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%\MyLogo{{\cyrmali Jeremi\cj{} \JB{}}}
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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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\vspace*{2.50truecm}


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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}
% 
% 
% 
% %\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  NSF--PEER \#~EEC-9701568,
% %Cal--EPA \#~99-01337V,
% \item Supported in part by the NSF, PEER, Caltrans, and Cal--EPA.
% 
% % \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  elastichno--plastichnih  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  Soil--Structure 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{Elasto--plastichnost  u kalupu}

\begin{normalsize}


{\cyr
\begin{itemize}

\vspace{2.4cm}
  \item Ve\cj{}ina elasto--plastichnih 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 elasto--plastichnih 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 elasto--plastichnosti}

\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{Elasto--plastichnost 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{Non--Level 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}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\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_e-K^{\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}


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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_e-K^{\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 pod--matricama $M_{be}$,$K_{be}$,$M_{eb}$,$K_{eb}$
%\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 ne--elastichan!}


% \item  The only input wave field is the one for the nodes of this layer of elements.
\end{itemize}
}
%\end{large}





% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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/PEER-Site-Visit/I880_system.jpg}}
\hfill
{\includegraphics[width=8cm]{/home/jeremic/tex/works/Presentation/2002/SFBayComputingDay/I-880_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   Stress--Strain 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/I-880_Bent16/Structure/HingeElement/Disp80FixSpr20hinge_ps.pdf}}
\hfill
{\includegraphics[width=11cm]
{/home/jeremic/oofep/OpenSees/EXAMPLES/ExampleScripts/I-880_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/I-880_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}{||r||r||r|r|r|r|r|r|r||} \hline
%%           &  & {\bf Hazard}
%%            & \multicolumn{2}{|c|}{  LP--Gilroy         }
%%            & \multicolumn{2}{|c|}{  LP--Corralitos     }
%%            & \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 Fixed--Based 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 Spring--Based 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 time-histories 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.
%   Fixed-Base Model Matched Hazard Curve at (a) T = 0.374 sec ; (b) T = 0.77 sec;
%   (c)  T = 1.54 sec ; Soil-Spring  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
%  Soil-Spring  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/I-880_Bent16/Structure/Earthquake/Damping/SFSI-beneficialA.pdf}}
\hfill
{\includegraphics[width=12cm]{/home/jeremic/oofep/OpenSees/EXAMPLES/ExampleScripts/I-880_Bent16/Structure/Earthquake/Damping/SFSI-beneficialB.pdf}}
\vspace*{-1.0cm}
%\end{center}
\end{figure}


\vspace*{2.2cm}

Kobe--JMA

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\slide{Interakcija nepovoljna}
\begin{figure}[!h]
%\begin{center}
\vspace*{-5.2cm}
{\includegraphics[width=12cm]{/home/jeremic/oofep/OpenSees/EXAMPLES/ExampleScripts/I-880_Bent16/Structure/Earthquake/Damping/SFSI-detrimentalA.pdf}}
\hfill
{\includegraphics[width=12cm]{/home/jeremic/oofep/OpenSees/EXAMPLES/ExampleScripts/I-880_Bent16/Structure/Earthquake/Damping/SFSI-detrimentalB.pdf}}
\vspace*{-1.0cm}
%\end{center}
\end{figure}
 
\vspace*{2.2cm}

LP--Corralitos 

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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  ne--elastichni  materijali (za tlo, beton, chelik, stenske
mase...),  
           
     \vspace*{0.35cm}
     \item mnoshtvo  elemenata  (solidi (4,8,20,27, $\bar{B}$, {\rm u--p--U}),  shtapovi (metoda
     krutosti, sila), ploche (savijanje, shajbne, ljuske),...),

     \vspace*{0.35cm}
     \item metode pra\cj{}enja ravnotezhne linije ({\rm Newton, Quasi--Newton, 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, Hilber--Hughes--Taylor}),

     \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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