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\title[Nonlinear ESSI for Design]
        {Use of Nonlinear, \\
        Time Domain Analysis for \\
        Design}


%\subtitle
%{Include Only If Paper Has a Subtitle}

%\author[Author, Another] % (optional, use only with lots of authors)
%{F.~Author\inst{1} \and S.~Another\inst{2}}
% - Give the names in the same order as the appear in the paper.
% - Use the \inst{?} command only if the authors have different
%   affiliation.
\pgfdeclareimage[height=0.2cm]{university-logo}{/home/jeremic/BG/amblemi/ucdavis_logo_blue_sm}
\pgfdeclareimage[height=0.7cm]{lbnl-logo}{/home/jeremic/BG/amblemi/lbnl-logo}


\author[Jeremi{\'c} et al.] % (optional, use only with lots of authors)
%{Boris~Jeremi{\'c}}
{
Neboj{\v s}a Orbovi{\'c}, 
{\bf Boris Jeremi{\'c}}, \\
Jos{\' e} Antonio Abell Mena,
Chao Luo,                \\
Robert P. Kennedy and
Andrei Blaihoanu,
}

%%\institute[Computational Geomechanics Group \hspace*{0.3truecm}
%\institute[\pgfuseimage{university-logo}\hspace*{0.1truecm}\pgfuseimage{lbnl-logo}] % (optional, but mostly needed)
%%{ Professor, University of California, Davis\\
%{ 
%%Professor, UCD\\
%%  Faculty Scientist, LBNL \\
%%  Consulting Engineer, Davis, CA, USA }
%%{ Professor, University of California, Davis, CA, USA\\
%%  Faculty Scientist, Lawrence Berkeley National Laboratory, Berkeley, CA, USA \\
%%  Consulting Engineer, Davis, CA, USA }
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%
%
\date[] % (optional, should be abbreviation of conference name)
{\small SMiRT, Manchester, UK, \\
        August 2015}

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% may not be suitable. Here are some rules that apply for this
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% - A conference audience is likely to know very little of what you
%   are going to talk about. So *simplify*!
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%   you think necessary.
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%   just say so once. Everybody will be happy with that.



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\section{Introduction}

\subsection*{Motivation}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Motivation}

\begin{itemize}



%\vspace*{0.3cm}
  \item  Improve  seismic  design,  safety  and economy, of Nuclear Power Plants
  (NPPs)


%\vspace*{0.1cm}
\vspace*{3mm}
  \item  Follow seismic energy within NPP ESSI system

  
\vspace*{3mm}
  \item   Accurate,   high   fidelity  numerical  modeling  and  simulation  of  Nonlinear
  {E}arthquake  {S}oil  {S}tructure  {I}nteraction  ({ESSI}),  in time and space,
  for realistic analysis of  NPP response




% 




%\vspace*{0.1cm}
\vspace*{3mm}
  \item  Use realistic nonlinear ESSI for design! 



% %\vspace*{0.1cm}
% \vspace*{1mm}
% %  \item  Development of  high  fidelity  numerical modeling and simulation tool
%   \item  High  fidelity  numerical modeling and simulation 
%   The {Real ESSI} Simulator
% %   (
% %   {\small aka}: {\cyrssDvanaest Stvarno  Lako},
% % {\small aka}: {\cyrssDvanaest Vrlo Prosto},
% % { Muy F{\'a}cil},
% % {Molto  Facile},
% % \raisebox{-1.2mm}{\includegraphics[height=5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Chinese.jpeg}},
% % \raisebox{-1.2mm}{\includegraphics[height=5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Japanese.jpg}},
% % {\greektext{Pragmatik'a E'ukolo}},
% % \raisebox{-1.2mm}{\includegraphics[height=5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Farsi.jpg}},
% % {Tr{\`e}s Facile},
% % {\cyrssDvanaest Vistinski Lesno},
% % {Wirklich Einfach})
% %
% %\vspace*{1mm}
% %     \item Goal is to predict and inform, not diagnose or fit.
% %     \item Modeling and simulation goal is to predict and inform, not diagnose or fit
% 
% 
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Predictive Capabilities}
% \frametitle{High Fidelity Modeling of SFS System:
% Verification, Validation and Prediction}

\begin{itemize}

     \item  High fidelity, accurate modeling and simulation: Verification and Validation


%\vspace*{1mm}
     \item  {{  Verification}  provides  evidence  that  the  model is solved
     correctly.} Mathematics issue.

%\vspace*{0.1cm}
%\vspace*{1mm}
     \item  {{  Validation}  provides  evidence  that  the  correct  model is
     solved.} Physics issue.

% %\vspace*{0.1cm}
% \vspace*{1mm}
%    \item {  Prediction under Uncertainty (!)}:  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*{1mm}
   \item Verification and validation (V\&V) require huge effort!

%\vspace*{1mm}
   \item  Verification  procedures in development 
%   (there is no published verification
%   work for solids/structures, we have a draft)

%\vspace*{1mm}
   \item   Validation  almost  non-existent  (new  U.S.  DOE  project  will  add
   significantly to ESSI validation data base)



%\vspace*{1mm}
   \item Modeling and Parametric Uncertainties (sensitivity studies are very important)

%
%   SENSITIVITY STUDIES
%
%\vspace*{1mm}
%   \item Predictive capabilities with {low Kolmogorov Complexity}

%
% \vspace*{3mm}
%      \item Modeling and simulation goal is to inform, not fit
% 
%
\end{itemize}


\end{frame}






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%
%\subsection*{Uncertainties}
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\begin{frame}
 \frametitle{Uncertainties}

\begin{itemize}

\item Modeling Uncertainty:   important features  are neglected (6D
  ground motions, inelasticity),  \\
   unrealistic   and   unnecessary  \\
   modeling
     simplifications

\vspace*{-14mm}
\begin{figure}[!hbpt]
\begin{flushright}
%
\hspace*{15mm}
\includegraphics[width=1.0truecm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/PresentDesign/Simple_NPP_stick_model.pdf}
\hspace*{1mm}
% \hfill
\includegraphics[width=3truecm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/PresentDesign/Full_NPP_shell_solids_model.jpeg}
%\hspace*{5mm}
% %
\end{flushright}
\end{figure}




%\vspace*{1mm}
\item Parametric Uncertainty: spatial variability, measuring and transformation errors 


%\vspace*{-3mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-7mm}
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01-Ed.pdf}
% \hfill
\includegraphics[width=4truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_Histogram_Normal_01-Ed.pdf}
%
\end{center}
\end{figure}

\vspace*{-3mm}
%\hspace*{-3.3cm}
\begin{center}
{\tiny
Transformation  of SPT $N$-value: 
1-D Young's modulus, $E$ \\
(cf. Phoon and Kulhawy (1999B))\\
~}
\end{center}



\end{itemize}






\end{frame}











%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Realistic, Nonlinear ESSI Modeling}



\begin{itemize}

  \item Nonlinear behavior
    
    \begin{itemize}
      \item Nonlinear, inelastic (saturated or dry) soil/rock
        \vspace*{0.5mm}
      \item Nonlinear, inelastic (saturated or dry) contact 
        \vspace*{0.5mm}
      \item Nonlinear, inelastic structures, systems and components
        \vspace*{0.5mm}
      \item Buoyant (nonlinear) forces
    \end{itemize}


%\vspace*{1mm}
\item  Full 3D  (6D)  Earthquake  motions 


%\vspace*{1mm}
\item Uncertain material and loads

%\vspace*{1mm}
\item Verification and validation for accurate  numerical simulations


%\vspace*{1mm}
\item  Real  ESSI  Simulator (developed in collaboration and with the support of
NRC, CNSC, DOE)


\end{itemize}

\end{frame}

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



% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Realistic, nonlinear ESSI for Design}


\begin{itemize}

% 
% \item High fidelity modeling:
% 
%   \begin{itemize}
% 
%     \item      Seismic      Motions:   6D,  inclined,  body  and  surface  waves
%     (translations, rotations); Incoherency
% 
% %\vspace*{3mm}
%     \item        Inelastic     material:    soil,   rock,   concrete,   steel;  
%     Contacts,  foundation--soil,  dry,  saturated  slip--gap;  Nonlinear buoyant
%     forces; Isolators, Dissipators
% 
% 
% %\vspace*{3mm}
%     \item Uncertain loading and material
%   \end{itemize}
% 
% 
% 
% 
%   \item Nonlinear analysis for design
% 
% 
%   \begin{itemize}

\vspace*{3mm}
    \item  Design  standards require structure to be elastic 
%    so we hard-code that
%    in our models (!?)

\vspace*{3mm}
    \item Anything below foundation can be modeled as nonlinear

\vspace*{3mm}
    \item Possible reduction of demand due to nonlinearities in soil/rock and contact zone

\vspace*{3mm}
    \item Assesment of NPP designs using sweeps of earthquakes/motions and realistic nonlinear ESSI analysis

%   \end{itemize}


\end{itemize}

\end{frame}

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



% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Nonlinear ESSI in Design}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection*{Results of Nonlinear Analysis}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Earthquake Motions}

\begin{itemize}

  \item  Earthquake record: Taiwan SMART1(45), Time: 11/14/1986, Station:SMART1 E02.
  %
\begin{figure}[!htb]
\begin{center}
\includegraphics[width=3cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/_XX_Use_of_Nonlinear_Time_Domain_Analysis_for_NPP_Design/Paper/acceleration_time_history.pdf}
\hfill
\includegraphics[width=3cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/_XX_Use_of_Nonlinear_Time_Domain_Analysis_for_NPP_Design/Paper/acceleration_FFT.pdf}
\hfill
\includegraphics[width=3cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/_XX_Use_of_Nonlinear_Time_Domain_Analysis_for_NPP_Design/Paper/acceleration_Response_Spectrum.pdf}
\end{center}
%\caption{Free field seismic motions at the surface: 
%         time history, FFT and response spectra.}
\label{motions}
\end{figure}

\vspace*{2mm}
  \item Horizontal \#1: 100\%,  horizontal \#2: 40\%, vertical: 40\%

\vspace*{2mm}
  \item Full application of 3D motions, no superposition allowed (nonlinear analysis)
%   NO SUPERPOSITION Used assumption of 3 $\times$ 1D earthquake motions (!?) as required 

\end{itemize}

\end{frame}
%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Earthquake Motion Input into FEM Model}

\begin{itemize}

  \item  Domain Reduction Method (Bielak et al.)

%\vspace*{2mm}
  \item    Capable of accurately inputting all body (P, SV, SH) and surface (Rayleigh, Love,
  etc.) earthquake waves into a finite element model

%\vspace*{2mm}
  \item Free field motions needed for input effective forces


%\vspace*{2mm}
  \item Radiated waves from the structures leave the system 

%\vspace*{2mm}
  \item Inside DRM finite element layer can be fully nonlinear (elastic-plastic)

\end{itemize}

%

\vspace*{-6mm}
\begin{figure}[!hbpt]
\begin{center}
\includegraphics[width=10cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/tex_works_psfigures_DRM_NPP_idea03_with_element.pdf}
\end{center}
\end{figure}



\end{frame}
%



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Finite Element Model}

\begin{itemize}

  \item  Soil/Rock,  solids,  linear  elastic  (can be  fully elastic-plastic)

  \item Contact (soil/rock -- foundation slab) fully nonlinear, Coulomb friction  
  (friction  coefficient  $\mu = 0.5$, taking into account plastic sheets beneath
  foundation) and gaping

  \item Structure (stick model) linear elastic (can use a far more sophisticated
  structural model, however this is  a demonstration)

  \item Seismic input using DRM

\end{itemize}


\vspace*{-13mm}
\begin{figure}[!htb]
\begin{center}
\hspace*{-6mm}
\includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/_XX_Use_of_Nonlinear_Time_Domain_Analysis_for_NPP_Design/Paper/fig01.jpg}
\hfill
\includegraphics[width=6cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/_XX_Use_of_Nonlinear_Time_Domain_Analysis_for_NPP_Design/Paper/fig02.jpg}
\hspace*{-6mm}
\end{center}
\label{Model}
\end{figure}
%         
\end{frame}
%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Foundation -- Soil/Rock Slip}

\begin{itemize}

  \item Foundation slab slips significantly during an earthquake
  
  \item Base isolation (?!) and energy dissipation
   
   \item Soil on the side restricts movements

   \item Minimal gaping as contact sleeps before slab lifts-off


\end{itemize}




     
\vspace*{-6mm}
\begin{figure}[!htb]
\begin{center}
\hspace*{-6mm}
\includegraphics[width=2.5cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/_XX_Use_of_Nonlinear_Time_Domain_Analysis_for_NPP_Design/Paper/slip_at_1_percent_02.jpg}
\hfill                     
\includegraphics[width=9cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/_XX_Use_of_Nonlinear_Time_Domain_Analysis_for_NPP_Design/Paper/Slipping.pdf}
\hspace*{-6mm}
%\caption{Snapshot  of  a  relative  displacements  between  foundation  slab and
%soil/rock  (left)  and  the  amount  of  slip  at  a center of a foundation slab
%(beneath containment and internal sticks).}
\end{center}
\label{slip}
\end{figure}


\end{frame}
%



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Nonlinear vs Linear Response, Top of Soil}

 
\begin{itemize}

  \item Reduction in soil horizontal demand

  \item Amplification of vertical due to pounding upon contact

  \item  Soil  horizontal  and  vertical  peaks  at the  same frequency, hence
  vertical motions are from a Rayleigh surface wave 

\end{itemize}


\vspace*{-7mm}
    %
\begin{figure}[!htb]
\begin{center}
\hspace*{-7mm}
\includegraphics[width=6cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/_XX_Use_of_Nonlinear_Time_Domain_Analysis_for_NPP_Design/Paper/results_24June2015/SA_X_base_soil_3d_nonlin_vs_linear.pdf}
% %\\
% \includegraphics[width=6cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/_XX_Use_of_Nonlinear_Time_Domain_Analysis_for_NPP_Design/Paper/results_24June2015/SA_Y_base_soil_3d_nonlin_vs_linear.pdf}
% %\\
\includegraphics[width=6cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/_XX_Use_of_Nonlinear_Time_Domain_Analysis_for_NPP_Design/Paper/results_24June2015/SA_Z_base_soil_3d_nonlin_vs_linear.pdf}
% %\includegraphics[width=12cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/_XX_Use_of_Nonlinear_Time_Domain_Analysis_for_NPP_Design/Paper/results_17June2015/Comparissons/FFT_Accel_containment_building_1percent_vs_10percent.pdf}
% \caption{\label{comparison_soil}  Comparison     of  spectral  accelerations  at
% the top of soil, beneath foundation slab for X directions (left),
% %Y direction (middle) 
% and 
% vertical directions (right).}
\end{center}
\end{figure}


\vspace*{-7mm}
\hspace*{1.7cm}horizontal\hspace*{4.3cm}vertical

\end{frame}
%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Nonlinear vs Linear Response, Foundation Slab}

 
\begin{itemize}

%  \item  Horizontal  and vertical peaks at same frequency, hence vertical motions are 
%  from a surface Rayleigh wave

  \item Horizontal reduced at high frequency, due to slip,  
  \item Horizontal slightly increased at low frequency, due to slip,  

  \item Vertical reduced 
\end{itemize}

\vspace*{-7mm}
\begin{figure}[!htb]
\begin{center}
\hspace*{-7mm}
\includegraphics[width=6cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/_XX_Use_of_Nonlinear_Time_Domain_Analysis_for_NPP_Design/Paper/results_24June2015/SA_X_base_footing_3d_nonlin_vs_linear.pdf}
%  %\\
% \includegraphics[width=4cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/_XX_Use_of_Nonlinear_Time_Domain_Analysis_for_NPP_Design/Paper/results_24June2015/SA_Y_base_footing_3d_nonlin_vs_linear.pdf}
% %\\
\includegraphics[width=6cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/_XX_Use_of_Nonlinear_Time_Domain_Analysis_for_NPP_Design/Paper/results_24June2015/SA_Z_base_footing_3d_nonlin_vs_linear.pdf}
%\includegraphics[width=12cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/_XX_Use_of_Nonlinear_Time_Domain_Analysis_for_NPP_Design/Paper/results_17June2015/Comparissons/FFT_Accel_containment_building_1percent_vs_10percent.pdf}
% \caption{\label{comparison_foundation} Comparison    of  spectral  accelerations  at the foundation slab for 
% X directions (left), 
% %Y direction (middle) and 
% and vertical directions (right).}
\end{center}
\end{figure}

\vspace*{-7mm}
\hspace*{1.7cm}horizontal\hspace*{4.3cm}vertical



\end{frame}
%


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\begin{frame}
\frametitle{Nonlinear vs Linear Response, Top of Containment}

 
\begin{itemize}

  \item Significant reduction of horizontal motions

  \item Reduction of vertical motions

\end{itemize}

\vspace*{-7mm}
\begin{figure}[!htb]
\begin{center}
\hspace*{-7mm}
%\includegraphics[width=6cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/_XX_Use_of_Nonlinear_Time_Domain_Analysis_for_NPP_Design/Paper/results_24June2015/SA_X_containment_building_top_3d_nonlin_vs_linear.pdf}
\includegraphics[width=6cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/PresentDesign/FromJose/SA_X_containment_building_top_3d_nonlin_vs_linear.pdf}
%\\
%\includegraphics[width=8cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/_XX_Use_of_Nonlinear_Time_Domain_Analysis_for_NPP_Design/Paper/results_24June2015/SA_Y_containment_building_top_3d_nonlin_vs_linear.pdf}
%\\
%\includegraphics[width=6cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/_XX_Use_of_Nonlinear_Time_Domain_Analysis_for_NPP_Design/Paper/results_24June2015/SA_Z_containment_building_top_3d_nonlin_vs_linear.pdf}
\includegraphics[width=6cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/PresentDesign/FromJose/SA_Z_containment_building_top_3d_nonlin_vs_linear.pdf}
%\includegraphics[width=12cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/_XX_Use_of_Nonlinear_Time_Domain_Analysis_for_NPP_Design/Paper/results_17June2015/Comparissons/FFT_Accel_containment_building_1percent_vs_10percent.pdf}
% \caption{\label{comparison_containment} Comparison    of  spectral  accelerations  at the top of a containment 
% structure  for 
% X directions (left), 
% %Y direction (middle) 
% and 
% vertical directions (right).}
\end{center}
\end{figure}

   
\vspace*{-7mm}
\hspace*{1.7cm}horizontal\hspace*{4.3cm}vertical





\end{frame}
%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Nonlinear vs Linear Response, Comments}
    
\begin{itemize}

\item In general, significant reductions in motions for nonlinear response, both
horizontally and vertically


\vspace*{4mm}
\item Larger horizontal slip, low frequency response
%df
, at $2$Hz, validated by slip response

\vspace*{4mm}
\item Structure is still linear elastic (by modeling) and hence satisfies standard design


\end{itemize}
%

 


\end{frame}
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\section{Summary}



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\begin{frame}
\frametitle{Concluding Remarks}

  \begin{itemize}

\vspace*{3mm}
  \item Nonlinear analysis can be used for design

\vspace*{3mm}
  \item Potential for reduction of demand with realistic nonlinear analysis

\vspace*{3mm}
  \item Assesment of  NPP SSI systems using fully nonlinear, realistic ESSI analysis

\end{itemize}

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% 
% 
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%   \item  Funding from and collaboration with the 
%          US-NRC, 
%          US-DOE, 
%          US-NSF,   
%          CNSC,
%          Shimizu Corp., and 
%          AREVA NP GmbH
%          is greatly appreciated,
% 
% %\vspace*{4mm}
%   \item  Collaborators:
%   Dr.   McCallen  (UCOP and LBNL),
%   Prof. Buckle (UNR),
%   Dr. Kammerer (UCB/PEER),
%   Dr.    Budnitz    (LBNL),
%   Prof. Kavvas (UCD),
%   Prof. Sett (UB),
%   Mr. Orbovi{\'c} (CNSC)
%   Prof. Pisan{\`o} (TU Delft),
%   Mr. Watanabe (Shimizu),
%   Mr. Vlaski (AREVA NP GmbH),
%   and
%   UCD students:
%   Mr. Abell,
%   Mr. Karapiperis,
%   Mr. Feng,
%   Mr. Sinha,
%   Mr. Luo
% % 
% % 
% \end{itemize}
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% \begin{figure}[!hbpt]
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% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SMR01_a.jpg}
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% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/consulting/2013/CNSC/ProgressReports/Progress_report_02_figs/single-NPP-FEM-model.jpg}
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% \includegraphics[width=2.10cm]{/home/jeremic/tex/works/Conferences/2014/DOE_Natural_Phenomena_Hazards_Germantown_MD-21-22Oct/present/Model01.jpeg}
% \includegraphics[width=2.10cm]{/home/jeremic/tex/works/Conferences/2014/DOE_Natural_Phenomena_Hazards_Germantown_MD-21-22Oct/present/Model02.jpeg}
% \includegraphics[width=2.10cm]{/home/jeremic/tex/works/Conferences/2014/DOE_Natural_Phenomena_Hazards_Germantown_MD-21-22Oct/present/Model03.jpeg}
% \includegraphics[width=2.10cm]{/home/jeremic/tex/works/Conferences/2014/DOE_Natural_Phenomena_Hazards_Germantown_MD-21-22Oct/present/Model04.jpeg}
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