foeppl_von_karman_elements.h

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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// Copyright (C) 2006-2022 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.
// LIC//
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// LIC// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// LIC// Lesser General Public License for more details.
// LIC//
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// LIC//
// LIC// The authors may be contacted at oomph-lib@maths.man.ac.uk.
// LIC//
// LIC//====================================================================
// Header file for FoepplvonKarman elements
#ifndef OOMPH_FOEPPLVONKARMAN_ELEMENTS_HEADER
#define OOMPH_FOEPPLVONKARMAN_ELEMENTS_HEADER
 
 
// Config header generated by autoconfig
#ifdef HAVE_CONFIG_H
#include <oomph-lib-config.h>
#endif
 
#include <sstream>
 
// OOMPH-LIB headers
#include "../generic/projection.h"
#include "../generic/nodes.h"
#include "../generic/Qelements.h"
#include "../generic/oomph_utilities.h"
 
 
namespace oomph
{
  //=============================================================
  //=============================================================
  class FoepplvonKarmanEquations : public virtual FiniteElement
  {
  public:
    typedef void (*FoepplvonKarmanPressureFctPt)(const Vector<double>& x,
                                                 double& f);
 
    FoepplvonKarmanEquations() : Pressure_fct_pt(0), Airy_forcing_fct_pt(0)
    {
      // Set all the physical constants to the default value (zero)
      Eta_pt = &Default_Physical_Constant_Value;
      Linear_bending_model = false;
 
      // No volume constraint
      Volume_constraint_pressure_external_data_index = -1;
    }
 
    FoepplvonKarmanEquations(const FoepplvonKarmanEquations& dummy) = delete;
 
    void operator=(const FoepplvonKarmanEquations&) = delete;
 
    // Access functions for the physical constants
 
    const double& eta() const
    {
      return *Eta_pt;
    }
 
    double*& eta_pt()
    {
      return Eta_pt;
    }
 
 
    void set_volume_constraint_pressure_data_as_external_data(Data* data_pt)
    {
#ifdef PARANOID
      if (data_pt->nvalue() != 1)
      {
        throw OomphLibError("Data object that contains volume control pressure "
                            "should only contain a single value. ",
                            OOMPH_CURRENT_FUNCTION,
                            OOMPH_EXCEPTION_LOCATION);
      }
#endif
 
      // Add as external data and remember the index in the element's storage
      // scheme
      Volume_constraint_pressure_external_data_index =
        add_external_data(data_pt);
    }
 
    virtual inline unsigned nodal_index_fvk(const unsigned& i = 0) const
    {
      return i;
    }
 
    void output(std::ostream& outfile)
    {
      const unsigned n_plot = 5;
      output(outfile, n_plot);
    }
 
    void output(std::ostream& outfile, const unsigned& n_plot);
 
    void output(FILE* file_pt)
    {
      const unsigned n_plot = 5;
      output(file_pt, n_plot);
    }
 
    void output(FILE* file_pt, const unsigned& n_plot);
 
    void output_fct(std::ostream& outfile,
                    const unsigned& n_plot,
                    FiniteElement::SteadyExactSolutionFctPt exact_soln_pt);
 
    virtual void output_fct(
      std::ostream& outfile,
      const unsigned& n_plot,
      const double& time,
      FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt)
    {
      throw OomphLibError(
        "There is no time-dependent output_fct() for Foeppl von Karman"
        "elements ",
        OOMPH_CURRENT_FUNCTION,
        OOMPH_EXCEPTION_LOCATION);
    }
 
 
    void compute_error(std::ostream& outfile,
                       FiniteElement::SteadyExactSolutionFctPt exact_soln_pt,
                       double& error,
                       double& norm);
 
 
    void compute_error(std::ostream& outfile,
                       FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt,
                       const double& time,
                       double& error,
                       double& norm)
    {
      throw OomphLibError(
        "There is no time-dependent compute_error() for Foeppl von Karman"
        "elements",
        OOMPH_CURRENT_FUNCTION,
        OOMPH_EXCEPTION_LOCATION);
    }
 
    FoepplvonKarmanPressureFctPt& pressure_fct_pt()
    {
      return Pressure_fct_pt;
    }
 
    FoepplvonKarmanPressureFctPt pressure_fct_pt() const
    {
      return Pressure_fct_pt;
    }
 
    FoepplvonKarmanPressureFctPt& airy_forcing_fct_pt()
    {
      return Airy_forcing_fct_pt;
    }
 
    FoepplvonKarmanPressureFctPt airy_forcing_fct_pt() const
    {
      return Airy_forcing_fct_pt;
    }
 
    inline virtual void get_pressure_fvk(const unsigned& ipt,
                                         const Vector<double>& x,
                                         double& pressure) const
    {
      // If no pressure function has been set, return zero
      if (Pressure_fct_pt == 0)
      {
        pressure = 0.0;
      }
      else
      {
        // Get pressure strength
        (*Pressure_fct_pt)(x, pressure);
      }
    }
 
    inline virtual void get_airy_forcing_fvk(const unsigned& ipt,
                                             const Vector<double>& x,
                                             double& airy_forcing) const
    {
      // If no pressure function has been set, return zero
      if (Airy_forcing_fct_pt == 0)
      {
        airy_forcing = 0.0;
      }
      else
      {
        // Get pressure strength
        (*Airy_forcing_fct_pt)(x, airy_forcing);
      }
    }
 
    void get_gradient_of_deflection(const Vector<double>& s,
                                    Vector<double>& gradient) const
    {
      // Find out how many nodes there are in the element
      const unsigned n_node = nnode();
 
      // Get the index at which the unknown is stored
      const unsigned w_nodal_index = nodal_index_fvk(0);
 
      // Set up memory for the shape and test functions
      Shape psi(n_node);
      DShape dpsidx(n_node, 2);
 
      // Call the derivatives of the shape and test functions
      dshape_eulerian(s, psi, dpsidx);
 
      // Initialise to zero
      for (unsigned j = 0; j < 2; j++)
      {
        gradient[j] = 0.0;
      }
 
      // Loop over nodes
      for (unsigned l = 0; l < n_node; l++)
      {
        // Loop over derivative directions
        for (unsigned j = 0; j < 2; j++)
        {
          gradient[j] += this->nodal_value(l, w_nodal_index) * dpsidx(l, j);
        }
      }
    }
 
    void fill_in_contribution_to_residuals(Vector<double>& residuals);
 
    // void fill_in_contribution_to_jacobian(Vector<double> &residuals,
    //                                      DenseMatrix<double> &jacobian);
 
    inline double interpolated_w_fvk(const Vector<double>& s,
                                     unsigned index = 0) const
    {
      // Find number of nodes
      const unsigned n_node = nnode();
 
      // Get the index at which the poisson unknown is stored
      const unsigned w_nodal_index = nodal_index_fvk(index);
 
      // Local shape function
      Shape psi(n_node);
 
      // Find values of shape function
      shape(s, psi);
 
      // Initialise value of u
      double interpolated_w = 0.0;
 
      // Loop over the local nodes and sum
      for (unsigned l = 0; l < n_node; l++)
      {
        interpolated_w += this->nodal_value(l, w_nodal_index) * psi[l];
      }
 
      return (interpolated_w);
    }
 
    void interpolated_stress(const Vector<double>& s,
                             double& sigma_xx,
                             double& sigma_yy,
                             double& sigma_xy);
 
    virtual double get_bounded_volume() const
    {
      // Number of nodes and integration points for the current element
      const unsigned n_node = nnode();
      const unsigned n_intpt = integral_pt()->nweight();
 
      // Shape functions and their derivatives
      Shape psi(n_node);
      DShape dpsidx(n_node, 2);
 
      // The nodal index at which the displacement is stored
      const unsigned w_nodal_index = nodal_index_fvk();
 
      // Initalise the integral variable
      double integral_w = 0;
 
      // Loop over the integration points
      for (unsigned ipt = 0; ipt < n_intpt; ipt++)
      {
        // Get the integral weight
        double w = integral_pt()->weight(ipt);
 
        // Get determinant of the Jacobian of the mapping
        double J = dshape_eulerian_at_knot(ipt, psi, dpsidx);
 
        // Premultiply the weight and Jacobian
        double W = w * J;
 
        // Initialise storage for the w value and nodal value
        double interpolated_w = 0;
        double w_nodal_value;
 
        // Loop over the shape functions/nodes
        for (unsigned l = 0; l < n_node; l++)
        {
          // Get the current nodal value
          w_nodal_value = raw_nodal_value(l, w_nodal_index);
          // Add the contribution to interpolated w
          interpolated_w += w_nodal_value * psi(l);
        }
 
        // Add the contribution from the current integration point
        integral_w += interpolated_w * W;
      }
 
      // Return the calculated integral
      return integral_w;
    }
 
    unsigned self_test();
 
    void use_linear_bending_model()
    {
      // Set the boolean flag
      Linear_bending_model = true;
 
      // Get the index of the first FvK nodal value
      unsigned first_fvk_nodal_index = nodal_index_fvk();
 
      // Get the total number of FvK nodal values (assuming they are stored
      // contiguously) at node 0 (it's the same at all nodes anyway)
      unsigned total_fvk_nodal_indicies = 8;
 
      // Get the number of nodes in this element
      unsigned n_node = nnode();
 
      // Loop over the appropriate nodal indices
      for (unsigned index = first_fvk_nodal_index + 2;
           index < first_fvk_nodal_index + total_fvk_nodal_indicies;
           index++)
      {
        // Loop over the nodes in the element
        for (unsigned inod = 0; inod < n_node; inod++)
        {
          // Pin the nodal value at the current index
          node_pt(inod)->pin(index);
        }
      }
    }
 
 
  protected:
    virtual double dshape_and_dtest_eulerian_fvk(const Vector<double>& s,
                                                 Shape& psi,
                                                 DShape& dpsidx,
                                                 Shape& test,
                                                 DShape& dtestdx) const = 0;
 
 
    virtual double dshape_and_dtest_eulerian_at_knot_fvk(
      const unsigned& ipt,
      Shape& psi,
      DShape& dpsidx,
      Shape& test,
      DShape& dtestdx) const = 0;
 
    // Pointers to global physical constants
 
    double* Eta_pt;
 
    FoepplvonKarmanPressureFctPt Pressure_fct_pt;
 
    // mjr Ridicu-hack for made-up second pressure, q
    FoepplvonKarmanPressureFctPt Airy_forcing_fct_pt;
 
  private:
    static double Default_Physical_Constant_Value;
 
    bool Linear_bending_model;
 
    int Volume_constraint_pressure_external_data_index;
  };
 
 
 
 
  // mjr QFoepplvonKarmanElements are untested!
 
  //======================================================================
  //======================================================================
 
  template<unsigned NNODE_1D>
  class QFoepplvonKarmanElement : public virtual QElement<2, NNODE_1D>,
                                  public virtual FoepplvonKarmanEquations
  {
  private:
    static const unsigned Initial_Nvalue;
 
  public:
    QFoepplvonKarmanElement()
      : QElement<2, NNODE_1D>(), FoepplvonKarmanEquations()
    {
    }
 
    QFoepplvonKarmanElement(const QFoepplvonKarmanElement<NNODE_1D>& dummy) =
      delete;
 
    void operator=(const QFoepplvonKarmanElement<NNODE_1D>&) = delete;
 
    inline unsigned required_nvalue(const unsigned& n) const
    {
      return Initial_Nvalue;
    }
 
    void output(std::ostream& outfile)
    {
      FoepplvonKarmanEquations::output(outfile);
    }
 
 
    void output(std::ostream& outfile, const unsigned& n_plot)
    {
      FoepplvonKarmanEquations::output(outfile, n_plot);
    }
 
 
    void output(FILE* file_pt)
    {
      FoepplvonKarmanEquations::output(file_pt);
    }
 
 
    void output(FILE* file_pt, const unsigned& n_plot)
    {
      FoepplvonKarmanEquations::output(file_pt, n_plot);
    }
 
 
    void output_fct(std::ostream& outfile,
                    const unsigned& n_plot,
                    FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
    {
      FoepplvonKarmanEquations::output_fct(outfile, n_plot, exact_soln_pt);
    }
 
 
    void output_fct(std::ostream& outfile,
                    const unsigned& n_plot,
                    const double& time,
                    FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt)
    {
      FoepplvonKarmanEquations::output_fct(
        outfile, n_plot, time, exact_soln_pt);
    }
 
 
  protected:
    inline double dshape_and_dtest_eulerian_fvk(const Vector<double>& s,
                                                Shape& psi,
                                                DShape& dpsidx,
                                                Shape& test,
                                                DShape& dtestdx) const;
 
 
    inline double dshape_and_dtest_eulerian_at_knot_fvk(const unsigned& ipt,
                                                        Shape& psi,
                                                        DShape& dpsidx,
                                                        Shape& test,
                                                        DShape& dtestdx) const;
  };
 
 
  // Inline functions:
 
 
  //======================================================================
  //======================================================================
  template<unsigned NNODE_1D>
  double QFoepplvonKarmanElement<NNODE_1D>::dshape_and_dtest_eulerian_fvk(
    const Vector<double>& s,
    Shape& psi,
    DShape& dpsidx,
    Shape& test,
    DShape& dtestdx) const
  {
    // Call the geometrical shape functions and derivatives
    const double J = this->dshape_eulerian(s, psi, dpsidx);
 
    // Set the test functions equal to the shape functions
    test = psi;
    dtestdx = dpsidx;
 
    // Return the jacobian
    return J;
  }
 
 
  //======================================================================
  //======================================================================
  template<unsigned NNODE_1D>
  double QFoepplvonKarmanElement<
    NNODE_1D>::dshape_and_dtest_eulerian_at_knot_fvk(const unsigned& ipt,
                                                     Shape& psi,
                                                     DShape& dpsidx,
                                                     Shape& test,
                                                     DShape& dtestdx) const
  {
    // Call the geometrical shape functions and derivatives
    const double J = this->dshape_eulerian_at_knot(ipt, psi, dpsidx);
 
    // Set the pointers of the test functions
    test = psi;
    dtestdx = dpsidx;
 
    // Return the jacobian
    return J;
  }
 
 
 
 
  //=======================================================================
  //=======================================================================
  template<unsigned NNODE_1D>
  class FaceGeometry<QFoepplvonKarmanElement<NNODE_1D>>
    : public virtual QElement<1, NNODE_1D>
  {
  public:
    FaceGeometry() : QElement<1, NNODE_1D>() {}
  };
 
 
 
  //==========================================================
  //==========================================================
  template<class FVK_ELEMENT>
  class ProjectableFoepplvonKarmanElement
    : public virtual ProjectableElement<FVK_ELEMENT>
  {
  public:
    Vector<std::pair<Data*, unsigned>> data_values_of_field(const unsigned& fld)
    {
#ifdef PARANOID
      if (fld > 7)
      {
        std::stringstream error_stream;
        error_stream
          << "Foeppl von Karman elements only store eight fields so fld must be"
          << "0 to 7 rather than " << fld << std::endl;
        throw OomphLibError(
          error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
      }
#endif
 
      // Create the vector
      unsigned nnod = this->nnode();
      Vector<std::pair<Data*, unsigned>> data_values(nnod);
 
      // Loop over all nodes
      for (unsigned j = 0; j < nnod; j++)
      {
        // Add the data value associated field: The node itself
        data_values[j] = std::make_pair(this->node_pt(j), fld);
      }
 
      // Return the vector
      return data_values;
    }
 
    unsigned nfields_for_projection()
    {
      return 8;
    }
 
    unsigned nhistory_values_for_projection(const unsigned& fld)
    {
#ifdef PARANOID
      if (fld > 7)
      {
        std::stringstream error_stream;
        error_stream
          << "Foeppl von Karman elements only store eight fields so fld must be"
          << "0 to 7 rather than " << fld << std::endl;
        throw OomphLibError(
          error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
      }
#endif
      return this->node_pt(0)->ntstorage();
    }
 
 
    unsigned nhistory_values_for_coordinate_projection()
    {
      return this->node_pt(0)->position_time_stepper_pt()->ntstorage();
    }
 
    double jacobian_and_shape_of_field(const unsigned& fld,
                                       const Vector<double>& s,
                                       Shape& psi)
    {
#ifdef PARANOID
      if (fld > 7)
      {
        std::stringstream error_stream;
        error_stream
          << "Foeppl von Karman elements only store eight fields so fld must be"
          << "0 to 7 rather than " << fld << std::endl;
        throw OomphLibError(
          error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
      }
#endif
      unsigned n_dim = this->dim();
      unsigned n_node = this->nnode();
      Shape test(n_node);
      DShape dpsidx(n_node, n_dim), dtestdx(n_node, n_dim);
      double J =
        this->dshape_and_dtest_eulerian_fvk(s, psi, dpsidx, test, dtestdx);
      return J;
    }
 
 
    double get_field(const unsigned& t,
                     const unsigned& fld,
                     const Vector<double>& s)
    {
#ifdef PARANOID
      if (fld > 7)
      {
        std::stringstream error_stream;
        error_stream
          << "Foeppl von Karman elements only store eight fields so fld must be"
          << "0 to 7 rather than " << fld << std::endl;
        throw OomphLibError(
          error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
      }
#endif
      // Find the index at which the variable is stored
      unsigned w_nodal_index = this->nodal_index_fvk(fld);
 
      // Local shape function
      unsigned n_node = this->nnode();
      Shape psi(n_node);
 
      // Find values of shape function
      this->shape(s, psi);
 
      // Initialise value of u
      double interpolated_w = 0.0;
 
      // Sum over the local nodes
      for (unsigned l = 0; l < n_node; l++)
      {
        interpolated_w += this->nodal_value(t, l, w_nodal_index) * psi[l];
      }
      return interpolated_w;
    }
 
 
    unsigned nvalue_of_field(const unsigned& fld)
    {
#ifdef PARANOID
      if (fld > 7)
      {
        std::stringstream error_stream;
        error_stream
          << "Foeppl von Karman elements only store eight fields so fld must be"
          << "0 to 7 rather than " << fld << std::endl;
        throw OomphLibError(
          error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
      }
#endif
      return this->nnode();
    }
 
 
    int local_equation(const unsigned& fld, const unsigned& j)
    {
#ifdef PARANOID
      if (fld > 7)
      {
        std::stringstream error_stream;
        error_stream
          << "Foeppl von Karman elements only store eight fields so fld must be"
          << "0 to 7 rather than " << fld << std::endl;
        throw OomphLibError(
          error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
      }
#endif
      const unsigned w_nodal_index = this->nodal_index_fvk(fld);
      return this->nodal_local_eqn(j, w_nodal_index);
    }
  };
 
  //=======================================================================
  //=======================================================================
  template<class ELEMENT>
  class FaceGeometry<ProjectableFoepplvonKarmanElement<ELEMENT>>
    : public virtual FaceGeometry<ELEMENT>
  {
  public:
    FaceGeometry() : FaceGeometry<ELEMENT>() {}
  };
 
 
  //=======================================================================
  //=======================================================================
  template<class ELEMENT>
  class FaceGeometry<FaceGeometry<ProjectableFoepplvonKarmanElement<ELEMENT>>>
    : public virtual FaceGeometry<FaceGeometry<ELEMENT>>
  {
  public:
    FaceGeometry() : FaceGeometry<FaceGeometry<ELEMENT>>() {}
  };
 
} // namespace oomph
 
#endif