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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)
% %\usepackage{myListings}
% \input{essi_listings_options.tex}
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%
% % for listing DSL
% \input{essi_listings_options.tex}
%
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% for inclusion of other PDF pages, in this case Frank's presentation
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% make sure figure syntax uses graphicx syntax NOT epsfig syntax
%from http://mailman.mit.edu/pipermail/macpartners/2005January/000780.html
%
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% \usetheme{Marburg} % ima naslov i sadrzaj sa desne strane
% \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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% colorlinks=true,
% linkcolor=webblue,
% citecolor=webblue,
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% linktocpage,
% pdftex]{hyperref}
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% or whatever
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% Or whatever. Note that the encoding and the font should match. If T1
% does not look nice, try deleting the line with the fontenc.
% Site Specific Dynamics of Structures:
%From Seismic Source to
%the Safety of Occupants and Content
\title[Plastic Energy Dissipation]
{Plastic Energy Dissipation \\
for Steel Building with BRBs }
%\subtitle
%{Include Only If Paper Has a Subtitle}
%\author[Author, Another] % (optional, use only with lots of authors)
%{F.~Author\inst{1} \and S.~Another\inst{2}}
%  Give the names in the same order as the appear in the paper.
%  Use the \inst{?} command only if the authors have different
% affiliation.
\pgfdeclareimage[height=0.2cm]{universitylogo}{/home/jeremic/BG/amblemi/ucdavis_logo_blue_sm}
\pgfdeclareimage[height=0.7cm]{lbnllogo}{/home/jeremic/BG/amblemi/lbnllogo}
%\author[Jeremi{\'c} et al.] % (optional, use only with lots of authors)
%\author[Jeremi{\'c} et al.] % (optional, use only with lots of authors)
\author[Yang and Jeremi{\'c}] % (optional, use only with lots of authors)
%{Boris~Jeremi{\'c}}
{Boris Jeremi{\'c} \hspace*{5mm} and \hspace*{5mm} Han Yang}
%\\
%{\cyss Boris Jeremi\cj{}}
% }
% \\
%Han Yang, Hexiang Wang, Sumeet Kumar Sinha }
%\institute[Computational Geomechanics Group \hspace*{0.3truecm}
%\institute[\pgfuseimage{universitylogo}\hspace*{0.1truecm}\pgfuseimage{lbnllogo}] % (optional, but mostly needed)
\institute[\pgfuseimage{universitylogo}] % (optional, but mostly needed)
%{ Professor, University of California, Davis\\
%{ University of California, Davis, CA, USA
{\hspace*{10mm} University of California, Davis
%\\
\hspace*{20mm}
% Tianjin University, Tianjin, PRC}
Tianjin University}
% % 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 $5^{th}$ SEECCM
{
~\\
CIVILCOMP 2023
\vspace*{2mm}
%\hspace*{5mm}
\\
%2831 August 2023
% \\ ~ \\
{P{\'e}cs, Hungary}}
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\subject{}
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% 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}
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{
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\titlepage
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\begin{frame}
\frametitle{Outline}
\begin{scriptsize}
\tableofcontents
% You might wish to add the option [pausesections]
\end{scriptsize}
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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}
% \subsection{\ }
%%%%%%%%%%%%%%%%%%%%%%%%%%%%dir
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\begin{frame}
\frametitle{Motivation}
\begin{itemize}
\vspace*{1mm}
\item[] Safety and economy of infrastructure
%\vspace*{0.3cm}
%\vspace*{2mm}
% \item[] Improve analysis of infrastructure objects
% %\vspace*{1mm}
% % \item[] Analysis of Earthquakes and/or Soils and/or Structures and their Interaction
% % \item[] Analysis of Earthquakes, Soils, Structures and their Interaction
% % \item[] Soils, Structures and their Interaction, statics and dynamics
% \item[] Soils, Structures, statics and dynamics
% \vspace*{1mm}
% \item[] Expert numerical modeling and simulation tool
%
% \vspace*{1mm}
% \item[] Use of numerical models to
% analyze statics and dynamics of soil/rockstructure systems
%
%
% %\vspace*{1mm}
% \item[] Analysis to predict and inform
% % rather than (force) fit
%\vspace*{1mm}
% \item[] Design, build and maintain sustainable objects
\vspace*{4mm}
\item[] Design, build and maintain sustainable infrastructure
\vspace*{4mm}
\item[] Responsible Engineer, with Executive Powers
%\vspace*{1mm}
% \item[] Engineer with executive powers
%\vspace*{2mm}
\vspace*{4mm}
\item[] Engineer with versatile, quality assured analysis tool to
\begin{itemize}
\vspace*{1mm}
% \item[] Explore various design concepts
\item[] Explore design concepts
\vspace*{1mm}
\item[] Assess infrastructure performance
\end{itemize}
% \vspace*{2mm}
% \item[] Choice of analysis/modeling level of sophistication
%
% \vspace*{1mm}
% \item[] Modeling simplifications, Epistemic uncertainty
%
% \vspace*{1mm}
% \item[] Variable, random material and loads, Aleatory uncertainty
%
\vspace*{4mm}
\item[] Engineering Analysis to Predict and Inform
%
%
%
% \vspace*{1mm}
% \begin{figure}[!hbpt]
% \begin{center}
% %
% %\hspace*{7mm}
% %\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Conferences/2021/CUBoulderGEGMseminarseries02Apr2021/present/Saint_Sophia_Constantinopolis.jpg}
% %\hspace*{1mm}
% \includegraphics[height=1.2truecm]{/home/jeremic/tex/works/Conferences/2023/5_SEECCM_Vrnjacka_Banja_56Jul2023/present/Parthenon_on_Acropolis_June2023.jpg}
% %\hspace*{2mm}
% \hspace*{2mm}
% \includegraphics[height=1.2truecm]{/home/jeremic/tex/works/Conferences/2021/ASCE4_Kennedy_Lecture/present/AyaSofia_03_1990.jpg}
% %\hspace*{2mm}
% \hspace*{2mm}
% \includegraphics[height=1.2truecm]{/home/jeremic/tex/works/Conferences/2021/ASCE4_Kennedy_Lecture/present/ZhaozhouBridge.jpg}
% \hspace*{2mm}
% %\hspace*{2mm}
% \includegraphics[height=1.2truecm]{/home/jeremic/tex/works/Conferences/2021/ASCE4_Kennedy_Lecture/present/Four_Water_Wheels_Hama_Syria.jpg}
% \hspace*{2mm}
% %\hspace*{2mm}
% \includegraphics[height=1.2truecm]{/home/jeremic/tex/works/Conferences/2023/5_SEECCM_Vrnjacka_Banja_56Jul2023/present/Eiffel_tower_design_drawings/Eiffel_tower_02.jpg}
% %
% %\vspace*{3mm}
% \end{center}
% \end{figure}
% %\vspace*{3mm}
%
% %\vspace*{1mm}
% \begin{figure}[!hbpt]
% \begin{center}
% %
% %\hspace*{7mm}
% %\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Conferences/2021/CUBoulderGEGMseminarseries02Apr2021/present/Saint_Sophia_Constantinopolis.jpg}
% %\includegraphics[height=1.8truecm]{/home/jeremic/tex/works/Conferences/2021/ASCE4_Kennedy_Lecture/present/AyaSofia_03_1990.jpg}
% %\hspace*{2mm}
% \includegraphics[height=3.5truecm]{/home/jeremic/tex/works/Conferences/2023/5_SEECCM_Vrnjacka_Banja_56Jul2023/present/Eiffel_tower_design_drawings/Eiffel_tower_force_diagram_shape.jpg}
% \hspace*{4mm}
% \includegraphics[height=3.5truecm]{/home/jeremic/tex/works/Conferences/2023/5_SEECCM_Vrnjacka_Banja_56Jul2023/present/Eiffel_tower_design_drawings/Eiffel_tower_foundation.jpg}
% %\hspace*{2mm}
% %
% %\vspace*{3mm}
% \vspace*{2mm}
% \end{center}
% \end{figure}
% %\vspace*{3mm}
%
%
%
% \vspace*{1mm}
% \item[] Follow the flow, input and dissipation, of seismic energy,
% \vspace*{2mm}
% \item[]
% %System for
% {\bf Real}istic modeling and simulation of
% {\bf E}arthquakes and/or
% {\bf S}oils and/or
% {\bf S}tructures and their
% {\bf I}nteraction:\\
% RealESSI
% \hspace*{5mm}
% \url{http://realessi.us/}
% % % % \hspace*{25mm}
% % \url{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
% % % \href{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}{{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
% % % % \url{http://msessi.us/}
% % %
%
%
%
%
% \vspace*{1mm}
% \item[] Follow the flow, input and dissipation, of seismic energy,
% \vspace*{2mm}
% \item[]
% %System for
% {\bf Real}istic modeling and simulation of
% {\bf E}arthquakes and/or
% {\bf S}oils and/or
% {\bf S}tructures and their
% {\bf I}nteraction:\\
% RealESSI
% \hspace*{5mm}
% \url{http://realessi.info/}
% % % % \hspace*{25mm}
% % \url{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
% % % \href{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}{{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
% % % % \url{http://msessi.info/}
% % %
%
\end{itemize}
\end{frame}
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%
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\begin{frame}
%\frametitle{ESSI Challenges}
\frametitle{Civil Engineering Analysis Challenges}
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%
\begin{figure}[!htb]
\begin{center}
% %\includegraphics[width=5cm]{Figurefiles/_Chapter_Applications_ESSI_BOOK/Building_modeling_Issues_01_pdf.pdf}
%\vspace*{3mm}
\includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_ESSI_BOOK/Seismic_Motions_modeling_Issues_01_pdf.pdf}
\includegraphics[width=5.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_ESSI_BOOK/Seismic_Motions_modeling_Issues_02_pdf.pdf}
\\
%\vspace*{2mm}
%\vspace*{8mm}
\vspace*{2mm}
\includegraphics[width=2.8cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_ESSI_BOOK/NPP_Modeling_Issues_03.jpg}
\includegraphics[width=2.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_ESSI_BOOK/SMR_Modeling_Issues_02_pdf.pdf}
\includegraphics[width=3.2cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_ESSI_BOOK/Building_modeling_Issues_03_pdf.pdf}
\includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_ESSI_BOOK/Building_modeling_Issues_02_pdf.pdf}
\\
\vspace*{2mm}
\includegraphics[width=2.5cm]{/home/jeremic/tex/Classes/2020/Spring_semester_ETH/ESSI/Term_Projects_from_Students/Tunnel02.pdf}
\includegraphics[width=1.2cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_ESSI_BOOK/Dam_modeling_Issues_01_pdf.pdf}
\includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_ESSI_BOOK/Dam_modeling_Issues_02_pdf.pdf}
\includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_ESSI_BOOK/Bridge_modeling_Issues_01_pdf.pdf}
% %\vspace*{8mm}
% \caption{\label{ESSI_Models_and_Challenges}
% ESSI modeling and simulation challenges:
% Free field motions, 3C/6C vs 3$\times$1C;
% Nuclear Power Plant structure  soil/rock system, Small Modular Reactor structure  soil/rock system;
% Low and High Buildingfoundationsoil system;
% DamFoundationFluid system;
% Bridgesoil system;
% %
% Aspects of modeling:
% 1) Seismic motions,
% 2) Inelastic soil and rock,
% 3) Inelastic interface/contact/joints, foundation with soil/rock and
% interfaces/contacts/joints within structure,
% 4) Inelastic structure, systems and components,
% 5) Solid, Structure  Fluid interaction, external (reservoirs, fluid pools...) and internal
% (fully saturated and partially, (un)saturated soil, rock and concrete).}
\end{center}
\end{figure}
%
%
% \begin{itemize}
%
% \item[] Linear elastic, all elements
%
% %\vspace*{1mm}
% \item[] Nonlinear elastic, solids
%
% %\vspace*{1mm}
% \item[] Soil, solids/3D, dry, saturated and partially saturated)
%
% %\vspace*{1mm}
% \item[] Rock, solids/3D, dry, saturated and partially saturated)
%
% %\vspace*{1mm}
% \item[] Interface/Contact, soft, hard, gap, dry, saturated
%
% %\vspace*{1mm}
% \item[] Base isolator and dissipator 2node/3D
%
%
% %\vspace*{1mm}
% \item[] Concrete, solids/3D, wall/2D, beam/1D, ASR
%
% %\vspace*{1mm}
% \item[] Steel, beam/1D and solid/3D
% %
%
%
% %\vspace*{1mm}
% \item[] Seismic input, DRM
%
% %\vspace*{1mm}
% \item[] Energy Dissipation
%
%
% \end{itemize}
\end{frame}
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%\section{Engineering Analysis Methods and Tools}
\section{Plastic Energy Dissipation}
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% \subsection{RealESSI }
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\begin{frame}
\frametitle{RealESSI Engineering Analysis System}
%\frametitle{RealESSI Simulator Analysis System}
\begin{itemize}
\vspace*{1mm}
\item[]
Statics and dynamics of rock, soil, structures, fluids...
\vspace*{1mm}
\item[]
Linear, Nonlinear, Inelastic
\vspace*{1mm}
\item[]
Deterministic and Probabilistic
\vspace*{1mm}
\item[]
High Performance Computing, HPC
\vspace*{1mm}
\item[]
% Reduction of modeling, epistemic uncertainty
Reduction of Modeling Uncertainty
\vspace*{1mm}
\item[]
% Propagation of parametric, aleatory uncertainty
Propagation of Parametric Uncertainty
\vspace*{1mm}
\item[]
% Quality assurance: verification and validation
QA: Verification and Validation
\vspace*{1mm}
\item[]
Infrastructure safety and economy
% All models available for civil engineers
\vspace*{1mm}
\item[]
\url{http://realessi.us/}
\end{itemize}
\vspace*{56mm}
%\begin{figure}[!hbpt]
\begin{flushright}
\hspace*{5mm}
\includegraphics[width=3.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Theory_Introduction/tex_works_psfigures_loading_stageincrementsiterations.pdf}
\end{flushright}
%\vspace*{0.5cm}
%\end{figure}
%
\end{frame}
%
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\begin{frame}
\frametitle{FEM for ESSI Analysis}
% \frametitle{Finite Element Method}
\begin{itemize}
% \vspace*{2mm}
% \item[] Virtual displacements cannot be zero, they cancel out
%
% \vspace*{2mm}
% \item[] Single Phase FEM
\item[] Single Phase FEM:
\hspace*{2mm}
% \\
%Final FEM equations:
%Single phase FEM
$
M_{AacB} \; \ddot{\bar{u}}_{Bc}
+
K_{AacB} \; \bar{u}_{Bc}
=
F_{Aa}
$
%\\ \nonumber
%A,B &=& 1,2,\dots,\mbox{\# of nodes}
%\\ \nonumber
%a,c &=& 1,\dots,\mbox{\# of dimensions (1, 2 or 3)}
% \vspace*{2mm}
\vspace*{4mm}
\item[] Two phase FEM, upU:
{\footnotesize
% \hspace*{25mm}
\begin{eqnarray}
\hspace*{15mm}
\left[ \begin{array}{ccc}
(M_s)_{KijL} & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & (M_f)_{KijL}
\end{array} \right]
\left[ \begin{array}{c}
\ddot{\overline{u}}_{Lj} \\
\ddot{\overline{p}}_N \\
\ddot{\overline{U}}_{Lj}
\end{array} \right]
+
\left[ \begin{array}{ccc}
(C_1)_{KijL} & 0 & (C_2)_{KijL} \\
0 & 0 & 0 \\
(C_2)_{LjiK} & 0 & (C_3)_{KijL} \\
\end{array} \right]
\left[ \begin{array}{c}
\dot{\overline{u}}_{Lj} \\
\dot{\overline{p}}_N \\
\dot{\overline{U}}_{Lj}
\end{array} \right]
\nonumber \\
+
\left[ \begin{array}{ccc}
(K^{EP})_{KijL} & (G_1)_{KiM} & 0 \\
(G_1)_{LjM} & P_{MN} & (G_2)_{LjM} \\
0 & (G_2)_{KiL} & 0
\end{array} \right]
\left[ \begin{array}{c}
\overline{u}_{Lj} \\
\overline{p}_M \\
\overline{U}_{Lj}
\end{array} \right]
=
\left[ \begin{array}{c}
\overline{f}_{Ki}^{solid} \\
0 \\
\overline{f}_{Ki}^{fluid}
\end{array} \right]
\nonumber
\end{eqnarray}
}
%
%\vspace*{4mm}
% \item[] Nonlinear FEM residuals, equilibrium:
\vspace*{4mm}
\item[] Equilibrium:
\hspace*{2mm}
% \\
$R = F_{external}  F_{internal}$
%$
%R_{Q} =
%F_{Q} 
%\left(
%M_{PQ} \; \ddot{\bar{u}}_{P}
%+
%K_{PQ} \; \bar{u}_{P}
%\right)
%$
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{Energy Input and Dissipation in ESSI System}
\begin{itemize}
\vspace*{1mm}
\item[] Energy input, forces/loads, static/dynamic
\vspace*{4mm}
\item[] Energy dissipation outside SSI domain:
\begin{itemize}
\item[] SSI system oscillation radiation
\item[] Reflected waves radiation
\end{itemize}
\vspace*{2mm}
\item[] Energy dissipation/conversion inside SSI domain:
\begin{itemize}
\vspace*{1mm}
\item[] Inelasticity of soil, interfaces, structure, dissipators
\vspace*{1mm}
\item[] Viscous coupling with internal/pore and external fluids
% % \item[] potential and kinetic energy
% \item[] potential $\leftarrow \! \! \! \! \! \! \rightarrow$ kinetic energy
\vspace*{1mm}
\item[] Energy deflectors, metamaterials
\end{itemize}
\vspace*{2mm}
%\vspace*{1mm}
% \item[] Numerical energy dissipation (numerical damping/production and period errors)
% \item[] Numerical energy dissipation (damping/production)
\item[] Numerical energy dissipation/production
\end{itemize}
%
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
\frametitle{Energy Dissipation within ESSI System}
\begin{itemize}
\vspace*{4mm}
\item[]
%Increment of
Plastic energy dissipation:
%$\Phi = \sigma_{ij} \dot{\epsilon}_{ij}  \sigma_{ij} \dot{\epsilon}_{ij}^{el}  \rho \dot{\psi}_{pl} \ge 0$
$\Delta \Phi = \sigma_{ij} \Delta {\epsilon}_{ij} 
\sigma_{ij} \Delta {\epsilon}_{ij}^{el} 
% \rho
\Delta {\psi}_{pl} \ge 0$
% %Following the first and second laws of thermodynamics, the equation for plastic
% %energy dissipation in decoupled material models was presented by
% %%\citeN7{Yang2017a}:
% %
% \begin{equation}
% \Phi = \sigma_{ij} \dot{\epsilon}_{ij}  \sigma_{ij} \dot{\epsilon}_{ij}^{el}  \rho \dot{\psi}_{pl} \ge 0
% \label{equation_plastic_dissipation_final}
% \end{equation}
% %
% where $\Phi$ is the rate of plastic energy dissipation per unit volume,
% $\sigma_{ij}$ is the stress tensor, $\epsilon_{ij}$ is the strain tensor,
% $\epsilon_{ij}^{el}$ is the elastic part of the strain tensor, $\rho$ is the
% mass density of the material, ${\psi}_{pl}$ is the plastic free energy per unit
% volume.
%
\vspace*{6mm}
\item[]
%Increment of
Viscous energy dissipation/damping: \\
%dissipation $\Delta {D}_V$,
$\Delta {D}_V = C_{ij} \dot{u}_j \Delta {u}_i $
%
% To compute the energy dissipation due to viscous damping, we start with the
% general form of the equation of motion:
% %
% \begin{equation}
% M_{ij} \ddot{u}_j(t) + C_{ij} \dot{u}_j(t) + K_{ij}^{elpl}(t) u_j(t) = f_i(t)
% \label{equation_of_motion}
% \end{equation}
% %
% where $u_j(t)$ is the vector of generalized displacements, $M_{ij}$ is the mass
% matrix, $C_{ij}$ is the damping matrix, $K_{ij}^{elpl}(t)$ is the
% inelastic stiffness matrix that generally evolves with time, $f_i(t)$ is
% the external load vector.
% %
% For linear viscous damping of the Rayleigh type, the damping matrix is
% expressed as
% %
% \begin{equation}
% C_{ij} = a_M M_{ij} + a_{K} K_{ij}^{el}
% \label{equation_damping_matrix}
% \end{equation}
% %
% where $a_M$ and $a_{K}$ are damping constants with units of s$^{1}$ and s,
% respectively.
% %
%
%
% %
% The incremental form of energy balance for a dynamic system with viscous damping can be expressed as
% %
% \begin{equation}
% \Delta {W}_{Input} = \Delta {E}_K + \Delta {D}_V + \Delta {W}_M
% \label{equation_energy_balance}
% \end{equation}
% %
% The left hand side of Equation~\ref{equation_energy_balance} is the
% increment of external input work
% %
% \begin{equation}
% \Delta {W}_{Input}= f_i \Delta {u}_i
% \label{equation_energy_balance_W_Input}
% \end{equation}
%
%
% %%
% The three terms on the right hand side of Equation~\ref{equation_energy_balance} are
% the increment of kinetic energy $\Delta {E}_K$, the increment of viscous energy
% dissipation $\Delta {D}_V$, and the increment of material work of the system $\Delta {W}_M$
% %
% \begin{equation}
% \begin{aligned}
% \Delta {E}_K &= M_{ij} \ddot{u}_j \Delta u_i \\
% \Delta {D}_V &= C_{ij} \dot{u}_j \Delta {u}_i \\
% \Delta {W}_M &= K_{ij}^{elpl} {u}_j \Delta {u}_i = \Delta {E}_S + \Delta {E}_P + \Delta {D}_P
% \end{aligned}
% \label{equation_energy_balance_components}
% \end{equation}
% %
% Note that the term of material work $W_M$ can be separated into an elastic part
% and a plastic part.
% These two components are known as the elastic strain energy $E_S$ and the plastic
% work of the system, respectively.
% %
% Then, as mentioned in the previous section, plastic work can be further
% decomposed into plastic free energy $E_P$ and plastic energy dissipation $D_P$.
\vspace*{6mm}
\item[]
Algorithmic, numerical energy dissipation/production:
\\
Newmark, HilberHughesTaylor, Houbolt, Bathe, Wilson...
%
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{Energy Dissipation Control}
\vspace*{3mm}
\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=8cm]{/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{Plastic Energy Dissipation}
\vspace*{2mm}
% Single elasticplastic element under cyclic shear loading
\begin{itemize}
\item[] Plastic work is NOT plastic dissipation !
\item[] Surface area of $F\Delta$ or $\sigma\epsilon$ is NOT plastic dissipation !
% \item[] Plastic dissipation always increases
\end{itemize}
%\vspace*{7mm}
\begin{figure}[!hbpt]
\begin{center}
\hspace*{5mm}
\includegraphics[width=11.0truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Dissipation_Material.png}
\end{center}
\end{figure}
\end{frame}
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\begin{frame}
\frametitle{Plastic Energy Dissipation}
\vspace*{6mm}
Increment of plastic energy dissipation:
%$\Phi = \sigma_{ij} \dot{\epsilon}_{ij}  \sigma_{ij} \dot{\epsilon}_{ij}^{el}  \rho \dot{\psi}_{pl} \ge 0$
$\Delta \Phi = \sigma_{ij} \Delta {\epsilon}_{ij}^{pl} 
% \sigma_{ij} \Delta {\epsilon}_{ij}^{el} 
% \rho
\Delta {\psi}_{pl} \ge 0$
\vspace*{6mm}
Plastic Free Energy $ \Delta {\psi}_{pl} $
\begin{itemize}
\vspace*{4mm}
\item[] 3D DruckerPrager El=Pl, Armstrong Frederick (soil) \\
$\Delta {\psi}_{pl}
=
\left(( 3/(2 h_a)) \alpha_{ij} \Delta \alpha_{ij}

m_{ii}^{vol} \Delta \lambda \right) (\sigma_{kk}/3 ) $
% m_{ii}^{vol} \Delta \lambda \right) p $
\vspace*{4mm}
\item[] 1D steel fiber (BRB) \\
$\Delta {\psi}_{pl} = \frac{1}{2}
\left(
(\sigma + \sigma^{r})\Delta \epsilon)
+
(\epsilon^{pl}  \epsilon^{r}) \Delta \sigma \right) $
\vspace*{4mm}
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{ASCE7, Steel Building with BRBs}
\vspace*{3mm}
\begin{figure}[!H]
\hspace*{5mm}
%\hspace*{10mm}
\includegraphics[width=12cm]{/home/jeremic/tex/works/Conferences/2023/CIVILCOMP2831Aug2023/present/ASCE7SteelbuildingBRB_model.jpg}
\end{figure}
\end{frame}
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\begin{frame}
\frametitle{ASCE7, Steel Building with BRBs, Soil}
Parabolic DruckerPrager with ArmstongFrederick rotational kinematic hardening
%\vspace*{3mm}
\begin{figure}[!H]
%\hspace*{10mm}
\includegraphics[width=6cm]{/home/jeremic/tex/works/Conferences/2023/CIVILCOMP2831Aug2023/present/ASCE7SteelbuildingBRB_soil_profile.jpg}
\\
\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Conferences/2023/CIVILCOMP2831Aug2023/present/ASCE7SteelbuildingBRB_upper_soil_response.jpg}
\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Conferences/2023/CIVILCOMP2831Aug2023/present/ASCE7SteelbuildingBRB_lower_soil_response.jpg}
% \includegraphics[width=3cm]{/home/jeremic/tex/works/Conferences/2023/CIVILCOMP2831Aug2023/present/from_Han_24Aug2023/}
% \includegraphics[width=3cm]{/home/jeremic/tex/works/Conferences/2023/CIVILCOMP2831Aug2023/present/from_Han_24Aug2023/}
% \includegraphics[width=3cm]{/home/jeremic/tex/works/Conferences/2023/CIVILCOMP2831Aug2023/present/from_Han_24Aug2023/}
\end{figure}
\end{frame}
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\begin{frame}
\frametitle{ASCE7, Steel Building with BRBs, Steel}
Giuffr{\'e}MenegottoPinto 1D Fiber steel model
\vspace*{3mm}
\begin{figure}[!H]
%\hspace*{10mm}
\includegraphics[width=8cm]{/home/jeremic/tex/works/Conferences/2023/CIVILCOMP2831Aug2023/present/ASCE7SteelbuildingBRB_BRB_calibration.jpg}
\end{figure}
\end{frame}
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\begin{frame}
\frametitle{Buckling Restrained Braces (BRB) Energy Dissipation}
%\vspace*{3mm}
\begin{flushleft}
\begin{figure}[!H]
\hspace*{20mm}
%\hspace*{10mm}
\includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2023/CIVILCOMP2831Aug2023/present/ASCE7SteelbuildingBRB_BRB_elements.jpg}
\hspace*{50mm}
\end{figure}
\end{flushleft}
\vspace*{12mm}
\begin{flushright}
\begin{figure}[!H]
\hspace*{42mm}
\includegraphics[width=7.5cm]{/home/jeremic/tex/works/Conferences/2023/CIVILCOMP2831Aug2023/present/from_Han_24Aug2023/Plastic_Dissipation_Density_Time_History.jpg}
\end{figure}
\end{flushright}
\end{frame}
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%
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\begin{frame}
\frametitle{ASCE721, Steel Building Energy Dissipation}
% \vspace*{5mm}
\begin{center}
% \hspace*{15mm}
%\movie[label=show3,width=10cm,poster,autostart,showcontrols]
\movie[label=show3,width=10cm,poster,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/tex/works/Thesis/HanYang/ASCE721_low_building_energy_dissipation/ATC_Short_Building_PD.jpg}}
{/home/jeremic/tex/works/Thesis/HanYang/ASCE721_low_building_energy_dissipation/ATC_Short_Building_PD.mp4}
\end{center}
% online
\vspace*{12mm}
\begin{flushleft}
\hspace*{4mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Energy_dissipation_frames/ATC_Short_Building_PD.mp4}
{\tiny (MP4)}
\end{flushleft}
% online
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%\vspace*{10mm}
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\begin{frame}
\frametitle{Building Seismic Response}
\vspace*{3mm}
\begin{figure}[!H]
%\hspace*{10mm}
\includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2023/CIVILCOMP2831Aug2023/present/from_Han_24Aug2023/response_acc_2.jpg}
\includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2023/CIVILCOMP2831Aug2023/present/from_Han_24Aug2023/response_disp_2.jpg}
\end{figure}
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%
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=10.0truecm]{/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/2D_Frame_Model.pdf}
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%
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% %\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
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% \movie[label=show3,width=61mm,poster, showcontrols]
% {\includegraphics[width=61mm]{/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/Continuous_Foundation_screen_grab.jpg}}
% {/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/Continuous_Foundation.mp4}
% \hspace*{16mm}
% \end{center}
% % local
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% % online
% \begin{center}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Energy_dissipation_frames/Individual_Foundation.mp4}
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\frametitle{Important Infrastructure, 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,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)}
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%
% % Elastoplastic soil with contact elements
% %% Both solid and contact elements dissipate energy
%
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% % \vspace*{5mm}
% \begin{center}
% % \hspace*{15mm}
% \movie[label=show3,width=10cm,poster,showcontrols]
% {\includegraphics[width=10cm]
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation_screen_grab.jpg}}
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mp4}
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% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mp4}
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%
% % 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}
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% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mp4}
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% % \hspace*{15mm}
% %\movie[label=show3,width=10cm,poster,autostart,showcontrols]
% \movie[label=show3,width=10cm,poster,showcontrols]
% {\includegraphics[width=10cm]
% {/home/jeremic/tex/works/Thesis/HanYang/ASCE721_low_building_energy_dissipation/ATC_Short_Building_PD.jpg}}
% {/home/jeremic/tex/works/Thesis/HanYang/ASCE721_low_building_energy_dissipation/ATC_Short_Building_PD.mp4}
% \end{center}
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% % online
% \vspace*{12mm}
% \begin{flushleft}
% \hspace*{4mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Energy_dissipation_frames/ATC_Short_Building_PD.mp4}
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\section{Summary}
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\frametitle{Summary}
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\item[] Engineering analysis to \underline{predict} and \underline{inform}
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% \url{http://realessi.us/}
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\item[] Engineer needs to know !
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% \url{http://realessi.us/}
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% \item[] Mechanical energy for design, assessment and infrastructure upgrades
\item[] Mechanical energy dissipation for design and assessment
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% \url{http://realessi.us/}
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\item[] Education and Training is the Key
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