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\begin{document}
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{\huge \bf
%\vspace*{1.5truecm} \\
\begin{center}
\end{center}
\rule[3mm]{0cm}{0.3cm} {\cyrnaslov Interakcija konstrukcije i tla} \\
\rule[3mm]{0cm}{2.3cm} {\cyrnaslov u toku zemljotresa:} \\
\rule[3mm]{0cm}{2.3cm} {\cyrnaslov numerichka analiza}
}
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\begin{center}
{\cyrpodnaslov
Boris Jeremi\cj{}\\
\vspace*{0.50truecm}
Vanredni Profesor Univerziteta u Kaliforniji \\
Dejvis, Kalifornija
}
\end{center}
% %\begin{large}
% \begin{center}
% {\bf Boris Jeremi{\' c}, Jinxiu Liao}
% \end{center}
% %\end{large}
%
% \vspace*{0.50truecm}
%
% \begin{small}
% \begin{center}
% {Department of Civil and Environmental Engineering }\\
% {University of California, Davis}\\
% \end{center}
% \end{small}
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% %\begin{large}
% \begin{center}
% {\bf Zhaohui Yang}
% \end{center}
% %\end{large}
%
% \vspace*{0.50truecm}
%
% \begin{small}
% \begin{center}
% {School of Engineering}\\
% {University of Alaska, Anchorage}\\
% \end{center}
% \end{small}
%
%
% %
%
%
% \begin{small}
%
% \begin{description}
% %\item Supported in part by the NSFPEER \#~EEC9701568,
% %CalEPA \#~9901337V,
% \item Supported in part by the NSF, PEER, Caltrans, and CalEPA.
%
% % \item Collaborators:
% Professors
% Zhaohui Yang (UAA),
% Sashi Kunnath (UCD),
% %Bruce Kutter (UCD),
% Gregory Fenves (UCB),
% Jacobo Bielak (CMU),
% %Bernd Hamann (UCD),
% %Zhaojun Bai (UCD),
% George Karypis (UMN),
% Drs.
% Francis McKenna (UCB),
% %and
% %graduate students
% %Xiaoyan Wu (UCD)
% %Ritu Jain (UCD),
% %Qing Liu (UCD),
% %Jinxiu Liao (UCD).
% \end{description}
%
% \end{small}
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\slide{\cyrslajd Motivacija}
%\begin{large}
{\cyr
\begin{itemize}
\vspace*{3.0cm}
\item Napraviti precizne modele gradjevinskih objekata (mostova, zgrada,
luchkih konstrukcija, brana...)
%
%Create high fidelity models of constructed facilities
%(bridges, buildings, port structures, dams...).
\vspace*{1.5cm}
\item Modeli \cj{}e da "zhive" zajedno sa objektom koje predstavljaju
%Models will live concurrently with the physical system
%they represent.
\vspace*{1.5cm}
\item Modeli \cj{}e da omogu\cj{}e vlasnicima u odrzhavanju objekata i u
proceni budu\cj{}eg ponashanja pri incidentnim optere\cj{}enjima
%Models to provide owners and operators with the
%capabilities to assess operations and future performance.
\vspace*{1.5cm}
\item Merenja ponashanja objekata \cj{}e se koristiti da se poboljshaju modeli
upotrebom numerichkih simulacija
% Use observed performance to update and validate models
%through simulations.
\end{itemize}
}
%\end{large}
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\slide{Pregled danashnjeg predavanja}
%\begin{large}
\vspace*{2.3cm}
{\cyr
\begin{itemize}
\vspace*{1.0cm}
\item Sklapanje elastichnoplastichnih modela za solide
\vspace*{1.0cm}
\item Zemljotresno optere\cj{}enje na sisteme tla i konstrukcije
\vspace*{1.0cm}
\item Utical tla na konstrukciju i utical konstrukcije na tlo pri zemljotresnom optere\cj{}enju
\vspace*{1.0cm}
\item Povoljnosti i nepovoljnosti sprege medjusobnih uticaja tla i konstrukije pri zemljotresima
\vspace*{1.0cm}
\item Kratak opis programskog sistema {\rm \large OpenSees, (Open System for Earthquake Engineeing Simulations)}
\end{itemize}
}
%\end{large}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \slide{ Presentation Overview}
% %\begin{large}
%
%
% {\cyr
% \begin{itemize}
%
%
% \vspace*{1.0cm}
% \item Domain Reduction Method basics
%
% \begin{itemize}
% \item Local geologic feature
% \item Background wave field + relative displacement field
% \item Dynamic forces
% \end{itemize}
%
% \vspace*{1.0cm}
% \item Application Examples
%
% \begin{itemize}
% % \vspace*{1.0cm}
% \item Seismic wave propagation
%
% % \vspace*{1.0cm}
% \item SoilStructure interaction
%
% \end{itemize}
%
%
% \vspace*{1.0cm}
% \item Work in Progress
%
% %\vspace*{1.0cm}
% %\item
%
% %\vspace*{1.0cm}
% %\item
%
% % \end{itemize}
% % }
% %
% %\end{large}
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\slide{Elastoplastichnost u kalupu}
\begin{normalsize}
{\cyr
\begin{itemize}
\vspace{2.4cm}
\item Ve\cj{}ina elastoplastichnih modela i implementacija se sastoji od:
\vspace{0.8cm}
\begin{enumerate}
\vspace{0.4cm}
\item Povrshi plastichnosti $F$ (i njenih prvih izvoda po naponu $n_{ij}$ i promenljivima stanja
$\xi_{\ast}$)
\vspace{0.4cm}
\item Pravca plastichnog techenja $m_{ij}$ (prvi $m_{ij}=\partial Q/\partial \sigma_{ij}$
i drugi izvodi potencijala plastichnosti $\partial m_{ij}/\partial \sigma_{mn}$,
$\partial m_{ij}/\partial q_{\ast}$ )
\vspace{0.4cm}
\item Zakona promene promenljivih stanja $q_{\ast}$ (skalarne ili tenzorske velichine)
\end{enumerate}
\vspace{0.8cm}
\item Ve\cj{}ina elastoplastichnih modela se na ovaj nachin mozhe implementirati u vrlo generalnom obliku
\vspace{0.8cm}
\item Korisnik mozhe sam da definishe nove modele kombinuju\cj{}i gornje funkcije
\end{itemize}
}
\end{normalsize}
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\slide{Implicitna numerichka integracija u elastoplastichnosti}
\begin{normalsize}
\begin{samepage}
\begin{eqnarray*}
d\sigma_{mn} &=&
\\
 \left(
{}^{old} \! r_{ij} \right.
&+&
\left.
\frac { {}^{n+1} \! F^{old}

{}^{n+1} \! n_{mn} \; {}^{old} \! r_{ij} {}^{n+1}\!T_{ijmn}^{1} }
{ {}^{n+1} \! n_{mn} E_{ijkl} \; {}^{n+1} \!H_{kl} {}^{n+1}\!T_{ijmn}^{1}

{}^{n+1} \! \xi_{\ast} \; h_{\ast} }
\; E_{ijkl} \; {}^{n+1} \!H_{kl}
\right)
{}^{n+1}\!T_{ijmn}^{1}
\label{dsigmasolution}
\end{eqnarray*}
\end{samepage}
%
\vspace*{0.5cm}
%
\begin{samepage}
\begin{eqnarray*}
d q_{\ast} =
\left(
\frac { {}^{n+1} \! F^{old}

{}^{n+1} \! n_{mn} \; {}^{old} \! r_{ij} {}^{n+1}\!T_{ijmn}^{1} }
{ {}^{n+1} \! n_{mn} E_{ijkl} \; {}^{n+1} \!H_{kl} {}^{n+1}\!T_{ijmn}^{1}
 {}^{n+1} \! \xi_{\ast} \; h_{\ast} }
\right)
h_{\ast}
\label{dqsolution}
\end{eqnarray*}
\end{samepage}
%
\vspace*{0.5cm}
%
%
\begin{samepage}
\begin{eqnarray*}
{}^{n+1} \!T_{ijmn} =
\delta_{im} \delta_{nj} +
\lambda \; E_{ijkl} \;
\left. % just because of the \right
\frac{ \partial m_{kl} }{\partial \sigma_{mn}} \right_{n+1}
\;\;\;\;\mbox{;}\;\;\;\;
{}^{n+1} \!H_{kl} =
{}^{n+1} \!m_{kl}
+
\left. % just because of the =right
\lambda \frac{ \partial m_{kl} }{\partial q_{\ast}} \right_{n+1} \! h_{\ast}
\label{T_ijmn}
\end{eqnarray*}
\end{samepage}
%
\vspace*{0.5cm}
%
%
\begin{eqnarray*}
{}^{n+1} \! \epsilon_{ij}^p = {}^{n} \! \epsilon_{ij}^p +
\lambda\; {}^{n+1} \!m_{ij}
\;\;\;\;\mbox{;}\;\;\;\;
{}^{n+1} \! q_{\ast} = {}^{n} \! q_{\ast} + \lambda\; {}^{n+1} \! h_{\ast}
\label{mid3}
\end{eqnarray*}
%%
\end{normalsize}
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\slide{Primeri: monotono optere\cj{}enje}
%\vspace*{1.0cm}
\begin{figure}[!hbpt]
\begin{center}
{\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/DP_DP_pp_q_eq.pdf}}
{\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/DP_DP_pp_ev_eq.pdf}}
{\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/DP_vM_ls_q_eq.pdf}}
{\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/DP_vM_ls_ev_eq.pdf}}
\vspace*{3cm}
\\
{\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cam_S_SOC_q_eq.pdf}}
{\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cam_S_SOC_ev_eq.pdf}}
{\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cam_S_HOC_q_eq.pdf}}
{\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cam_S_HOC_ev_eq.pdf}}
\vspace*{3cm}
\\
{\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/DP_MD_ltmd_NC_q_eq.pdf}}
{\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/DP_MD_ltmd_NC_ev_eq.pdf}}
{\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/DP_MD_ltmd_HOC_q_eq.pdf}}
{\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/DP_MD_ltmd_HOC_ev_eq.pdf}}
\end{center}
\end{figure}
%
\vspace*{1.0cm}
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\slide{Primeri: ciklichno optere\cj{}enje}
%\vspace*{2cm}
%
\begin{figure}[!hbpt]
\begin{center}
{\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/DP_vM_nlt_cyc_q_eq.pdf}}
{\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/DP_vM_nlt_cyc_ev_eq.pdf}}
\vspace*{3cm}
\\
{\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cam01_SOC_cyc_q_eq.pdf}}
{\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cam01_SOC_cyc_ev_eq.pdf}}
\vspace*{3cm}
\\
{\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/DP_MD_ltmd_cyc_q_eq.pdf}}
{\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/DP_MD_ltmd_cyc_ev_eq.pdf}}
\end{center}
\end{figure}
%
\vspace*{1.0cm}
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\slide{Nehomogeno ponashanje}
%\begin{large}
{\cyr
\begin{itemize}
\item Nehomogena deformacija pri chistom smicanju (virtuelni uzorak, konstitutivno ponashanje?)
%
\vspace*{1.0cm}
\begin{figure}[!hbpt]
\begin{center}
{\includegraphics[width=4.6cm,angle=90]{/home/jeremic/tex/works/Conferences/2002/DEM/Ray101_00199.pdf}}
\hfill
{\includegraphics[width=4.6cm,angle=90]{/home/jeremic/tex/works/Conferences/2002/DEM/Ray102_00199.pdf}}
\hfill
{\includegraphics[width=4.6cm,angle=90]{/home/jeremic/tex/works/Conferences/2002/DEM/Ray103_00199.pdf}}
\hfill
{\includegraphics[width=4.6cm,angle=90]{/home/jeremic/tex/works/Conferences/2002/DEM/Ray105_00199.pdf}}
%\caption{\label{Displacement 01} Shear velocity $v=5$. Vertical stress
%$\sigma_v = 2.5$.
%Displaced assemblies for (a) round particles, (b) $2:1$ particle chain, (c) $3:1$
%particle chain, and (d) $5:1$ particle chain. Light regions experience high
%normal stresses.}
\end{center}
\end{figure}
%
% \begin{figure}[!hbpt]
% \begin{center}
% {\includegraphics[width=4.6cm]{/home/jeremic/tex/works/Conferences/2002/DEM/Ray101_00199.jpg}}
% \hfill
% {\includegraphics[width=4.6cm]{/home/jeremic/tex/works/Conferences/2002/DEM/Ray102_00199.jpg}}
% \hfill
% {\includegraphics[width=4.6cm]{/home/jeremic/tex/works/Conferences/2002/DEM/Ray103_00199.jpg}}
% \hfill
% {\includegraphics[width=4.6cm]{/home/jeremic/tex/works/Conferences/2002/DEM/Ray105_00199.jpg}}
% %\caption{\label{Displacement01} Shear velocity $v=5$. Vertical stress
% %$\sigma_v = 2.5$.
% %Displaced assemblies for (a) round particles, (b) $2:1$ particle chain, (c) $3:1$
% %particle chain, and (d) $5:1$ particle chain. Light regions experience high
% %normal stresses.}
% \end{center}
% \end{figure}
%
%\vspace*{0.5cm}
\item Stvarni uzorak (tomografija)
{\includegraphics[width=12cm]{/home/jeremic/oofep/experiment/MGM/images/MGM_1.jpg}}
\end{itemize}
}
%\end{large}
%
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\slide{Uticaji opreme za testiranje}
\vspace*{1.5cm}
%
\begin{figure}[!hbpt]
\begin{center}
{\includegraphics[width=3truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_Inc02.jpg}}
{\includegraphics[width=3truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_Inc04.jpg}}
{\includegraphics[width=3truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_Inc06.jpg}}
{\includegraphics[width=3truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_Inc07.jpg}}
{\includegraphics[width=3truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_Inc09.jpg}}
{\includegraphics[width=3truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_Inc11.jpg}}
{\includegraphics[width=3truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_Inc12.jpg}}
%\caption{\label{deformed_elogated_Inc} Deformed elongated
%specimen and a propagation of plastic zone for a specimen with
%friction and inclined end platens.}
\end{center}
\end{figure}
%
%
\begin{figure}[!hbpt]
\vspace*{4.0cm}
\begin{center}
%{\includegraphics[width=12truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/eq_DiffSam_fri_nof_com.pdf}}
%\hfill
{\includegraphics[width=14truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Phi_Cu21_Inclined_fri_com.pdf}}
%\caption{\label{Inclined_response02} Comparison of the
%mobilized friction angle at 2\% shear strain for various max.
%inclinations of end platens. Actual material friction angle is
%$37^{o}$.}
\end{center}
\vspace*{8.0cm}
\end{figure}
%
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\slide{Elastoplastichnost i verovatno\cj{}a}
%\begin{large}
{\cyr
\begin{itemize}
\vspace{3.0cm}
\item Uticaj nehomogenosti uzorka na mehanichko ponashanje (ojachanje, idealna plastichnost, omekshanje...)
\vspace{1.0cm}
\item Ponashanje materijala proizilazi iz verovatno\cj{}a ojachanja, idealne
plastichnosti ili omekshanja
\vspace{1.0cm}
\item "Idealan" uzorak bi trebao da ima homogeno polje napona i deformacija i
da se ponasha u skladu za mikromehanikom deformacije
\vspace{1.0cm}
\item Ponashanja svih ostalih uzoraka (stvarnih materijala) su usko povezana
sa prostornom raspodelom materijalnih osobina (sttistikom) i mogu biti
predstavljena samo pomo\cj{}u verovatno\cj{}a
\end{itemize}
}
%\end{large}
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%
% \slide{Long Specimen}
%
% %\begin{large}
%
% %
% \begin{figure}[!hbpt]
% \begin{center}
% {\includegraphics[width=3.8truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_lev01.jpg}}
% {\includegraphics[width=3.8truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_lev02.jpg}}
% {\includegraphics[width=3.8truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_lev03.jpg}}
% {\includegraphics[width=3.8truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_lev04.jpg}}
% {\includegraphics[width=3.8truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_lev05.jpg}}
% {\includegraphics[width=3.8truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_lev06.jpg}}
% %
% %{\includegraphics[width=3.8truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_lev07.jpg}}
% %{\includegraphics[width=3.8truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_lev08.jpg}}
% {\includegraphics[width=3.8truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_lev09.jpg}}
% %{\includegraphics[width=3.8truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_lev10.jpg}}
% %{\includegraphics[width=3.8truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_lev11.jpg}}
% {\includegraphics[width=3.8truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_lev12.jpg}}
% %{\includegraphics[width=3.8truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_lev13.jpg}}
% %{\includegraphics[width=3.8truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_lev14.jpg}}
% {\includegraphics[width=3.8truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_lev15.jpg}}
% {\includegraphics[width=3.8truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_lev16.jpg}}
% {\includegraphics[width=3.8truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_lev17.jpg}}
% {\includegraphics[width=3.8truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_lev18.jpg}}
% %\caption{\label{deformed_cubic2_1} Deformed elongated specimen
% %propagation of plastic zone for a simulation using $10 \times
% %10\times 20$ mesh with fixed level end platens.}
% \end{center}
% \end{figure}
%
% \vspace*{0.8cm}
%
%
% Progression of plastic zone for a long speciment with high friction end
% plattens
%
%
%
% %\end{large}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \slide{NonLevel End Plattens}
%
%
% %
% \begin{figure}[!hbpt]
% \begin{center}
% {\includegraphics[width=4truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_Inc02.jpg}}
% {\includegraphics[width=4truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_Inc03.jpg}}
% {\includegraphics[width=4truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_Inc04.jpg}}
% {\includegraphics[width=4truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_Inc05.jpg}}
% {\includegraphics[width=4truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_Inc06.jpg}}
% \\
% {\includegraphics[width=4truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_Inc07.jpg}}
% {\includegraphics[width=4truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_Inc08.jpg}}
% {\includegraphics[width=4truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_Inc09.jpg}}
% %{\includegraphics[width=4truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_Inc10.jpg}}
% {\includegraphics[width=4truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_Inc11.jpg}}
% {\includegraphics[width=4truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cu2_1_pl_Inc12.jpg}}
% %\caption{\label{deformed_elogated_Inc} Deformed elongated
% %specimen and a propagation of plastic zone for a specimen with
% %friction and inclined end platens.}
% \end{center}
% \end{figure}
% %
% %
% %
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \slide{Constitutive Response?}
%
%
%
%
%
% %
% \begin{figure}[!hbpt]
% \vspace*{6.0cm}
% \begin{center}
% {\includegraphics[width=22truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/eq_DiffSam_fri_nof_com.pdf}}
% %\hfill
% %{\includegraphics[width=12truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Phi_Cu21_Inclined_fri_com.pdf}}
% %\caption{\label{Inclined_response02} Comparison of the
% %mobilized friction angle at 2\% shear strain for various max.
% %inclinations of end platens. Actual material friction angle is
% %$37^{o}$.}
% \end{center}
% \vspace*{8.0cm}
% \end{figure}
% %
%
% % %
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \slide{Constitutive Response?}
%
%
%
%
%
% %
% \begin{figure}[!hbpt]
% \vspace*{6.0cm}
% \begin{center}
% %{\includegraphics[width=12truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/eq_DiffSam_fri_nof_com.pdf}}
% %\hfill
% {\includegraphics[width=22truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Phi_Cu21_Inclined_fri_com.pdf}}
% %\caption{\label{Inclined_response02} Comparison of the
% %mobilized friction angle at 2\% shear strain for various max.
% %inclinations of end platens. Actual material friction angle is
% %$37^{o}$.}
% \end{center}
% \vspace*{8.0cm}
% \end{figure}
% %
%
% % %
%
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\slide{Zemljotresno optere\cj{}enje}
%\begin{large}
{\cyr
\begin{itemize}
\vspace*{3.5cm}
\item Unos zemljotresnog optere\cj{}enja (ili pomeranja?)
\vspace*{2.0cm}
\item Uticaj konachne velichine modela (zarobljavanje zemljotresne energije)
\vspace*{2.0cm}
\item Trodimenziono prostiranje zemljotresnih talasa
%\vspace*{0.5cm}
% \item
\end{itemize}
}
%\end{large}
% \begin{normalsize}
% \begin{figure}[!htbp]
% \vspace*{0.50cm}
% \begin{center}
% {\includegraphics[width=16cm]{/home/jeremic/tex/works/Conferences/2001/PEERInitMeet/DRM01.pdf}}
% \vspace*{0.50cm}
% \end{center}
% %\vspace*{0.3cm}
% \end{figure}
% \end{normalsize}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\slide{Metoda redukcije domena}
%\begin{large}
{\cyr
\begin{itemize}
\vspace*{2.5cm}
\item Bazirano na radovima grupe saradnika (Prof. Bielak sa KMU)
\vspace*{1.5cm}
\item Dvostepena procedura
\vspace*{1.5cm}
\item Osnovne nepoznate
\begin{itemize}
\item Kompletno polje pomeranja u lokalnom domenu
\item Dodatno polje pomeranja u spoljnom domenu
\end{itemize}
\vspace*{1.5cm}
\item Polje pomeranja koje se prostire od hipocentra se redukuje na jednu
konkavnu povrsh koja obuhvata lokalni model
\end{itemize}
}
%\end{large}
% \begin{normalsize}
% \begin{figure}[!htbp]
% \vspace*{0.50cm}
% \begin{center}
% {\includegraphics[width=16cm]{/home/jeremic/tex/works/Conferences/2001/PEERInitMeet/DRM01.pdf}}
% \vspace*{0.50cm}
% \end{center}
% %\vspace*{0.3cm}
% \end{figure}
% \end{normalsize}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\slide{Pozadinsko polje pomeranja}
%\begin{large}
{\cyr
\begin{itemize}
\vspace*{1.5cm}
\item Mozhe se odrediti merenjima ili nekom od postoje\cj{}ih analitichkih metoda
hafdgt hbgyrf hbasdefdeawqsdwa
\vspace*{0.35cm}
\item Potrebno je polje pomeranja i ubrzanja
% \vspace*{0.35cm}
% \item Green's functions solutions, Quake system, SCEC database, SHAKE...
% \vspace*{0cfbxvfdgv fvcADV vcend{itemize}
\end{itemize}
}
%\end{large}
\begin{normalsize}
\begin{figure}[!htbp]
%\vspace*{0.70cm}
\begin{center}
{\includegraphics[width=18cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DRM0102.pdf}}
\vspace*{2.50cm}
\end{center}
%\vspace*{0.3cm}
\end{figure}
\end{normalsize}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\slide{Osnovna ideja}
%\begin{large}
{\cyr
\begin{itemize}
\item Pojednostavljen originalni model
\item Lokalni model \\(koji je realan, \\ne mora se uprosh\cj{}avati)
\end{itemize}
}
%\end{large}
\begin{normalsize}
\begin{figure}[!htbp]
\vspace*{3.50cm}
\begin{center}
%\hspace*{1cm}
%{\includegraphics[angle=90,width=10cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DRM03.pdf}}
{\includegraphics[width=12cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DRM03.pdf}}
\hfill
%{\includegraphics[angle=90,width=10cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DRM04.pdf}}
{\includegraphics[width=12cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DRM04.pdf}}
%\hspace*{1cm}
\vspace*{2.50cm}
\end{center}
%\vspace*{0.3cm}
\end{figure}
\end{normalsize}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\slide{Dinamika sistema}
\vspace*{0.5cm}
\begin{eqnarray*}
\left[\begin{array}{cc} M^\Omega_{ii} & M^\Omega_{ib} \\ M^\Omega_{bi} & M^\Omega_{bb}\end{array}\right]
\left\{\begin{array}{c}\ddot{u}_i \\ \ddot{u}_b\end{array}\right\}+\left[\begin{array}{cc} K^\Omega_{ii
} & K^\Omega_{ib} \\ K^\Omega_{bi} & K^\Omega_{bb}\end{array}\right]
\left\{\begin{array}{c} u_i \\ u_b \end{array}\right\}=\left\{\begin{array}{c} 0 \\ P_b\end{array}\right\} ,\mbox{\cyr u} \ \Omega
\label{e11}
\end{eqnarray*}
\vspace*{2.0cm}
\begin{eqnarray*}
\left[\begin{array}{cc} M^{\Omega+}_{bb} & M^{\Omega+}_{be} \\ M^{\Omega+}_{eb} & M^{\Omega+}_{ee}\end{array}\right]
\left\{\begin{array}{c}\ddot{u}_b \\ \ddot{u}_e\end{array}\right\}+\left[\begin{array}{cc}K^{\Omega+}_{bb} & K^{\Omega+}_{be} \\
K^{\Omega+}_{eb} & K^{\Omega+}_{ee}\end{array}\right]
\left\{\begin{array}{c}u_b \\ u_e \end{array}\right\}=\left\{\begin{array}{c}P_b \\ P_e \end{array}\right\}, \mbox{\cyr u} \ \Omega^+
\label{e12}
\end{eqnarray*}
%Summed up $\Rightarrow$ classical form
\vspace*{1.5cm}
\begin{eqnarray*}
\left[\begin{array}{ccc}M^{\Omega}_{ii} & M^{\Omega}_{ib} & 0 \\
M^\Omega_{bi} & M^\Omega_{bb}+M^{\Omega+}_{bb} & M^{\Omega+}_{be}\\ 0 & M^{\Omega+}_{eb} & M^{\Omega+}_{ee} \end{array}\right]
\left\{\begin{array}{c}\ddot{u}_i \\ \ddot{u}_b \\ \ddot{u}_e\end{array}\right\}
+
\\
\left[ \begin{array}{ccc}K^\Omega_{ii} & K^{\Omega}_{ib} & 0 \\
K^{\Omega}_{bi} & K^{\Omega}_{bb}+K^{\Omega+}_{bb} & K^{\Omega+}_{be} \\
0 & K^{\Omega+}_{eb} & K^{\Omega+}_{ee} \end{array}\right] \left\{\begin{array}{c} u_i \\ u_b \\ u_e \end{array} \right\}
=
\left\{\begin{array}{c} 0 \\ 0 \\ P_e\end{array}\right\}
%\nonumber \\ \label{e13}
\end{eqnarray*}
\vspace*{0.5cm}
\begin{normalsize}
\begin{figure}[!htbp]
\vspace*{4.50cm}
\begin{center}
%\hspace*{1cm}
%{\includegraphics[angle=90,width=10cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DRM03.pdf}}
{\includegraphics[width=8cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DRM03.pdf}}
%\hfill
%\hspace*{1cm}
\vspace*{2.50cm}
\end{center}
%\vspace*{0.3cm}
\end{figure}
\end{normalsize}
%
% %\begin{large}
% \begin{itemize}
% \item Simplified original model
% \item Local geological feature
% \end{itemize}
%
%\end{large}
%
%
% \begin{normalsize}
% \begin{figure}[!htbp]
% \vspace*{0.50cm}
% \begin{center}
% \hspace*{1cm}
% {\includegraphics[angle=90,width=10cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DRM03.pdf}}
% \hfill
% {\includegraphics[angle=90,width=10cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DRM04.pdf}}
% \hspace*{1cm}
% \vspace*{2.50cm}
% \end{center}
% %\vspace*{0.3cm}
% \end{figure}
% \end{normalsize}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\slide{Zamena promenljivih}
\noindent
{\cyr Jednachine pomeranja (ravnotezhe) u $\Omega^+$ za promenjeni model}
%\vspace*{1.5cm}
\begin{eqnarray*}
\left[\begin{array}{cc}M^{\Omega+}_{bb} & M^{\Omega+}_{be} \\ M^{\Omega+}_{eb} & M^{\Omega+}_{ee} \end{array} \right]
\left\{\begin{array}{c}\ddot{u}^0_b \\ \ddot{u}^0_e \end{array}\right\}+\left[\begin{array}{cc}K^{\Omega+}_{bb} & K^{\Omega+}_{be} \\
K^{\Omega+}_{eb} & K^{\Omega+}_{ee}\end{array}\right]
\left\{\begin{array}{c} u^0_b \\ u^0_e\end{array}\right\}=\left\{\begin{array}{c}P^0_b \\ P_e\end{array}\right\}
\Rightarrow
\label{e14}
\end{eqnarray*}
%
\vspace*{1.2cm}
\begin{eqnarray*}
P_e = M^{\Omega+}_{eb}\ddot{u}^0_b+ M^{\Omega+}_{ee}\ddot{u}^0_e+
K^{\Omega+}_{eb}u^0_b+K^{\Omega+}_{ee}u^0_e
\label{e15}
\end{eqnarray*}
\noindent
{\cyr Zamena promenjljivih $u_e=u^0_e+w_e$}
{\cyr
\begin{itemize}
%\vspace*{0.5cm}
\item Ukupno polje pomeranja $u_e$
%\vspace*{0.5cm}
\item Pozadinsko polje pomeranja $u^0_e$
%\vspace*{0.5cm}
\item Rezidualno polje pomeranja (relativno u odnosu na referentno, pozadinsko polje pomeranja) $w_e$
\end{itemize}
}
\vspace*{0.5cm}
\begin{footnotesize}
\begin{eqnarray*}
\left[\begin{array}{ccc}M^{\Omega}_{ii} & M^{\Omega}_{ib} & 0 \\
M^\Omega_{bi} & M^\Omega_{bb}+M^{\Omega+}_{bb} & M^{\Omega+}_{be}
\\ 0 & M^{\Omega+}_{eb} & M^{\Omega+}_{ee} \end{array}\right]
\left\{\begin{array}{c}\ddot{u}_i \\ \ddot{u}_b \\ \ddot{w}_e\end{array}\right\}+
\left[ \begin{array}{ccc}K^\Omega_{ii} & K^{\Omega}_{ib} & 0 \\
K^{\Omega}_{bi} & K^{\Omega}_{bb}+K^{\Omega+}_{bb} & K^{\Omega+}_{be} \\
0 & K^{\Omega+}_{eb} & K^{\Omega+}_{ee} \end{array}\right]
\left\{\begin{array}{c} u_i \\ u_b \\ w_e \end{array} \right\}
=
\left\{\begin{array}{c} P^{eff}_i \\ P^{eff}_b \\ P^{eff}_e \end{array}\right\}
%
% \nonumber \\ \left\{\begin{array}{c} 0 \\ M^{\Omega+}_{be} \ddot{u}^0_eK^{\Omega+}_{be}u^0_e
% \\ M^{\Omega+}_{eb}\ddot{u}^0_b+K^{\Omega+}_{eb}u^0_b\end{array}\right\}
\label{e18}
\end{eqnarray*}
\end{footnotesize}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\slide{Dinamichke (zemljotresne) sile}
\vspace*{3cm}
%After substitions
\begin{figure}[!htb]
%
%\unitlength 1cm
%%\begin{large}
\begin{minipage}[t]{6cm}
%
\begin{eqnarray*}
\left\{\begin{array}{c} P^{eff}_i \\ P^{eff}_b \\ P^{eff}_e \end{array}\right\}
= \left\{\begin{array}{c} 0 \\ M^{\Omega+}_{be} \ddot{u}^0_eK^{\Omega+}_{be}u^0_e
\\ M^{\Omega+}_{eb}\ddot{u}^0_b+K^{\Omega+}_{eb}u^0_b\end{array}\right\}
\end{eqnarray*}
\end{minipage}
%%\end{large}
%
\hfill
%
\begin{minipage}[t]{10cm}
\begin{normalsize}
% \begin{picture}(10.0 ,2.0)
% \begin{picture}(10.0 ,2.0)(4.0, 0.0)
\begin{figure}[!h]
%\vspace*{0.50cm}
%\begin{center}
%\hspace*{1cm}
\vspace*{4.50cm}
{\includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DRM05.pdf}}
\vspace*{5.50cm}
%\hspace*{1cm}
%\vspace*{2.50cm}
%\end{center}
%\vspace*{0.3cm}
\end{figure}
% \end{picture}
\end{normalsize}
\end{minipage}
%
\end{figure}
\vspace*{1.5cm}
%\begin{large}
{\cyr
\begin{itemize}
%\vspace*{0.5cm}
\item Stvarne zemljotresne sile $P_e$ zamenjene sa efektivnim chvornim
optere\cj{}enjima $P^{eff}$,
%\vspace*{0.5cm}
\item $P^{eff}$ se pojavljuju samo sa podmatricama $M_{be}$,$K_{be}$,$M_{eb}$,$K_{eb}$
%\vspace*{0.5cm}
\item Postoje samo u jednom sloju konachnih elemenata u $\Omega^+$
koji se granishi sa $\Gamma$.
%\vspace*{0.5cm}
\item Ne postoje nikakvi specijalni zahtevi za materijal u $\Omega$, {\cyb
mozhe da bude i neelastichan!}
% \item The only input wave field is the one for the nodes of this layer of elements.
\end{itemize}
}
%\end{large}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\slide{Primeri}
%\begin{large}
{\cyr
\begin{itemize}
\vspace*{2.0cm}
\item Prostiranje zemljotresnih talasa
\begin{itemize}
\item Efekti plastifikacije tla na zemljotresne talase
\end{itemize}
\vspace*{1.0cm}
\item Interakcija konstrukcije i tla
\begin{itemize}
\item Efekti plastifikacije tla na dinamichki odgovor konstrukcije (vrlo uprosh\cj{}ene)
\end{itemize}
\end{itemize}
}
%\end{large}
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\slide{Model konachnih elemenata za prostiranje talasa}
\begin{figure}[!h]
\vspace*{0.0cm}
\begin{center}
{\includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/thesis/figures/model1a.jpg}}
\\
\vspace*{3.8cm}
{\includegraphics[width=10.5cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/thesis/figures/Inp_acc0507.pdf}}
%\hfill
{\includegraphics[width=10.5cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/thesis/figures/Inp_dis0507.pdf}}
\vspace*{4.8cm}
\end{center}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\slide{ Prostiranje zemljotresnih talasa \\ kruta tla}
\begin{figure}[!h]
%\begin{center}
\vspace*{2.5cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/thesis/figures/TS/DL_TS.pdf}}
\hspace{1.8cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/thesis/figures/TS/DY_TS.pdf}}
\vspace*{5.0cm}
%\end{center}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\slide{ Prostiranje zemljotresnih talasa \\ meka tla}
\begin{figure}[!h]
%\begin{center}
\vspace*{3.5cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/thesis/figures/TS/DL_SS.pdf}}
\hspace{1.8cm}
{\includegraphics[width=13.7cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/thesis/figures/TS/DY_SS.pdf}}
\vspace*{5.0cm}
%\end{center}
\end{figure}
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\slide{Model konachnih elemenata \\
interakcija konstrukcije i tla}
\begin{figure}[!h]
\vspace*{0.0cm}
\begin{center}
{\includegraphics[width=12cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/model3.jpg}}
\\
\vspace*{4.8cm}
{\includegraphics[width=10.5cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/newthesis/figures/Model3/AT.pdf}}
%\hfill
{\includegraphics[width=10.5cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/newthesis/figures/Model3/DT.pdf}}
\vspace*{4.8cm}
\end{center}
\end{figure}
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\slide{Model bez konstrukcije \\ kruto tlo}
\begin{figure}[!h]
%\begin{center}
\vspace*{2.5cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DL_T617.pdf}}
\hspace{1.8cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DY_T617.pdf}}
\vspace*{5.0cm}
%\end{center}
\end{figure}
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\slide{Model sa konstrukcijom \\ kruto tlo}
\begin{figure}[!h]
%\begin{center}
\vspace*{2.5cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DL_T615.pdf}}
\hspace{1.8cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DY_T615.pdf}}
\vspace*{5.0cm}
%\end{center}
\end{figure}
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\slide{ Model bez konstrukcije \\ meko tlo}
\begin{figure}[!h]
%\begin{center}
\vspace*{2.5cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DL_M617.pdf}}
\hspace{1.8cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DY_M617.pdf}}
\vspace*{5.0cm}
%\end{center}
\end{figure}
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\slide{ Model sa konstrukcijom \\ meko tlo}
\begin{figure}[!h]
%\begin{center}
\vspace*{2.5cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DL_M615.pdf}}
\hspace{1.8cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DY_M615.pdf}}
\vspace*{5.0cm}
%\end{center}
\end{figure}
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\slide{Ponashanje konstrukcije }
\vspace*{1.5cm}
\noindent
{\cyr konstrukcija je u ovom sluchaju uprosh\cj{}ena na ship, stub i masu na vrhu}
\begin{figure}[!h]
%\begin{center}
\vspace*{5.5cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/Top_T615.pdf}}
\hspace{1.8cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/Top_M615.pdf}}
\vspace*{5.0cm}
%\end{center}
\end{figure}
{\cyr \hspace*{4cm} kruto tlo \hspace*{8cm} meko tlo }
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\slide{Pojachanje zemljotresnih talasa}
\begin{figure}[!h]
%\begin{center}
\vspace*{2.5cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/newthesis/figures/Eq_P/P_T_DL_NS.pdf}}
\hspace{1.8cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/newthesis/figures/Eq_P/P_S_DL_NS.pdf}}
\vspace*{5.0cm}
%\end{center}
\end{figure}
{\cyr \hspace*{4cm} Kruto tlo \hspace*{8cm} Meko tlo}
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\slide{Model mosta}
\begin{figure}[!h]
\vspace*{0.2cm}
\begin{center}
{\includegraphics[width=16cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/soilmeshDEEP02.jpg}}
\hspace*{7cm}
\\
\vspace*{4cm}
{\includegraphics[width=11cm]{/home/jeremic/tex/works/Presentation/2003/PEERSiteVisit/I880_system.jpg}}
\hfill
{\includegraphics[width=8cm]{/home/jeremic/tex/works/Presentation/2002/SFBayComputingDay/I880_02.jpg}}
\vspace*{4cm}
\end{center}
\end{figure}
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\slide{Model armirano betonskog rama}
\begin{figure}[!hbpt]
\vspace*{8cm}
\begin{center}
{\includegraphics[width=20cm]{/home/jeremic/tex/works/Papers/2002/PBSE/struct1a.pdf}}
%\caption{\label{struct1a} \small \bf Bent configuration and section details.}
\vspace*{8cm}
\end{center}
\end{figure}
%
% \begin{eqnarray*}
% f_c = f_c^{\prime}
% \left[\
% \frac{2 \epsilon}{\epsilon_0}
% 
% \left( \frac{\epsilon}{\epsilon_0} \right)^2
% \right]
% \;\;\;\;\;
% \mbox{\cyr kada je}
% \;\;\;\;\;
% \epsilon \leq \epsilon_0
% \label{concrete01}
% \end{eqnarray*}
\begin{figure}[!hbpt]
\vspace*{12cm}
\begin{center}
{\includegraphics[width=8cm]{/home/jeremic/tex/works/Papers/2002/PBSE/concretepic01.pdf}}
\hfill
{\includegraphics[width=8cm]{/home/jeremic/tex/works/Papers/2002/PBSE/steelpic01.pdf}}
\hfill
{\includegraphics[width=8cm]{/home/jeremic/tex/works/Papers/2002/PBSE/section03.pdf}}
%\caption{\label{concretepic01} \small \bf StressStrain modeling of concrete.}
\vspace*{8cm}
\end{center}
\end{figure}
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\slide{Temelji i tlo}
%
\begin{figure}[!hbpt]
\vspace*{15cm}
\begin{center}
{\includegraphics[width=18cm]{/home/jeremic/tex/works/Papers/2002/PBSE/bent16meters.pdf}}
%\vspace*{8cm}
\\
\vspace*{14cm}
{\includegraphics[width=30cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/sgBW.pdf}}
\end{center}
\vspace*{16cm}
\end{figure}
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\slide{Prirodni period \\ sistema konstrukcije i tla}
%
\vspace*{4cm}
\begin{figure}[!hbpt]
\begin{center}
{\includegraphics[width=12cm]
{/home/jeremic/oofep/OpenSees/EXAMPLES/ExampleScripts/I880_Bent16/Structure/HingeElement/Disp80FixSpr20hinge_ps.pdf}}
\hfill
{\includegraphics[width=11cm]
{/home/jeremic/oofep/OpenSees/EXAMPLES/ExampleScripts/I880_Bent16/Structure/HingeElement/period20Hinge_ps.pdf}}
\end{center}
\end{figure}
{\cyr
\begin{itemize}
% \vspace*{2.0cm}
\item Veliko omekshanje sistema konstrukcije i tla ako se uzima u obzir interakcija
% \vspace*{1.0cm}
\item Promena prvog prirodnog perioda
\end{itemize}
}
%
%
% \begin{figure}[!hbpt]
% \begin{center}
% {\includegraphics[width=10cm]
% {/home/jeremic/oofep/OpenSees/EXAMPLES/ExampleScripts/I880_Bent16/Structure/HingeElement/period20Hinge.ps.eps}}
% \caption{\label{period01} \small \bf Both
% fully supported and elastic springs cases shown.}
% \end{center}
% \end{figure}
%
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\slide{Usmerenost zemljtresnog udara}
%% %%
%% \begin{table}[!htb]
%% %\vspace*{0.2cm}
%% \caption{\label{scaling} \small \bf Scaling of Earthquake Records to Match Hazard Spectra.}
%% %\vspace*{0.5cm}
%% \begin{center}
%% \begin{tabular}{rrrrrrrrr} \hline
%% & & {\bf Hazard}
%% & \multicolumn{2}{c}{ LPGilroy }
%% & \multicolumn{2}{c}{ LPCorralitos }
%% & \multicolumn{2}{c}{ Kobe } \\ \hline
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Tag & Period &
%% {\bf Spectra} &
%% Sp. Ac~\footnotemark[1] & {\bf Scale } &
%% Sp. Ac~\footnotemark[1] & {\bf Scale } &
%% Sp. Ac~\footnotemark[1] & {\bf Scale } \\ \hline
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% \multicolumn{9}{c} {\bf FixedBased Model } \\ \hline
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% {\bf A} & 0.37 & {\bf 1.470}& 0.611& {\bf 2.41}& 1.146& {\bf 1.28} & 2.482& {\bf 0.59}
%% \\ \hline
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% {\bf B} & 0.77 & {\bf 1.053} & 0.268 & {\bf 3.94} & 1.349 & {\bf 0.78} & 2.482 &
%% {\bf 0.42} \\ \hline
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% {\bf C} & 1.54 & {\bf 0.699} & 0.311 & {\bf 2.25} & 0.239 & {\bf 2.92} & 0.709 &
%% {\bf 0.99} \\ \hline
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% \multicolumn{9}{c} {\bf SpringBased Model } \\ \hline
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% {\bf D} & 1.24 & {\bf 0.820} & 0.301 & {\bf 2.72} & 0.376 & {\bf 2.18} & 0.922 &
%% {\bf 0.89} \\ \hline
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% {\bf E} & 1.60 & {\bf 0.675} & 0.285 & {\bf 2.37} & 0.193 & {\bf 3.50} & 0.639 &
%% {\bf 1.06} \\ \hline
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% {\bf F} & 2.00 & {\bf 0.513} & 0.170 & {\bf 3.02} & 0.175 & {\bf 2.93} & 0.422 &
%% {\bf 1.22} \\ \hline
%% \end{tabular}
%% %\vspace*{1.7cm}
%% \end{center}
%% \end{table}
%% %
%% %
%% \footnotetext[1]{\scriptsize
%% corresponds to the spectral acceleration (Sp. Ac) at the
%% designated period value.}
%%
%
\begin{figure}[!hbpt]
\vspace*{9cm}
\begin{center}
{\includegraphics[width=18cm]{/home/jeremic/tex/works/Papers/2002/PBSE/Map02.pdf}}
\end{center}
\end{figure}
%
%
%
%
% \begin{eqnarray}
% Transverse Component = FP \cos{\theta} + FN \sin{\theta}
% \end{eqnarray}
% %
% The response spectra of the resulting timehistories are displayed in Figures
% \ref{fixedBases}(a)(f).
% %
% \begin{figure}[!hbpt]
% \begin{center}
% \mbox{(a)}{\includegraphics[width=6.3cm]{/home/jeremic/tex/works/Papers/2002/PBSE/fixedBasea.pdf}}
% \hfill
% \mbox{(b)}{\includegraphics[width=6.3cm]{/home/jeremic/tex/works/Papers/2002/PBSE/fixedBaseb.pdf}}
% \\
% \mbox{(c)}{\includegraphics[width=6.3cm]{/home/jeremic/tex/works/Papers/2002/PBSE/fixedBasec.pdf}}
% \hfill
% \mbox{(d)}{\includegraphics[width=6.3cm]{/home/jeremic/tex/works/Papers/2002/PBSE/springBasea.pdf}}
% \\
% \mbox{(e)}{\includegraphics[width=6.3cm]{/home/jeremic/tex/works/Papers/2002/PBSE/springBaseb.pdf}}
% \hfill
% \mbox{(f)}{\includegraphics[width=6.3cm]{/home/jeremic/tex/works/Papers/2002/PBSE/springBasec.pdf}}
% \caption{\label{fixedBases} \small \bf Response Spectra of Scaled Accelerograms.
% FixedBase Model Matched Hazard Curve at (a) T = 0.374 sec ; (b) T = 0.77 sec;
% (c) T = 1.54 sec ; SoilSpring Model: Matched Hazard Curve at (d) T = 1.2 sec
% ; (e) T = 1.6 sec ;
% (f) T = 2.0 sec .}
% \end{center}
% \end{figure}
%
%
% \begin{figure}[!hbpt]
% \begin{center}
% \mbox{(a)}{\includegraphics[width=6cm]{springBasea.ps}}
% \\
% \mbox{(b)}{\includegraphics[width=6cm]{springBaseb.ps}}
% \\
% \mbox{(c)}{\includegraphics[width=6cm]{springBasec.ps}}
% \caption{\label{springBase} \small \bf Response Spectra of Scaled Accelerograms for
% SoilSpring Model: Matched Hazard Curve at (a) T = 1.2 sec ; (b) T = 1.6 sec ;
% (c) T = 2.0 sec .}
% \end{center}
% \end{figure}
%
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\slide{Interakcija povoljna}
\begin{figure}[!h]
%\begin{center}
\vspace*{5.2cm}
{\includegraphics[width=12cm]{/home/jeremic/oofep/OpenSees/EXAMPLES/ExampleScripts/I880_Bent16/Structure/Earthquake/Damping/SFSIbeneficialA.pdf}}
\hfill
{\includegraphics[width=12cm]{/home/jeremic/oofep/OpenSees/EXAMPLES/ExampleScripts/I880_Bent16/Structure/Earthquake/Damping/SFSIbeneficialB.pdf}}
\vspace*{1.0cm}
%\end{center}
\end{figure}
\vspace*{2.2cm}
KobeJMA
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\slide{Interakcija nepovoljna}
\begin{figure}[!h]
%\begin{center}
\vspace*{5.2cm}
{\includegraphics[width=12cm]{/home/jeremic/oofep/OpenSees/EXAMPLES/ExampleScripts/I880_Bent16/Structure/Earthquake/Damping/SFSIdetrimentalA.pdf}}
\hfill
{\includegraphics[width=12cm]{/home/jeremic/oofep/OpenSees/EXAMPLES/ExampleScripts/I880_Bent16/Structure/Earthquake/Damping/SFSIdetrimentalB.pdf}}
\vspace*{1.0cm}
%\end{center}
\end{figure}
\vspace*{2.2cm}
LPCorralitos
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\slide{Dalja analiza ponashanja mosta je u toku}
%\begin{large}
{\cyr
\begin{itemize}
\vspace*{1.0cm}
\item Kompletan model mosta sa tlom
\begin{itemize}
\item Efekti prostiranja zemljotresnih talasa (veza sa regionalnim simulacijama koje rade geofizichari)
\item Lokalno pojachanje i umanjenje zemljotresnog udara
\item Brzina prostiranja zemljotresnih talasa kroz tlo i mostovsku konstrukciju
\item Zemljotresna izolacija
\end{itemize}
%\vspace*{1.0cm}
%\item
%
%\vspace*{1.0cm}
%\item
%
%%\vspace*{1.0cm}
%\item
\begin{normalsize}
\begin{figure}[!htbp]
\vspace*{0.50cm}
\begin{center}
{\includegraphics[width=18cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DRM0101.pdf}}
\vspace*{2.50cm}
\end{center}
%\vspace*{0.3cm}
\end{figure}
\end{normalsize}
\end{itemize}
}
%\end{large}
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\slide{Programski sistem {\rm \Large OpenSees}}
%\begin{large}
{\cyr
\begin{itemize}
\vspace*{3.0cm}
\item Rezultat rada grupa istrazhivacha sa Berklija, Dejvisa, Stanforda i San Diega (za sada)
\vspace*{1.0cm}
\item Programski okvir koji omogu\cj{}ava razvoj i nadgradnju raznih metoda
konachnih elemenata za statichku i dinamichku analizu solida i konstrukcija napravnjenih od
gradjevinskih materijala
\vspace*{1.0cm}
\item Labav konglomerat procedura, funkcija, metoda, pisanih u programskim
jezicima {\rm C, C++, Fortran, Tcl})
\vspace*{1.0cm}
\item Programski sistem {\rm OpenSees, (Open System for Earthquake Engineeing
Simulations)}
\vspace*{1.0cm}
\item U toku je vrlo aktivan razvoj i nadgradnja:
\end{itemize}
}
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\slide{Izbor elemenata, materijala, metoda...}
%\begin{large}
{\cyr
\begin{itemize}
\vspace*{1.05cm}
\item elastichni i neelastichni materijali (za tlo, beton, chelik, stenske
mase...),
\vspace*{0.35cm}
\item mnoshtvo elemenata (solidi (4,8,20,27, $\bar{B}$, {\rm upU}), shtapovi (metoda
krutosti, sila), ploche (savijanje, shajbne, ljuske),...),
\vspace*{0.35cm}
\item metode pra\cj{}enja ravnotezhne linije ({\rm Newton, QuasiNewton, BFGS,...}),
\vspace*{0.35cm}
\item kontrola inkrementalnog koraka (kontola optere\cj{}enja, pomeranja, duzhina
luka,...),
\vspace*{0.35cm}
\item dinamichke metode analize ({\rm Newmark, Wilson, HilberHughesTaylor}),
\vspace*{0.35cm}
\item solveri linearnih sistema ({\rm UMFPack, SkyLine, BandGeneral,...})
\vspace*{0.35cm}
\item sekvencijalno i paralelno izvrshenje (rachunari sa raspodeljenom memorijom)
\vspace*{0.35cm}
\item baze podataka o modelima i rezultatima ({\rm mySQL, BerkeleyDB, XML})
\vspace*{0.35cm}
\item grafichko postprocesiranje ({\rm Fantom, Joey3D, VisSees, GID,...})
\vspace*{0.35cm}
\item {\rm OpenSees} sistem je dostupan u izvornom kodu, uz veliki broj
primera, uput\/stvo se stalno nadogradjuje...
\end{itemize}
%\vspace*{1.0cm}
%\item
}
%\end{large}
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\slide{Umesto zakljuchaka}
%\begin{large}
{\cyr
\begin{itemize}
\vspace*{2.0cm}
\item Potreba da se shto bolje modeluje ponashanje konstrukcija i tla pri
normalnim i izvanrednim optere\cj{}enjima
\vspace*{1.5cm}
\item Omogu\cj{}iti projektantu, inzhinjeru da ima pri ruci shto bolja orudja za
predvidjanje ponashanja konstrukcije
\vspace*{1.5cm}
\item Razvoj sistema {\rm OpenSees} upravo prolazi kroz promene,
\vspace*{1.5cm}
\item Ve\cj{}a otvorenost za saradnju i nadgradnju
\vspace*{1.5cm}
\item Predvidjena namena sistema za opshte drushtvenu korist
%\vspace*{1.0cm}
%\item
\end{itemize}
}
%\end{large}
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% \\
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\end{document}
\bye