displacement_based_foeppl_von_karman_elements.cc

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//LIC// ====================================================================
//LIC// This file forms part of oomph-lib, the object-oriented, 
//LIC// multi-physics finite-element library, available 
//LIC// at http://www.oomph-lib.org.
//LIC// 
//LIC//    Version 1.0; svn revision $LastChangedRevision$
//LIC//
//LIC// $LastChangedDate$
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//LIC// Copyright (C) 2006-2016 Matthias Heil and Andrew Hazel
//LIC// 
//LIC// This library is free software; you can redistribute it and/or
//LIC// modify it under the terms of the GNU Lesser General Public
//LIC// License as published by the Free Software Foundation; either
//LIC// version 2.1 of the License, or (at your option) any later version.
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//LIC// Lesser General Public License for more details.
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//LIC// The authors may be contacted at oomph-lib@maths.man.ac.uk.
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//LIC//====================================================================
//Non-inline functions for FoepplvonKarman displacement elements

#include "displacement_based_foeppl_von_karman_elements.h"

#include <iostream>

namespace oomph
{
  
 // Foeppl von Karman displacement equations static data
 
 /// Default value for Poisson's ratio
 double DisplacementBasedFoepplvonKarmanEquations::Default_Nu_Value = 0.5;
 
  /// Default value physical constants
 double DisplacementBasedFoepplvonKarmanEquations::
 Default_Physical_Constant_Value = 0.0;


//======================================================================
/// Self-test:  Return 0 for OK
//======================================================================
unsigned DisplacementBasedFoepplvonKarmanEquations::self_test()
{
  
  bool passed=true;
  
  // Check lower-level stuff
  if (FiniteElement::self_test()!=0)
    {
      passed=false;
    }
  
  // Return verdict
  if (passed)
    {
      return 0;
    }
  else
    {
      return 1;
    }
  
}

//======================================================================
/// Output function:
///
///   x,y,w
///
/// nplot points in each coordinate direction
//======================================================================
void DisplacementBasedFoepplvonKarmanEquations::output(std::ostream &outfile,
                                                  const unsigned &nplot)
{
  
  // Vector of local coordinates
  Vector<double> s(2);
  // Vector of Eulerian coordinates
  Vector<double> x(2);
  
  // Sigma_{\alpha \beta}
  DenseMatrix<double> sigma(2,2);
  
  // E_{\alpha \beta}
  DenseMatrix<double> strain(2,2);
  
  // Tecplot header info
  outfile << tecplot_zone_string(nplot);
  
  // Loop over plot points
  unsigned num_plot_points=nplot_points(nplot);
  for (unsigned iplot=0;iplot<num_plot_points;iplot++)
    {
      
      // Get local coordinates of plot point
      get_s_plot(iplot,nplot,s);
      
      // Get the Eulerian coordinates
      for(unsigned i=0;i<2;i++)
        {
          x[i] = interpolated_x(s,i);
          outfile << x[i] << " ";
        }
      
      outfile << interpolated_w_fvk(s,0) << " "; // w
      outfile << interpolated_w_fvk(s,1) << " "; // Laplacian W
      outfile << interpolated_w_fvk(s,2) << " "; // Ux
      outfile << interpolated_w_fvk(s,3) << " "; // Uy
      //      outfile << std::endl; // New line
      
      // Get the stresses at local coordinate s
      this->get_stress_and_strain_for_output(s,sigma,strain);
      
      // Output stress
      outfile << sigma(0,0) << " ";  // sigma_xx
      outfile << sigma(0,1) << " ";  // sigma_xy
      outfile << sigma(1,1) << " ";  // sigma_yy
      
      // Output strain
      outfile << strain(0,0) << " "; // E_xx
      outfile << strain(0,1) << " "; // E_xy
      outfile << strain(1,1) << " "; // E_yy
      outfile << std::endl;

    }
  
  // Write tecplot footer (e.g. FE connectivity lists)
  write_tecplot_zone_footer(outfile,nplot);
  
}
  
  
//======================================================================
/// C-style output function:
///
///   x,y,w
///
/// nplot points in each coordinate direction
//======================================================================
void  DisplacementBasedFoepplvonKarmanEquations::output(FILE* file_pt,
                                             const unsigned &nplot)
{
  //Vector of local coordinates
  Vector<double> s(2);
  
  // Tecplot header info
  fprintf(file_pt,"%s",tecplot_zone_string(nplot).c_str());
  
  // Loop over plot points
  unsigned num_plot_points=nplot_points(nplot);
  for (unsigned iplot=0;iplot<num_plot_points;iplot++)
    {
      // Get local coordinates of plot point
      get_s_plot(iplot,nplot,s);
      
      for(unsigned i=0;i<2;i++)
        {
          fprintf(file_pt,"%g ",interpolated_x(s,i));
        }
      fprintf(file_pt,"%g \n",interpolated_w_fvk(s));
    }
  
  // Write tecplot footer (e.g. FE connectivity lists)
  write_tecplot_zone_footer(file_pt,nplot);
}
  
  
  
//======================================================================
 /// Output exact solution
 ///
 /// Solution is provided via function pointer.
 /// Plot at a given number of plot points.
 ///
 ///   x,y,w_exact
//======================================================================
 void DisplacementBasedFoepplvonKarmanEquations::output_fct(std::ostream &outfile,
                                                 const unsigned &nplot,
                                                 FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
 {
   //Vector of local coordinates
   Vector<double> s(2);

   // Vector for coordintes
   Vector<double> x(2);

   // Tecplot header info
   outfile << tecplot_zone_string(nplot);

   // Exact solution Vector (here a scalar)
   //Vector<double> exact_soln(1);
   Vector<double> exact_soln(3);

   // Loop over plot points
   unsigned num_plot_points=nplot_points(nplot);
   for (unsigned iplot=0;iplot<num_plot_points;iplot++)
     {

       // Get local coordinates of plot point
       get_s_plot(iplot,nplot,s);

       // Get x position as Vector
       interpolated_x(s,x);

       // Get exact solution at this point
       (*exact_soln_pt)(x,exact_soln);

       //Output x,y,w_exact
       for(unsigned i=0;i<2;i++)
         {
           outfile << x[i] << " ";
         }
       outfile << exact_soln[0] << " ";
       outfile << exact_soln[1] << " ";
       outfile << exact_soln[2] << std::endl;
     }

   // Write tecplot footer (e.g. FE connectivity lists)
   write_tecplot_zone_footer(outfile,nplot);
 }




//======================================================================
/// Validate against exact solution
///
/// Solution is provided via function pointer.
/// Plot error at a given number of plot points.
///
//======================================================================
 void DisplacementBasedFoepplvonKarmanEquations::compute_error(std::ostream &outfile,
                   FiniteElement::SteadyExactSolutionFctPt exact_soln_pt,
                   double& error, double& norm)
 {
   // Initialise
   error=0.0;
   norm=0.0;
   
   //Vector of local coordinates
   Vector<double> s(2);
   
   // Vector for coordintes
   Vector<double> x(2);
   
   //Find out how many nodes there are in the element
   unsigned n_node = nnode();
   
   Shape psi(n_node);
   
   //Set the value of n_intpt
   unsigned n_intpt = integral_pt()->nweight();
   
   // Tecplot
   outfile << "ZONE" << std::endl;
   
   // Exact solution vector
   Vector<double> exact_soln(3);
   
   //Loop over the integration points
   for(unsigned ipt=0;ipt<n_intpt;ipt++)
     {
       
       //Assign values of s
       for(unsigned i=0;i<2;i++)
         {
          s[i] = integral_pt()->knot(ipt,i);
         }
       
       //Get the integral weight
       double w = integral_pt()->weight(ipt);
       
       // Get jacobian of mapping
       double J=J_eulerian(s);
       
       //Premultiply the weights and the Jacobian
       double W = w*J;
       
       // Get x position as Vector
       interpolated_x(s,x);
       
       // Get FE function value
       double w_fe=interpolated_w_fvk(s);
       
       // Get exact solution at this point
       (*exact_soln_pt)(x,exact_soln);
       
       //Output x,y,error
       for(unsigned i=0;i<2;i++)
         {
           outfile << x[i] << " ";
         }
       outfile << exact_soln[0] << " " << exact_soln[0]-w_fe << std::endl;
       
       // Add to error and norm
       norm+=exact_soln[0]*exact_soln[0]*W;
       error+=(exact_soln[0]-w_fe)*(exact_soln[0]-w_fe)*W;
       
     }
   
 }
  
} // namespace oomph