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%{\footnotesize
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\vspace*{0.0truecm}
\begin{center}
{\Large \bf
%\vspace*{1.5truecm} \\
\rule[-3mm]{0cm}{1.3cm} A Brief Overview of the \\
\rule[-3mm]{0cm}{1.3cm} NEESgrid Simulation Platform OpenSees:    \\
\rule[-3mm]{0cm}{1.3cm} Application to the   \\
\rule[-3mm]{0cm}{1.3cm} Soil--Foundation--Structure Interaction Problems  \\
}
\end{center}
%%%%%%%%%%%%%%%%%%%%%%%%%%





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\vspace*{1.0truecm}


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\begin{large}
\begin{center}
{\bf Boris Jeremi{\' c}}
\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{small}
\begin{center}
{Third  UJNR  Workshop on Soil-Structure  Interaction}\\
{March  29-30,  2004, Vallombrosa  Center,  Menlo  Park,  California}\\
\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
research  students
Xiaoyan Wu (UW)
Ritu Jain (UCD),
%Qing Liu (UCD),
Jinxiu Liao (UCD).
\end{description}

\end{small}
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\slide{Leitmotiv}


\begin{large}


\begin{itemize}


\vspace*{1.0cm}
\item  Create  high  fidelity  models of constructed facilities
(bridges, buildings, port structures, dams...).

\vspace*{1.0cm}
\item Models will live concurrently  with  the  physical  system
they  represent.

\vspace*{1.0cm}
\item Models to provide  owners  and  operators  with  the
capabilities to assess operations and future performance.

\vspace*{1.0cm}
\item  Use  observed  performance  to update and validate models
through simulations.

\end{itemize}
\end{large}
%
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\slide{Presentation Overview}
\begin{large}


\begin{itemize}


\vspace*{1.0cm}
\item The NEES MiniGrand Challenge Project

  \begin{itemize}
    \item  Validation experiments
    \item  Simulation challenge
  \end{itemize}

\vspace*{1.0cm}
\item  OpenSees NEESgrid simulation platform

  \begin{itemize}
%    \vspace*{1.0cm}

        \vspace*{-0.1cm}
        \item  Template Elasto--Plasticity

        \vspace*{-0.1cm}
        \item Full Coupling of Solid and Fluid

        \vspace*{-0.1cm}
        \item Seismic Motions (FEM input)

        \vspace*{-0.1cm}
        \item Distributed Memory Parallel Computing

        \vspace*{-0.1cm}
        \item  General Large Deformations

%        \item Visualization



  \end{itemize}

%\item

\end{itemize}

\end{large}






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% 
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \slide{Goals of Validation}
%  
%  \begin{large}
%  
%  Quantification  of  uncertainties  and errors in the computational model and the
%  experimental measurements
%  
%  
%  
%  \begin{itemize}
%  
%  \vspace*{-0.4cm}
%   \item Goals on validation
%     \begin{itemize}
%       \item  Tactical  goal:  Identification  and minimization of uncertainties and
%       errors in the computational model
%       \item  Strategic  goal:  Increase  confidence  in the quantitative predictive
%       capability of the computational model
%     \end{itemize}
%  
%  \vspace*{-0.4cm}
%   \item Strategy  is to reduce as much as possible the following:
%     \begin{itemize}
%       \item Computational model uncertainties and errors
%       \item Random (precision) errors and bias (systematic) errors in the experiments
%       \item Incomplete physical characterization of the experiment
%    \end{itemize}
%  
%  \end{itemize}
%  
%  
%  \end{large}
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%  
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%--- \slide{Validation Procedure Uncertainty}
%--- 
%--- \begin{large}
%--- 
%--- \begin{itemize}
%--- 
%--- \vspace*{1cm}
%---  \item  Aleatory uncertainty $\rightarrow$ inherent variation associated with the
%---  physical  system  of  the environment (variation in external excitation, material
%---  properties...).  Also  know  known  as irreducible uncertainty, variability and
%---  stochastic uncertainty.
%--- 
%--- 
%--- \vspace*{1cm}
%---  \item  Epistemic uncertainty $\rightarrow$ potential deficiency in any phase of
%---  the  modeling  process  that is due to lack of knowledge (poor understanding of
%---  mechanics...).  Also known as reducible uncertainty, model form uncertainty and
%---  subjective uncertainty
%---  
%--- 
%--- \end{itemize}
%--- 
%--- 
%--- \end{large}
%--- 
%--- 
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%--- \slide{Types of Physical Experiments}
%--- 
%--- \begin{large}
%--- \begin{itemize}
%--- 
%---    \vspace*{1.0truecm}
%---    \item {\bf Traditional Experiments}
%---      \begin{itemize}
%---        \item Improve the fundamental understanding of physics involved
%---        \item Improve the mathematical models for physical phenomena
%---        \item Assess component performance 
%---      \end{itemize}
%--- 
%---    \vspace*{1.0truecm}
%---    \item {\bf Validation Experiments}
%---      \begin{itemize}
%---        \item Model validation experiments
%---        \item  Designed  and  executed  to  quantitatively estimate mathematical
%---        model's ability to simulate well defined physical behavior
%---        \item   The  simulation  tool (SimTool) (conceptual  model,  computational  model,
%---        computational solution) is the customer
%---      \end{itemize}
%--- 
%--- 
%--- \end{itemize}
%--- \end{large}
%--- 
%--- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\slide{Validation Experiments }

\begin{large}
\begin{itemize}

   \vspace*{0.0truecm}
   \item  A  validation  experiment  should be jointly designed and executed by
   experimentalist and computationalist
     \begin{itemize}
       \item Need for close working relationship from inception to documentation
       \item Elimination of typical competition between each
       \item  Complete  honesty  concerning  strengths  and  weaknesses  of both
       experimental and computational simulations
     \end{itemize}


   \vspace*{0.0truecm}
   \item A validation Experiment should be designed to capture the relevant physics
     \begin{itemize}
       \item Measure all important modeling data in the experiment
       \item  Characteristics  and  imperfections  of  the experimental facility
       should be included in the model
     \end{itemize}


\end{itemize}
\end{large}

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%--- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%--- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%--- \slide{Validation Experiments (contd)}
%--- 
%--- \begin{large}
%--- \begin{itemize}
%--- 
%---    \vspace*{0.0truecm}
%---    \item  A  validation  experiment  should  use any possible synergism between
%---    experiment and computational approaches
%---      \begin{itemize}
%---        \item Offset strength and weaknesses of computations and experiments
%---        \item  Use high confidence simulations for simple physics to calibrate or
%---        improve the characterization of the experimental facility
%---        \item    Conduct  experiments  with a  hierarchy of physics complexity  to
%---        determine where the computational simulation breaks (remember, SimTool is
%---        the customer!)
%---      \end{itemize}
%--- 
%--- 
%---    \vspace*{0.0truecm}
%---    \item  Maintain independence  between computational and experimental results
%---      \begin{itemize}
%---        \item Blind comparison, the computational simulations should be predictions
%---        \item Neither side is allowed to use fudge factors, parameters
%---      \end{itemize}
%--- 
%--- 
%--- \end{itemize}
%--- \end{large}
%--- 
%--- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%--- % %%%%
%--- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%--- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%--- \slide{Validation Experiments (contd)}
%--- 
%--- \begin{large}
%--- \begin{itemize}
%--- 
%---    \vspace*{0.0truecm}
%---    \item  Validate experiments on unit level problems, hierarchy of experimental
%---    measurements   should   be   made   which  present  an  increasing  range  of
%---    computational difficulty
%---      \begin{itemize}
%---        \item Use of qualitative data (e.g. visualization) and quantitative data
%---        \item  Computational  data  should be processed to match the experimental
%---        measurement techniques
%---      \end{itemize}
%--- 
%---    \vspace*{0.0truecm}
%---    \item Experimental uncertainty analysis should be developed and employed
%---      \begin{itemize}
%---        \item Distinguish and quantify random and correlated bias errors
%---        \item   Use  symmetry  arguments  and  statistical  methods  to  identify
%---        correlated bias errors
%---        \item Make uncertainty estimates on input quantities needed by the SimTool
%---      \end{itemize}
%--- 
%--- 
%--- 
%--- 
%--- 
%--- 
%--- \end{itemize}
%--- \end{large}
%--- 
%--- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%--- % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%--- 
%--- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%--- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%--- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%--- \slide{Prediction}
%--- 
%--- \begin{large}
%--- \begin{itemize}
%--- 
%---    \vspace*{0.7truecm}
%---    \item  Prediction:  use  of  computational  model  to foretell the state of a
%---    physical   system   under  consideration  under  conditions  for  which  the
%---    computational model has not been validated
%--- 
%---    \vspace*{0.7
%---    truecm}
%---    \item Validation does not directly make a claim about the accuracy of a prediction
%---      \begin{itemize}
%---        \item Computational models are easily misused (unintentionally or intentionally)
%---        \item  How  closely  related  are  the  conditions  of the prediction and
%---        specific cases in validation database
%---        \item How well is physics of the problem understood
%--- 
%---      \end{itemize}
%--- 
%--- 
%--- \end{itemize}
%--- \end{large}
%--- 
%--- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \slide{Relation Between Validation and Prediction}
% 
% \begin{large}
% 
% Quantification of confidence in a prediction: 
% 
% \begin{itemize}
% 
%    \vspace*{0.8truecm}
%    \item How do I quantify validation and its inference value in a predictions?
% 
%    \vspace*{0.8truecm}
%    \item  How do I quantify verification and its inference value in a prediction?
% 
%    \vspace*{0.8truecm}
%    \item  How  far are individual experiments in my validation database from my
%    physical system of interest?
% 
% %   \item 
% 
% \end{itemize}
% \end{large}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\slide{Application Domain}

\begin{large}



\vspace*{0.3cm}

\begin{figure}[!h]
\begin{center}
%\vspace*{-2.5cm}
{\includegraphics[width=8.0cm]{/home/jeremic/tex/works/Presentation/2004/VandV/VPI03.pdf}}
%\vspace*{-1.0cm}
\end{center}
\end{figure}

%\vspace*{-0.4cm}

\begin{itemize}
\vspace*{-0.1cm}
 \item Inference $\Rightarrow$ Based on {\bf physics} or {\bf statistics}
\vspace*{-0.1cm}
 \item  Validation domain $\rightarrow$ non--convex aggregation of physical tests 
\vspace*{-0.1cm}
 \item Physical experiments (NEES) provide for non--overlapping validation domain
\end{itemize}


\end{large}

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




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\slide{NEES SFSI Project}

%\begin{large}



\vspace*{-0.60cm}

\begin{figure}[!h]
\begin{center}
%\vspace*{-2.5cm}
{\includegraphics[width=19.0cm]{/home/jeremic/tex/works/Conferences/2004/SSI-US-Japan-inPaloAlto/Present/NEESminichallengeConcept.jpg}}
\end{center}
\end{figure}
\vspace*{-0.5cm}


Participants:  Wood  (UT),  Anagnos  (SHSU), Arduino (UW), Eberhard (UW), Fenves
(UCB),  Finholt  (UM),  Futrelle  (NCSA),  Grant (UK), Jeremi{\'c} (UCD), Kramer
(UW),  Kutter (UCD), Matamoros (UK), McMullin (SHSU), Ramirez (PU), Rathje (UT),
Saidi (UNR), Sanders (UNR), Stokoe (UT), Wilson (UCD).
              
%
%  \begin{figure}[!h]
%  \begin{center}
%  %\vspace*{-2.5cm}
%  {\includegraphics[width=14.0cm]{/home/jeremic/tex/works/Conferences/2004/SSI-US-Japan-inPaloAlto/Present/PrototypeBridgeDRM.jpg}}
%  %\vspace*{-5.0cm}
%  \end{center}
%  \end{figure}
%  
%\vspace*{-0.4cm}

% \begin{itemize}
% %\vspace*{0.2cm}
%  \item 
% %\vspace*{0.2cm}
%  \item 
% %\vspace*{0.2cm}
%  \item 
% \end{itemize}
% 

%\end{large}

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


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\slide{Validation SFSI Experiments}

\begin{large}



\vspace*{0.5cm}

\begin{figure}[!h]
\begin{center}
%\vspace*{-2.5cm}
{\includegraphics[width=8.1cm]{/home/jeremic/tex/works/Conferences/2004/SSI-US-Japan-inPaloAlto/Present/UCDavis.jpg}}
\hfill
{\includegraphics[width=8.1cm]{/home/jeremic/tex/works/Conferences/2004/SSI-US-Japan-inPaloAlto/Present/UTAustin.jpg}}
\hfill
{\includegraphics[width=8.1cm]{/home/jeremic/tex/works/Conferences/2004/SSI-US-Japan-inPaloAlto/Present/UNReno}}
%\vspace*{-5.0cm}
\end{center}
\end{figure}


%
%  \begin{figure}[!h]
%  \begin{center}
%  %\vspace*{-2.5cm}
%  {\includegraphics[width=14.0cm]{/home/jeremic/tex/works/Conferences/2004/SSI-US-Japan-inPaloAlto/Present/PrototypeBridgeDRM.jpg}}
%  %\vspace*{-5.0cm}
%  \end{center}
%  \end{figure}
%  
%\vspace*{-0.4cm}

\begin{itemize}
\vspace*{-0.1cm}
 \item UC Davis centrifuge, single piles, bents,  frames, scale 1/50
\vspace*{-0.1cm}
 \item UT Austin, pile, pile--column, bent, scale 1/4
\vspace*{-0.1cm}
 \item UN Reno, frame (3 bents), scale 1/4
\vspace*{-0.1cm}
 \item Purdue U., pier components, scale 1/2 and 1/1 
\end{itemize}


\end{large}

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







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\slide{The OpenSees Platform \\ SFSI components}
\begin{large}

\begin{itemize}


%%\vspace*{0.3cm}
%\item Fairly strictly based on Thermodynamics (Geomechanics)

\vspace*{-0.4cm}
\item    Small  deformation,  single  phase, linear and nonlinear elasticity and
incremental template elasto--plasticity  (PY springs, 2D/3D solids)

%\vspace*{0.3cm}
\vspace*{-0.4cm}
\item  General, large deformation huperelasticity and hyperelasto--plasticity for solids

%\vspace*{0.2cm}
\vspace*{-0.4cm}
\item  Full  coupling  of  solid  and  fluid  ($u-p-U$), (small deformations only at the moment)

\vspace*{-0.4cm}  
\item  Elastic  and  inelastic  beam--column elements, elastic
plate and plane stress elements (shells), small and large deformations

%\vspace*{0.3cm}
\vspace*{-0.4cm}
\item  Seismic  input  through  the  Domain Reduction Method

\end{itemize}
%
\end{large}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \slide{Enabling Technologies }
% \begin{large}
% 
% \begin{description}
% 
% \vspace*{0.5cm}
% \item  Template Elasto--Plasticity
% 
% \vspace*{0.5cm}
% \item  General Large Deformations
% 
% \vspace*{0.5cm}
% \item Full Coupling of Solid and Fluid
% 
% \vspace*{0.5cm}
% \item Domain Reduction Method
% 
% \vspace*{0.5cm}
% \item Distributed Memory Parallel Computing
% 
% \vspace*{0.5cm}
% \item Visualization
% 
% 
% \end{description}
% %
% \end{large}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\slide{Template Elasto--Plasticity }

\begin{large}
\begin{itemize}
    \item Yield surfaces: von Mises,
                          Drucker--Prager,
                          Rounded Mohr--Coulomb,
                          Cam--Clay,
%                          Manzari--Dafalias (bounding surface plasticity) \verb!MD!,
                          Parabolic Leon,
%       \vspace{1.0cm}
    \item Plastic flow directions (potential surfaces): von Mises,
                          Drucker--Prager,
                          Rounded Mohr--Coulomb,
                          Cam--Clay,
                          Manzari--Dafalias,
                          Parabolic Leon,
    \item Isotropic or kinematic hardening/softening
      \begin{itemize}
        \item linear and/or nonlinear isotropic hardening/softening
        \item linear or nonlinear kinematic hardening/softening
%          \begin{itemize}
%            \item Armstrong--Fredericks nonlinear kinematic hardening/softening  of up to 4 tensorial internal variables
%            \item Bounding surface nonlinear (Dafalias--Popov) kinematic hardening/softening  of up to 4 tensorial internal variables
%          \end{itemize}
      \end{itemize}
%        \vspace{0.4cm}
    \item Hierarchical database of models (by materials)
\end{itemize}
\end{large}

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\slide{Template  Examples}



\vspace*{-0.5cm}

\begin{figure}[!hbpt]
\begin{center}
%{\includegraphics[width=5.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/DP_DP_pp_q_eq.pdf}}
%{\includegraphics[width=5.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/DP_DP_pp_ev_eq.pdf}}
%\hspace*{0.4cm}
%{\includegraphics[width=5.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/DP_vM_ls_q_eq.pdf}}
%{\includegraphics[width=5.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/DP_vM_ls_ev_eq.pdf}}
%\vspace*{-3cm}
%\\
{\includegraphics[width=5.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cam_S_SOC_q_eq.pdf}}
{\includegraphics[width=5.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cam_S_SOC_ev_eq.pdf}}
\hspace*{0.4cm}
{\includegraphics[width=5.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cam_S_HOC_q_eq.pdf}}
{\includegraphics[width=5.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cam_S_HOC_ev_eq.pdf}}
\vspace*{-3cm}
\\
{\includegraphics[width=5.45cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/DP_MD_ltmd_NC_q_eq.pdf}}
{\includegraphics[width=5.45cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/DP_MD_ltmd_NC_ev_eq.pdf}}
\hspace*{0.4cm}
{\includegraphics[width=5.45cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/DP_MD_ltmd_HOC_q_eq.pdf}}
{\includegraphics[width=5.45cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/DP_MD_ltmd_HOC_ev_eq.pdf}}
\vspace*{-3cm}
\\
{\includegraphics[width=5.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cam01_SOC_cyc_q_eq.pdf}}
{\includegraphics[width=5.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cam01_SOC_cyc_ev_eq.pdf}}
\hspace*{0.4cm}
{\includegraphics[width=5.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/DP_MD_ltmd_cyc_q_eq.pdf}}
{\includegraphics[width=5.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/DP_MD_ltmd_cyc_ev_eq.pdf}}
\vspace*{-3cm}
\end{center}
\end{figure}
%

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \slide{Template Cyclic Examples}
% 
% \vspace*{-1cm}
% 
% %
% \begin{figure}[!hbpt]
% \begin{center}
% {\includegraphics[width=6.2cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/DP_vM_nlt_cyc_q_eq.pdf}}
% {\includegraphics[width=6.2cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/DP_vM_nlt_cyc_ev_eq.pdf}}
% \vspace*{-3cm}
% \\
% {\includegraphics[width=6.2cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cam01_SOC_cyc_q_eq.pdf}}
% {\includegraphics[width=6.2cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cam01_SOC_cyc_ev_eq.pdf}}
% \vspace*{-3cm}
% \\
% {\includegraphics[width=6.2cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/DP_MD_ltmd_cyc_q_eq.pdf}}
% {\includegraphics[width=6.2cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/DP_MD_ltmd_cyc_ev_eq.pdf}}
% \end{center}
% \end{figure}
% %
% \vspace*{-2cm}
% 
% 
% 
% 
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
\slide{ Single Pile in Layered Soils}

\vspace*{-4.5truecm}


\begin{figure}[!htbp]
\begin{center}
\includegraphics[width=11.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/MQP_dsand_UFmid2hdp0.pdf}
\hfill
\includegraphics[width=11.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/MQP_sand_wsfclay_UFmid2hdp0.pdf}
\end{center}
%\vspace*{-0.3cm}
\end{figure}

\vspace*{-4.5truecm}
\begin{normalsize}
\begin{figure}[!hbpt]
\begin{center}
%{\includegraphics[height=7.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/spUF_plastified_clay_xz_gs.jpg}}
%{\includegraphics[height=7.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/spUF_plastified_clay_sand_xz_gs.jpg}}
{\includegraphics[height=8.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/spUF_plastified_sand_xz_gs.jpg}}
\hfill
\includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/spUFmesh.jpg}
\hfill
{\includegraphics[height=8.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/spUF_plastified_sand_clay_xz_gs.jpg}}
\end{center}
\vspace*{-1truecm}
\end{figure}
\end{normalsize}




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

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\slide{ Pile Group Simulations}

\vspace*{-3.5cm}
\begin{figure}[!hbpt]
\begin{center}
%{\includegraphics*[width=12cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/PileGroups/p4X3_Joey_iso.pdf}}
%\hfill
{\includegraphics*[width=12cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/PileGroups/p4X3_PlasticZone_iso.pdf}}
\hfill
{\includegraphics*[width=12cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/PileGroups/LoadRatio_per_pile_Dense_pg4x3.pdf}}
%{\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/PileGroups/p4X3_PlasticZone_xz.pdf}}
%\\
\end{center}
\end{figure}
\vspace*{-2.3cm}

\begin{itemize}
 \item Plastic zone
 \item Load distribution
 \item Pile interactions (P-Y)

\end{itemize}

\vspace*{-9.0cm}
\begin{figure}[!hbpt]
%\begin{center}
\hspace*{8.0cm}
{\includegraphics[width=16cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/PileGroups/pg4x3_p_y_allpiles_20.jpg}}
%\end{center}
\vspace*{-2.3cm}
\end{figure}



% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \slide{Validation with Centrifuge Tests}
% 
% \begin{figure}[!hbpt]
% \vspace*{-8.3cm}
% \begin{center}
% {\includegraphics[width=22.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/PileGroups/Com_LoadRatio_per_row_Dense_pg4x3.pdf}}
% \end{center}
% \vspace*{-8.3cm}
% \end{figure}
% %
% %
% %   \begin{large}
% %   \begin{itemize}
% %   \item Good agreement for larger loads
% %   \end{itemize}
% %   \end{large}
% %
% %
% %



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\slide{Full Coupling of Solid and Fluid }

%\begin{large}



%\begin{itemize}
%
%%\vspace*{0.5cm}
%%\item  General  form, full coupling, (currently only small deformations)
%
%
%%%\vspace*{0.5cm}
%%\item DOFs: $\bar{u}_{Lj} \rightarrow$ solid displacement
%%$\bar{p}_L \rightarrow$ fluid pressure
%%$\bar{U}_{Lj} \rightarrow$ fluid displacement
%
%
%%% 
%\end{itemize}

% \vspace*{-1.0cm}
 
 \begin{small}
%  \begin{eqnarray}
\noindent
$
  \left[
  \begin{array}{ccc}
   (M_s)_{KijL} & 0 & 0 \\
  0         & 0 & 0 \\
  0 & 0 & (M_f)_{KijL} \\
  \end{array}
  \right]
  \left[
  \begin{array}{c}
  \ddot{\bar{u}}_{Lj} \\
  \ddot{\bar{p}}_L \\
  \ddot{\bar{U}}_{Lj} \\
  \end{array}
  \right]
  +
\\
  \left[
  \begin{array}{ccc}
  (C_1)_{KijL} & 0 & -(C_2)_{KijL} \\
  0         & 0 & 0 \\
  -(C_2)_{LjiK} & 0 & (C_3)_{KijL} \\
  \end{array}
  \right]
  \left[
  \begin{array}{c}
  \dot{\bar{u}}_{Lj} \\
  \dot{\bar{p}}_L \\
  \dot{\bar{U}}_{Lj} \\
  \end{array}
  \right]   
   +
\\
  \left[
  \begin{array}{ccc}
  (K^{EP})_{KijL} &  -(G_1)_{KiL}  & 0 \\
   -(G_1)_{LjK} &  -(P)_{KL} & -(G_2)_{LjK}  \\
   0  & -(G_2)_{KiL}   & 0 \\
  \end{array}
  \right]
  \left[
  \begin{array}{c}
  {\bar{u}}_{Lj} \\
  {\bar{p}}_L \\
  {\bar{U}}_{Lj} \\
  \end{array}
  \right]
  =
\\
  \left[
  \begin{array}{c}
  ({\bar{f}}_s)_{Ki} \\
  {0}                \\
  ({\bar{f}}_f)_{Ki} \\
  \end{array}
  \right]
$
%  \end{eqnarray}
  %
%\vspace*{1.0cm}
%where
 
 \vspace*{2.5cm}
%   \begin{eqnarray*}
  $(C_1)_{KijL} =  (C_2)_{KijL}  =  (C_3)_{KijL}    = $
  \\ ~ \\
  $\int_\Omega N_K^{u,U} n^2 k_{ij}^{-1} N_L^{u,U} d\Omega $
% \nonumber
% \end{eqnarray*}

 
 \end{small}


\vspace*{-17.5cm}
\begin{figure}[!hbpt]
\begin{center}
\hspace*{14cm}
%\includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/XiaoyanWu/06sept2002/40elementlink_2.pdf}
%\hspace*{-2cm}
\includegraphics[width=14cm]{/home/jeremic/tex/works/Thesis/XiaoyanWu/06sept2002/40elementlink_3.pdf}
%\hspace*{-4cm}
%\includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/XiaoyanWu/06sept2002/40elementlink_5.pdf}
%\hspace*{-2cm}
%\includegraphics[width=10cm]{paper.ps}
\end{center}
\end{figure}


%Half space, ramp load $k=10^{-3,5}m/s$



%
%\end{large}
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\slide{Seismic Input}


\begin{large}
\begin{itemize}
  \item  Domain Reduction Method, (Bielak et al.  at CMU)
%  \item Superposition of the large scale domain $+$ local geologic  feature
  \item Seismic motions  and  accelerations input  at the layer of
  elements that encompass an elastic--plastic zone (using SHAKE,
  Green's functions, Quake, SCEC...), non--reflective boundaries
\end{itemize}
\end{large}

\begin{normalsize}
\begin{figure}[!htbp]
\vspace*{-1.0cm}
\begin{center}
{\includegraphics[width=25cm]{/home/jeremic/tex/works/Conferences/2004/SSI-US-Japan-inPaloAlto/Present/DRM-NEES.jpg}}
\vspace*{-1.50cm}
\end{center}
%\vspace*{-0.3cm}
\end{figure}
\end{normalsize}

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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \slide{ Seismic Wave Propagation Model}
% 
% \begin{figure}[!h]
% \vspace*{-0.8cm}
% \begin{center}
% {\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/thesis/figures/model1a.jpg}}
% \\
% \vspace*{-4.0cm}
% {\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}
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \slide{ Seismic Wave Propagation \\ Soft Soil}
% 
% 
% \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}
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \slide{ Seismic Wave Propagation \\ Stiff Soil}
% 
% 
% \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{Verification SFSI Model}

\begin{figure}[!h]
\vspace*{-0.0cm}
\begin{center}
{\includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/model3.jpg}}
\\
\vspace*{-3.8cm}
{\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*{-2.8cm}
\end{center}
\end{figure}




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\slide{ SFSI: Stiff Soil Model}



\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/DL_T615.pdf}}
\vspace*{-5.0cm}
%\end{center}
\end{figure}


 \hspace*{4cm} Free Field  \hspace*{10cm}  SFSI



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\slide{ SFSI: Soft Soil Model}


\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/DL_M615.pdf}}
\vspace*{-5.0cm}
%\end{center}
\end{figure}


 \hspace*{4cm} Free Field  \hspace*{10cm}  SFSI



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\slide{SFSI Model: Pile--Column Behavior}


\begin{figure}[!h]
%\begin{center}
\vspace*{-2.5cm}
{\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}


 \hspace*{4cm} Stiff soil   \hspace*{10cm}  Soft soil



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\slide{SFSI Model: Seismic Results}


\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}


 \hspace*{4cm} Stiff soil   \hspace*{10cm}  Soft soil



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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \slide{ Wave Propagation (DRM)}
%
% \begin{figure}[!h]
% \vspace*{-3.8cm}
% \begin{center}
% {\includegraphics[width=8.5cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/thesis/figures/Inp_acc0507.pdf}}
% %\hfill
% {\includegraphics[width=8.5cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/thesis/figures/Inp_dis0507.pdf}}
% \hfill
% {\includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/thesis/figures/model1a.jpg}}
% \end{center}
% \end{figure}
%
% \begin{figure}[!h]
% %\begin{center}
% \vspace*{-6.5cm}
% {\includegraphics[width=12.5cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/thesis/figures/TS/DL_SS.pdf}}
% \hspace{-1cm}
% {\includegraphics[width=12.7cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/thesis/figures/TS/DY_SS.pdf}}
% \vspace*{-5.0cm}
% %\end{center}
% \end{figure}
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\slide{I--880 SFSI Example}

\begin{figure}[!h]
\vspace*{-0.6cm}
\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{ SFSI Advantageous}
\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{ SFSI Disadvantageous}
\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{Conclusions}

\begin{large}


\begin{itemize}

\vspace*{0.5cm}
\item SFSI problem requires close cooperation of experimentalists, modelers and simulators,



\vspace*{0.5cm}
\item {\bf Validation domain} and {\bf Application domain} to be bridged using simulation  tools, 


\vspace*{0.5cm}
\item One such simulation tool is OpenSees, the NEESgrid simulation platform


\vspace*{0.5cm}
\item  The  main  OpenSees  web  site \texttt{http://opensees.berkeley.edu/} has
links to documentation, examples, source code, executables, message board...


%\vspace*{1.0cm}
%\item


\end{itemize}

\end{large}

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%
%    \newpage
%  \begin{center}
%  \includegraphics[height=5.5truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/PileGroups/Plastified_3X3pg_skewCOLOR.jpg}
%  \includegraphics[height=5.5truecm]{/home/jeremic/public_html/GeoWulf/GeoWulf_01_Nov2001a.jpg}
%  \includegraphics[height=5.5truecm]{/home/jeremic/tex/works/Papers/2001/Visualization/pic30.jpg}
%  \includegraphics[height=5.5truecm]{/home/jeremic/tex/works/Papers/2001/Visualization/pic71.jpg}
%  \\
%  \includegraphics[height=6.0truecm]{/home/jeremic/tex/works/Papers/2001/Visualization/pic80.jpg}
%  \includegraphics[height=6.0truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/MQP_sand_wsfclay_UFmid2hdp0.pdf}
%  \includegraphics[height=6.0truecm]{/home/jeremic/tex/works/Reports/2001/PEER/FinalReport/sp2_stress_pile_isoSmall.jpg}
% % \includegraphics[height=5.0truecm]{/home/jeremic/tex/works/Reports/2001/PEER/FinalReport/sp2_MQP_pile.jpg}
%  \\
%  \includegraphics[height=6.0truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cubic_el_05.jpg}
%  \includegraphics[height=6.0truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cubic_pl_05.jpg}
%  \includegraphics[height=6.0truecm]{/home/jeremic/tex/works/Conferences/2002/WCCM/Keynote/Present/p-version_slope.jpg}
%  \end{center}
%













%\vspace*{1cm}

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\end{document}
\bye





