uncover<2> {\vec{d}_2} \\
%\\
%\uncover<2> \vdots \\
%\\
%\uncover<2> \vdots \\
%\\
%\uncover<2> {\vec{d}_{P_{\scaleto{3}{3pt}}}}
%\end{array} \right]
%%
%=
%%
%\left[ \begin{array}{c}
%\uncover<2> {\displaystyle \sum_{j=1}^{P_{\scaleto{2}{3pt}}} C_{j1}} \only<1> {\vec{f}_1} \only<2> {\vec{f}_j}\\
%\uncover<2> {\displaystyle \sum_{j=1}^{P_{\scaleto{2}{3pt}}} C_{j2} \vec{f}_j} \\
%\uncover<2> \vdots \\
%\uncover<2> \vdots \\
%\uncover<2> {\displaystyle \sum_{j=1}^{P_{\scaleto{2}{3pt}}} C_{j P_{\scaleto{3}{3pt}}} \vec{f}_j}
%\end{array} \right]
%\end{equation}
%
%\tiny
%{
%
%\only<1>
%{
%Note: $K_1$ is the deterministic stiffness matrix; \\
%\vspace{0.1cm}
%\hspace{0.55cm} $\vec{d}_1$ is the displacement vector for all the nodes; \\
%\vspace{0.1cm}
%\hspace{0.55cm} $\vec{f}_1$ is the forcing vector for all the nodes; \\
%\vspace{0.1cm}
%\hspace{0.55cm} Size of the stiffness matrix is $N \times N$, $N$ is the number of deterministic DOFs. \\
%\vspace{0.1cm}
%\hspace{0.55cm} \color{white}{deterministic DOFs;} \\
%}
%\only<2>
%{
%Note: $C_{ijk}= \langle \Psi_i \Psi_j \Psi_k \rangle$, $C_{ij}= \langle \Psi_i \Psi_j \rangle$; \\
%\vspace{0.1cm}
%\hspace{0.55cm} $K_i$ is the block stiffness matrix with $i$th PC coefficients of modulus, {\tiny for example, $K_1$ is the deterministic matrix}; \\
%\vspace{0.1cm}
%\hspace{0.55cm} $\vec{d}_i$ is the block vector for $i$th PC coefficients of displacement for all the nodes; \\
%\vspace{0.1cm}
%\hspace{0.55cm} $\vec{f}_i$ is the block vector for $i$th PC coefficients of forcing for all the nodes; \\
%\vspace{0.1cm}
%\hspace{0.55cm} Size of the global matrix is $(N \times P_3) \times (N \times P_3)$, $N$ is the number of deterministic DOFs; \\
%
%}
%}
%
%\begin{flushright}
%\tiny
%\hyperlink{3D_matrix}{\beamergotobutton{}}
%\end{flushright}
%
%
%\end{frame}
%\begin{frame}{Size of the stochastic stiffness matrix}
%\begin{itemize}
%
%\item Governed by:
%\begin{itemize}
%\item PC dimension $\rightarrow$ function of correlation length
%\item PC order $\rightarrow$ function of COV
%\end{itemize}
%
%\begin{small}
%
%\begin{table}
%\begin{center}
%\begin{tabular}{clr}
%\hline
%PC dimension & Order of PC & Size of Stiffness Matrix \\
% \hline \hline
%2 & 1 & Real DOFs x 3 \\
% & 2 & x 6 \\
% & 4 & x 15 \\
% \hline
%4 & 1 & Real DOFs x 5 \\
% & 2 & x 15 \\
% & 4 & x 70 \\
% \hline
%6 & 1 & Real DOFs x 7 \\
% & 2 & x 28 \\
% & 4 & x 210 \\
% \hline
%\end{tabular}
%\end{center}
%\end{table}
%
%\end{small}
%
%\end{itemize}
%\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection[Constitutive update]{Intrusive constitutive update}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\frame{\tableofcontents[currentsubsection,sectionstyle=show/shaded]}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Stochastic ElasticPlastic Response}
\begin{flushleft}
Governing equation: $d\sigma_{ij} = E_{ijkl} d\epsilon_{kl}$
\end{flushleft}
%\vspace*{1.0truecm}
\begin{eqnarray}
\nonumber
E_{ijkl} = \left\{\begin{array}{ll}
%
E^{el}_{ijkl}
%
%
\;\;\; & \mbox{\large{~for elastic}} \\
%
\\
%
E^{el}_{ijkl}

\displaystyle \frac{E^{el}_{ijmn} m_{mn} n_{pq} E^{el}_{pqkl}}
{ n_{rs} E^{el}_{rstu} m_{tu}

\xi_* h_* }
\;\;\; & \mbox{\large{~for elasticplastic}}
%
\end{array} \right.
\end{eqnarray}
%\footnotesize{If the material properties ($D^{el}$, $f$, $U$, $q_*$, and $r_*$) are uncertain, then the above equation becomes a nonlinear SDE with random coefficients!}
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}{ZeroElastic Region Material}
% \footnotesize
% Assume material with zeroelastic region, the general form reduces to elasticplastic steps only:
%
% \begin{eqnarray}
% \nonumber
% D_{ijkl} = D^{el}_{ijkl} 
% \displaystyle \frac{ D^{el}_{ijmn}
% \displaystyle \frac{\partial U}{\partial \sigma_{mn}}
% \displaystyle \frac{\partial f}{\partial \sigma_{pq}}
% D^{el}_{pqkl} }
% {\displaystyle \frac{\partial f}{\partial \sigma_{rs}}
% D^{el}_{rstu}
% \displaystyle \frac{\partial U}{\partial \sigma_{tu}}
% 
% \displaystyle \frac{\partial f}{\partial q_*}r_*}
% % \;\;\; & \mbox{\large{~for elasticplastic}}
% \end{eqnarray}
%
% For 1D vonMises material with ArmstrongFrederick hardening, the above equation simplifies to:
%
% \begin{equation}
% \nonumber
% E=H_a \pm C_r \sigma
% \end{equation}
% where $h_a$ and $C_r$ are the two material parameters. Use + sign for positive incremental strain; use  sign for negative incremental strain.
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \begin{frame}{zeroelastic vonMises material with ArmstrongFrederick hardening}
% \footnotesize
% The incremental stress can be updated as:
% \begin{equation}
% \nonumber
% \Delta \sigma=H_a \Delta \epsilon \pm C_r \sigma \Delta \epsilon
% \end{equation}
% \begin{figure}
% \includegraphics[scale=0.3]{Fangbo_figs/constitutive_pureAF_deterministic_ha6e7_Cr600}
% \caption{\scriptsize hysteretic behavior of material using $H_a=6e7, C_r=600$}
% \end{figure}
%
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \begin{frame}{Stochastic Galerkin projection at local level}
%
% Represent uncertain material parameters $H_a, C_r$ with PC:
% \begin{equation*}
% H_a(x)= \displaystyle \sum_{i=1}^{P_3} H_{a_i}(x) \Psi_i(\left\{\xi_r(\theta)\right\})
% \end{equation*}
% \begin{equation*}
% C_r(x)= \displaystyle \sum_{i=1}^{P_3} C_{r_i}(x) \Psi_i(\left\{\xi_r(\theta)\right\})
% \end{equation*}
%
% Apply stochastic Galerkin projection to get PC coefficients of $E$ and $\Delta \sigma$:
% \begin{align*}
% \Delta \sigma_i(x,t) & =\frac{ H_{a_j} \Delta \epsilon_l \langle \Psi_i \Psi_j \Psi_l \rangle
% \pm
% C_{r_j} \sigma_k \Delta \epsilon_l \langle \Psi_i \Psi_j \Psi_k \Psi_l \rangle }{\langle \Psi_i^2 \rangle} \\
% E_i(x,t) & =H_{a_i} \pm C_{r_j} \sigma_k \langle \Psi_i \Psi_j \Psi_k \rangle \mathbin{/} \langle \Psi_i^2 \rangle \\
% \end{align*}
%
%
%
% \end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\begin{frame}{Application of FP equation to material models}
%
%\begin{itemize}
%\item FP eq. is applicable to any material models
%\item Different material models $\rightarrow$ different $N_{ab}^{(1)}$ and $N_{abcd}^{(2)}$
%\end{itemize}
%
%\begin{equation}
%\nonumber
%\frac{\partial P(\sigma_{ij},t)}{\partial t} = \frac{\partial}{\partial \sigma_{ab}}\left[N_{ab}^{(1)}P(\sigma_{ij},t)\frac{\partial}{\partial \sigma_{cd}}
%\left\{N_{abcd}^{(2)} P(\sigma_{ij},t)\right\} \right]
%\end{equation}
%
%Salient Features:
%
%\begin{itemize}
%
%\item Nonlinear SDE in real space to Linear PDE in probability density space $\rightarrow$ simplifies the numerical solution process
%\vspace*{0.1truecm}
%\item Complete probabilistic description of response $\rightarrow$ joint PDF
%\vspace*{0.1truecm}
%\end{itemize}
%
%
%\end{frame}
%\begin{frame}{Linearize the FP eq. to update tangent stiffness PC coefficients as the material plastifies}
%
%\begin{itemize}
%\item Linearized form of the FP eq.:
%\begin{equation}
%\nonumber
%\frac{\partial P^{lin}(\sigma_{ij},t)}{\partial t} =  N_{(1)_{ab}}^{lin} \frac{\partial P(\sigma_{ij},t)}{\partial \sigma_{ab}} + N_{(2)_{mnab}}^{lin} \frac{\partial^2 P(\sigma_{ij},t)}{\partial \sigma_{mn} \sigma_{ab}}
%\end{equation}
%where $N_{(1)_{ab}}^{lin}$ and $N_{(2)_{mnab}}^{lin}$ are functions of statistics of material parameters expressed in terms of PC coefficients
%
%\item Update the PC coefficients as material plastifies by solving an overdetermined residual system of eqs.:
%\begin{equation}
%\nonumber
%\frac{\partial P^{lin}(\sigma_{ij}, t)}{\partial t}  \frac{\partial P(\sigma_{ij}, t)}{\partial t} =0
%\end{equation}
%
%\end{itemize}
%
%\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]
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% {/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}
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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$1D (it is done all the time!)
%
% \item Excellent fit
% % (goal is to predict and inform and not (force) fit)
%
%
% \end{itemize}
%
%
%
%
% % local
% %\vspace*{2mm}
% \begin{center}
% \hspace*{16mm}
% %\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
% \movie[label=show3,width=61mm,poster, showcontrols]
% {\includegraphics[width=60mm]{/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_ff_3d_mp4_icon.jpeg}}
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% %\hfill
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% \movie[label=show3,width=61mm,poster, showcontrols]
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% {/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_ff_1d_mp4_icon.jpeg}}
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% \end{center}
% % local
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% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_3d.mp4}
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% %
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% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% % \frametitle{1D vs 3$\times$1D vs 3D Seismic Motions}
% %
% %
% % \begin{itemize}
% %
% % \vspace{2mm}
% % \item 1D is required by the code
% %
% % \vspace{4mm}
% % \item 3$\times$1D can be used depending on frequency/wave length of interest,
% %
% % \vspace{4mm}
% % \item 3D is more realistic, however it is challenging to define motions in full 3D
% %
% % \end{itemize}
% % \end{frame}
% %
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% % \frametitle{When to use 3D and/or 3$\times$1D}
% %
% %
% % \begin{figure}[!hbpt]
% % \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}
% % \end{center}
% % \end{figure}
% %
% % \end{frame}
% %
% %
% %
% %
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% % \frametitle{1D vs 3D, Bottom Control Point}
% %
% %
% %
% %
% %
% %
% % \begin{center}
% % \includegraphics[width=5truecm]{/home/jeremic/tex/works/Thesis/HexiangWang/3Dvs1D_29Nov2017/images/XY_plane_acc_637.jpg}
% % \includegraphics[width=5truecm]{/home/jeremic/tex/works/Thesis/HexiangWang/3Dvs1D_29Nov2017/images/YZ_plane_acc_534.jpg}
% % \end{center}
% %
% % \end{frame}
% %
% %
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% % \frametitle{Free Field 3D vs 1D Convolution From Base Point}
% %
% %
% %
% %
% % \begin{center}
% % \includegraphics[width=3.4truecm]{/home/jeremic/tex/works/Thesis/HexiangWang/3Dvs1D_29Nov2017/images/motion_compare_surface_ax.pdf}
% % \includegraphics[width=3.4truecm]{/home/jeremic/tex/works/Thesis/HexiangWang/3Dvs1D_29Nov2017/images/motion_compare_surface_ay.pdf}
% % \includegraphics[width=3.4truecm]{/home/jeremic/tex/works/Thesis/HexiangWang/3Dvs1D_29Nov2017/images/motion_compare_surface_az.pdf}
% % \end{center}
% %
% % \end{frame}
% %
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% % \frametitle{3D vs 3$\times$1D vs 1D, Top of SMR}
% %
% %
% %
% %
% % \begin{center}
% % \includegraphics[width=3.4truecm]{/home/jeremic/tex/works/Thesis/HexiangWang/3Dvs1D_29Nov2017/images/point1Ax.pdf}
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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*{10mm}
%\vspace*{4mm}
\begin{figure}[!htb]
\begin{flushleft}
\hspace*{5mm}
\includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2018/BestPSHANI/Presentation/stress_test_Best_SHANI_May2018.jpg}
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\includegraphics[width=6cm]{/home/jeremic/tex/works/consulting/2017/IAEA/TECDOC/Version_14Mar2017/1Dvs3x1Dvs3D_waves.pdf}
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\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]
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{\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}
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\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]
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{\includegraphics[width=10cm]
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{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/SMR_frequency.mp4}
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\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}
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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
%% Both solid and contact elements dissipate energy
% \vspace*{5mm}
\begin{center}
% \hspace*{15mm}
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{\includegraphics[width=10cm]
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{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMRESSI_real_time_four_freq.mp4}
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\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}
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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
%% Both solid and contact elements dissipate energy
% \vspace*{5mm}
\begin{center}
% \hspace*{15mm}
%\movie[label=show3,width=10cm,poster,autostart,showcontrols]
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{\includegraphics[width=10cm]
{/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}
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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{Free Field vs ESSI  Different Frequencies}
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%
% \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
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% \tiny Z direction
% \end{textblock*}
% \begin{textblock*}{3cm}(2.4cm,7.6cm) % {block width} (coords)
% \tiny (a) $f=1Hz \ \ \theta=60^{o}$
% \end{textblock*}
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% \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*}
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% \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}
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% \\
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\subsection{Plastic Energy Dissipation}
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\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}
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\end{frame}
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\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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% \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_plasticity.pdf}
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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}
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% % \begin{tikzpicture}[remember picture,overlay]
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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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%
%
%
%
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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 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}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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=60mm]{/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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Wall, Regular and ASR Concrete}
%\vspace{5mm}
\begin{figure}[!h]
\begin{center}
\hspace*{15mm}
\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=2.8truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Reg_A_Force_Displacement.pdf}
\includegraphics[width=2.8truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/ASR_A1_Force_Displacement.pdf}
\hspace*{15mm}
\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}
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% \begin{frame}
%
% \frametitle{Reinforced Concrete Wall, Evolution of Plastic Dissipation}
%
%
%
% \vspace*{2mm}
% \begin{center}
% \hspace*{7mm}
% \movie[label=show3,width=90mm,poster,showcontrols]
% {\includegraphics[width=90mm]{/home/jeremic/tex/works/Conferences/2018/ENSI_meeting_Brugg_18May2018/Present/Shear_wall_frame.jpg}}{/home/jeremic/tex/works/Thesis/HanYang/Shear_Wall_Presentation_26Apr2018/Presentation/Figures/Shear_Wall_Plastic_Dissipation.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/ESSI_VisIt_movies_Jose_01AApr2015/movie_input_closeup.mp4}
% % % \href{./homo_50mmesh_45degree_Ormsby.mp4}
% % {\tiny (MP4)}
% % \end{flushleft}
% % %
%
%
% %
% %
% % \vspace*{3mm}
% % \begin{center}
% % % \hspace*{15mm}
% % \includemedia[width=\linewidth,height=0.6\linewidth,activate=pageopen,addresource=/home/jeremic/tex/works/Thesis/HanYang/Shear_Wall_Presentation_26Apr2018/Presentation/Figures/Shear_Wall_Plastic_Dissipation.mp4,
% % flashvars={source=/home/jeremic/tex/works/Thesis/HanYang/Shear_Wall_Presentation_26Apr2018/Presentation/Figures/Shear_Wall_Plastic_Dissipation.mp4&autoPlay=true&loop=true}]{VPlayer.swf}
% % \end{center}
% %
%
%
% \end{frame}
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\begin{frame}
\frametitle{Buoyant Force Simulation}
\begin{figure}[!H]
\hspace*{20mm}
\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}
\hspace*{20mm}
\end{figure}
%  %
%  % \begin{tikzpicture}[remember picture,overlay]
%  % \node[anchor=south west,inner sep=0pt] at ($(current page.south west)+(7.5cm,2.5cm)$) {
%  % \includegraphics[width=0.4\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/bouyant_displacement.pdf}};
%  % \end{tikzpicture}
% 
%  % \vspace{1.4cm}
% \begin{itemize}
% \item \scriptsize Upward structural displacement under buoyant force
% \end{itemize}
\end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Solid, StructureFluid Interaction: gmFoam}
\begin{columns}[T]
\begin{column}{.65\textwidth}
\begin{itemize}
% \vspace{0.4cm}
\item[] Mesh separation
\begin{itemize}
\item[] integrated geometry model %(solid \& fluid) based on gmsh
\item[] FEM \& FVM mesh conversion
\item[] handle discontinuous mesh
\end{itemize}
\item[] Incorporate gmESSI
% \begin{itemize}
% \item[] conveniently set BCs
% \item[] input files easy generation
% \end{itemize}
\item[] Interface geometry extraction
\item[] Interface class \textbf{SSFI} in RealESSI
% \begin{itemize}
% \item[] interface geometrical mapping
% \item[] handle different mesh size
% \item[] BCs interpolation \& updating
% \item[] boundary mass conservation iteration
% \end{itemize}
\item[] RealESSI $\leftrightarrow$ SSFI $\leftrightarrow$ OpenFoam
% \item[] Shepherd method
% \begin{itemize}
% \item[] RealESSI $\Longleftrightarrow$ SSFI $\Longleftrightarrow$ OpenFoam
% \item[] explicit transient algorithm
% \item[] handle different time step length
% \end{itemize}
\end{itemize}
\vspace{0.2cm}
% \scriptsize gmFoam: https://github.com/hexiang6666/gmFoam
\end{column}
\begin{column}{.35\textwidth}
\vspace{1cm}
\begin{figure}[!H]
\begin{center}
\includegraphics[width=\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_08June2017/pic/gmFoam.pdf}
\end{center}
\end{figure}
\end{column}
\end{columns}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \begin{frame}
% \frametitle{SemiCoupled Solid Fluid Interaction}
% \begin{itemize}
% \item[] Utilize VOF implemented in interFoam
% \setbeamertemplate{itemize items}[circle]
% \begin{itemize}
% \item[] avoid tracking free surface
% \item[] relatively fixed BCs
% \item[] relatively fixed background mesh
% \end{itemize}
% \end{itemize}
% \vspace{0.3cm}
% \begin{itemize}
% \item[] Interface class \textbf{SSFI} added in RealESSI
% \setbeamertemplate{itemize items}[circle]
% \begin{itemize}
% \item[] interface geometrical mapping
% \item[] handle different mesh size
% \item[] BCs interpolation \& updating
% \item[] boundary mass conservation iteration
% \end{itemize}
% \end{itemize}
% \vspace{0.3cm}
% \begin{itemize}
% \item[] Shepherd method
% \setbeamertemplate{itemize items}[circle]
% \begin{itemize}
% \item[] RealESSI $\Longleftrightarrow$ SSFI $\Longleftrightarrow$ InterFoam
% \item[] explicit transient algorithm
% \item[] handle different time step length
% \end{itemize}
% \end{itemize}
%
% \end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
% \begin{frame}
% \frametitle{SemiCoupled Solid Fluid Interaction}
% Implemented in RealESSI based on explicit transient algorithm
% \begin{figure}[!H]
% \begin{center}
% \includegraphics[width=.5\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_08June2017/pic/No_SSFI.pdf}\enspace
% \includegraphics[width=0.5\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_08June2017/pic/SSFI.pdf}\enspace
% \end{center}
% \end{figure}
% \quad \href{http://cml08.engr.ucdavis.edu/for_professor/fluid_model_simulation.mp4}{Water Break without SFI}\quad \quad \quad \quad \quad \href{http://cml08.engr.ucdavis.edu/for_professor/Solid_Fluid_Interaction.mp4}{Box Sloshing with SFI}
% \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{Real ESSI Examples}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Energy Input and Dissipation}
%
% \begin{itemize}
%
% \vspace*{1mm}
% \item[] Energy input, static and dynamic forcing
%
%
% \vspace*{6mm}
% \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 Inelastic soil, contacts, structure, foundation, dissipators
% \item Viscous coupling with internal 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}
% \vspace*{1mm}
% \item[] Algorithmic/Numerical energy dissipation/production
%
%
% \end{itemize}
%
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% \end{frame}
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% % \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}
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% \begin{frame}
%
% \frametitle{Energy Dissipation on Material Level}
%
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% \vspace*{2mm}
% %
% % Single elasticplastic element under cyclic shear loading
% %
%
%
% %\begin{itemize}
% %\item[] Difference between plastic work and plastic dissipation
%
% %\item[] Plastic work can decrease, plastic dissipation always increases
% Plastic work can decrease, plastic 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}
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% % \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}
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% % \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}
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% % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% \begin{frame}
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% \frametitle{Energy Dissipation Control Mechanisms}
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% \begin{figure}[!H]
% %\hspace*{10mm}
% \includegraphics[width=3.0cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_plasticity.pdf}
% \includegraphics[width=3.0cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_Rayleigh.pdf}
% \includegraphics[width=3.0cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_Newmark.pdf}
% \end{figure}
%
% \vspace*{4mm}
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% % \hspace*{10mm} Numerical \hspace*{20mm} Viscous \hspace*{20mm} Plasticity
% \hspace*{10mm} \small{Plasticity} \hspace*{20mm} \small{Viscous} \hspace*{20mm} \small{Numerical}
%
%
% \vspace*{2mm}
% \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=5.5cm]{/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}
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% % \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}
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% % \frametitle{Inelastic Modeling for NPP Soil Structure System}
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% % \begin{itemize}
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% % %\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)
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% \frametitle{Nuclear Power Plant Model }
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% \includegraphics[width=8.5cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/NPP_With_Shallow_Foundation.pdf}
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% % \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
% \end{figure}
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% % \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}};
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% % \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}
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% %
% % \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}
% %
% %
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% % \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}
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% \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}
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% % \vspace*{5mm}
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% \movie[label=show3,width=10cm,poster,autostart,showcontrols]
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% % %% Both solid and contact elements dissipate energy
% %
% %
% % % \vspace*{5mm}
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% % % \hspace*{15mm}
% % \movie[label=show3,width=10cm,poster,autostart,showcontrols]
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% % {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mp4}
% % \end{center}
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% % \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}
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% % \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}
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% % % \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}
% % %
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% % % \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}
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% % %OVDE dodaj link na online...
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% % {/home/jeremic/tex/works/Thesis/HexiangWang/Files_06June2017/pic/Solid_Fluid_Interaction.mp4}
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\subsection{Uncertain Inelasticity}
%\section[1D stochastic structural dynamic analysis]{1D stochastic structural dynamic analysis}
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\begin{frame}{Uncertain Stiffness}
\begin{columns}
\column{0.5\textwidth}
\vspace{0.5cm}
\begin{figure}
\includegraphics[scale=0.4]{Fangbo_figs/four_story_building.pdf}
\end{figure}
%\hspace{1.5cm} \footnotesize{Schematic model}
\column{0.5\textwidth}
{\footnotesize
{Lognormal random field for stiffness $\bar{k}$:} \\
Marginal mean: 9.84 MN/m \\
Marginal COV: 10\% \\
Correlation structure: \\
\vspace{0.2cm}
\hspace{0.5cm}
$ \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} $
PC rep: dimension 4 order 2
}
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\scriptsize
{
Uncertain bedrock seismic motion:
\begin{itemize}
\item Stochastic ground motion modeling
\item Marginal PDF: Gaussian $\rightarrow$ order 1
\item PC dimension 150 order 1 to quantify motion random process
\end{itemize}
}
\vspace{0cm}
\flushleft \scriptsize{PC synthesized statistics $\Longleftarrow$ of bedrock motion}
\column{0.65\textwidth}
\vspace{0.4truecm}
\begin{figure}
\includegraphics[scale=0.23]{Fangbo_figs/KL_mean_dis_from_dis_equal_scale.pdf}
\includegraphics[scale=0.23]{Fangbo_figs/KL_var_dis_from_dis.pdf} \\
\tiny{(a) Displacement} \\
\includegraphics[scale=0.23]{Fangbo_figs/KL_mean_acc_from_acc_equal_scale.pdf}
\includegraphics[scale=0.23]{Fangbo_figs/KL_var_acc_from_acc.pdf} \\
\tiny{(b) Acceleration} \\
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\begin{frame}{Uncertain Motion: Nonstationary Correlation Structure}
\hspace{2.0cm} \underline{Displacement} \hspace{2.0cm} \underline{Acceleration}
\begin{figure}
\includegraphics[scale=0.25]{Fangbo_figs/KL_exact_dis_correlation_from_dis.pdf} \hspace{1cm}
\includegraphics[scale=0.25]{Fangbo_figs/KL_exact_acc_correlation_from_acc.pdf} \\
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\begin{frame}{Uncertain Response on Top}
\begin{columns}
\column{0.6\textwidth}
\begin{figure}
\includegraphics[height=3cm]{Fangbo_figs/dynamic_disp_linear_vs_nonlinear.pdf} \\
\includegraphics[height=3cm]{Fangbo_figs/dynamic_acc_linear_vs_nonlinear.pdf} \\
%\caption{\footnotesize Synthesized displacement and acceleration at the top of structure}
\end{figure}
\column{0.4\textwidth}
\begin{itemize}
\footnotesize
\item Smaller St.Dev. for nonlinear case
\item Magnitude of mean is negligible compared to standard deviation
\end{itemize}
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\begin{frame}{Evolution of Stress and Stiffness at Top Floor}
\begin{columns}
\column{0.6\textwidth}
\begin{figure}
\includegraphics[height=3cm]{Fangbo_figs/dynamic_stress_linear_vs_nonlinear.pdf} \\
\includegraphics[height=3cm]{Fangbo_figs/dynamic_stiffness_linear_vs_nonlinear.pdf} \\
%\caption{\footnotesize Synthesized displacement and acceleration at the top of structure}
\end{figure}
\column{0.4\textwidth}
\begin{itemize}
\footnotesize
\item Smaller St.Dev. of stress for nonlinear case
\item Larger St.Dev. of stiffness introduced by nonlinearity
\end{itemize}
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\section{Conclusion}
\subsection{\ }
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% \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."
% w
% \end{itemize}
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\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: Wang, Feng, Yang, Behbehani, Sinha, Wang,
Pisan{\'o}, Abell, Yang, Cheng, Jie, Tafazzoli, Preisig, Tasiopoulou, Watanabe
\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://realessi.info/}
\end{itemize}
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