Tdisplacement_based_foeppl_von_karman_elements.h

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// LIC// ====================================================================
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// LIC// multi-physics finite-element library, available
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// LIC//
// LIC// Copyright (C) 2006-2025 Matthias Heil and Andrew Hazel
// LIC//
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// Header file for TFoepplvonKarman elements
#ifndef OOMPH_TFOEPPLVONKARMAN_DISPLACEMENT_ELEMENTS_HEADER
#define OOMPH_TFOEPPLVONKARMAN_DISPLACEMENT_ELEMENTS_HEADER
 
 
// Config header
#ifdef HAVE_CONFIG_H
#include <oomph-lib-config.h>
#endif
 
 
// OOMPH-LIB headers
#include "generic/nodes.h"
#include "generic/oomph_utilities.h"
#include "generic/Telements.h"
#include "generic/error_estimator.h"
 
#include "displacement_based_foeppl_von_karman_elements.h"
 
namespace oomph
{
  /////////////////////////////////////////////////////////////////////////
  /////////////////////////////////////////////////////////////////////////
  // TDisplacementBasedFoepplvonKarmanElement
  ////////////////////////////////////////////////////////////////////////
  ////////////////////////////////////////////////////////////////////////
 
 
  // -----------------------------------------------------------------------
  // THE TRIANGLE ELEMENT
  // -----------------------------------------------------------------------
 
 
  //======================================================================
  /// TDisplacementBasedFoepplvonKarmanElement<NNODE_1D> elements are
  /// isoparametric
  /// triangular 2-dimensional Foeppl von Karman elements with NNODE_1D
  /// nodal points along each element edge. Inherits from TElement and
  /// DisplacementBasedFoepplvonKarmanEquations
  //======================================================================
  template<unsigned NNODE_1D>
  class TDisplacementBasedFoepplvonKarmanElement
    : public virtual TElement<2, NNODE_1D>,
      public virtual DisplacementBasedFoepplvonKarmanEquations,
      public virtual ElementWithZ2ErrorEstimator
  {
  public:
    /// Constructor: Call constructors for TElement and
    /// Foeppl von Karman equations
    TDisplacementBasedFoepplvonKarmanElement()
      : TElement<2, NNODE_1D>(), DisplacementBasedFoepplvonKarmanEquations()
    {
    }
 
 
    /// Broken copy constructor
    TDisplacementBasedFoepplvonKarmanElement(
      const TDisplacementBasedFoepplvonKarmanElement<NNODE_1D>& dummy) = delete;
 
    /// Broken assignment operator
    void operator=(const TDisplacementBasedFoepplvonKarmanElement<NNODE_1D>&) =
      delete;
 
    /// Access function for Nvalue: # of `values' (pinned or
    /// dofs) at node n (always returns the same value at every node, 4)
    inline unsigned required_nvalue(const unsigned& n) const
    {
      return Initial_Nvalue;
    }
 
    /// The number of dof types that degrees of freedom in this
    /// element are sub-divided into
    unsigned ndof_types() const
    {
      // NOTE: this assumes "clamped" bcs
      // [0]: laplacian w interior
      // [1]: laplacian w boundary
      // [2]: W
      // [3]: Ux
      // [4]: Uy
      return 5;
    }
 
    /// Create a list of pairs for all unknowns in this element,
    /// so that the first entry in each pair contains the global
    /// equation number of the unknown, while the second one contains
    /// the number of the dof type that this unknown is associated with.
    /// (Function can obviously only be called if the equation numbering
    /// scheme has been set up.)
    /// Dof_types
    /// 0,1: Laplacian;
    /// 2: Bending w
    /// 3: Displacements Ux and Uy
    /// The indexing of the dofs in the element is like below
    /// [0]: w
    /// [1]: laplacian w
    /// [2]: U_x
    /// [3]: U_y
    void get_dof_numbers_for_unknowns(
      std::list<std::pair<unsigned long, unsigned>>& dof_lookup_list) const
    {
      // number of nodes
      const unsigned n_node = this->nnode();
 
      // temporary pair (used to store dof lookup prior to being added to list)
      std::pair<unsigned, unsigned> dof_lookup;
 
      // loop over the nodes
      for (unsigned n = 0; n < n_node; n++)
      {
        // Zeroth nodal value: displacement
        //---------------------------------
        unsigned v = 0;
 
        // determine local eqn number
        int local_eqn_number = this->nodal_local_eqn(n, v);
 
        // ignore pinned values
        if (local_eqn_number >= 0)
        {
          // store dof lookup in temporary pair: Global equation
          // number is the first entry in pair
          dof_lookup.first = this->eqn_number(local_eqn_number);
 
          // set dof type numbers: Dof type is the second entry in pair
          dof_lookup.second = 2;
 
          // add to list
          dof_lookup_list.push_front(dof_lookup);
        }
 
        // First nodal value: Laplacian
        //-----------------------------
        v = 1;
 
        // determine local eqn number
        local_eqn_number = this->nodal_local_eqn(n, v);
 
        // ignore pinned values
        if (local_eqn_number >= 0)
        {
          // store dof lookup in temporary pair: Global equation
          // number is the first entry in pair
          dof_lookup.first = this->eqn_number(local_eqn_number);
 
          // Is it a boundary node? If so: It's dof type 1
          if (node_pt(n)->is_on_boundary(0) || node_pt(n)->is_on_boundary(1))
          {
            dof_lookup.second = 1;
          }
          // otherwise it's in the interior: It's dof type 0
          else
          {
            dof_lookup.second = 0;
          }
 
          // add to list
          dof_lookup_list.push_front(dof_lookup);
        }
 
        // Second nodal value: U_x
        //---------------------------------
        v = 2;
 
        // determine local eqn number
        local_eqn_number = this->nodal_local_eqn(n, v);
 
        // ignore pinned values
        if (local_eqn_number >= 0)
        {
          // store dof lookup in temporary pair: Global equation
          // number is the first entry in pair
          dof_lookup.first = this->eqn_number(local_eqn_number);
 
          // set dof type numbers: Dof type is the second entry in pair
          dof_lookup.second = 3;
 
          // add to list
          dof_lookup_list.push_front(dof_lookup);
        }
 
        // Third nodal value: U_y
        //---------------------------------
        v = 3;
 
        // determine local eqn number
        local_eqn_number = this->nodal_local_eqn(n, v);
 
        // ignore pinned values
        if (local_eqn_number >= 0)
        {
          // store dof lookup in temporary pair: Global equation
          // number is the first entry in pair
          dof_lookup.first = this->eqn_number(local_eqn_number);
 
          // set dof type numbers: Dof type is the second entry in pair
          dof_lookup.second = 4;
 
          // add to list
          dof_lookup_list.push_front(dof_lookup);
        }
 
      } // for (n < n_node)
    }
 
    /// Output function:
    ///  x,y,w
    void output(std::ostream& outfile)
    {
      DisplacementBasedFoepplvonKarmanEquations::output(outfile);
    }
 
    ///  Output function:
    ///   x,y,w at n_plot^2 plot points
    void output(std::ostream& outfile, const unsigned& n_plot)
    {
      DisplacementBasedFoepplvonKarmanEquations::output(outfile, n_plot);
    }
 
 
    /// C-style output function:
    ///  x,y,w
    void output(FILE* file_pt)
    {
      DisplacementBasedFoepplvonKarmanEquations::output(file_pt);
    }
 
 
    ///  C-style output function:
    ///   x,y,w at n_plot^2 plot points
    void output(FILE* file_pt, const unsigned& n_plot)
    {
      DisplacementBasedFoepplvonKarmanEquations::output(file_pt, n_plot);
    }
 
 
    /// Output function for an exact solution:
    ///  x,y,w_exact
    void output_fct(std::ostream& outfile,
                    const unsigned& n_plot,
                    FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
    {
      DisplacementBasedFoepplvonKarmanEquations::output_fct(
        outfile, n_plot, exact_soln_pt);
    }
 
 
    /// Output function for a time-dependent exact solution.
    ///  x,y,w_exact (calls the steady version)
    void output_fct(std::ostream& outfile,
                    const unsigned& n_plot,
                    const double& time,
                    FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt)
    {
      DisplacementBasedFoepplvonKarmanEquations::output_fct(
        outfile, n_plot, time, exact_soln_pt);
    }
 
  protected:
    /// Shape, test functions & derivs. w.r.t. to global coords. Return
    /// Jacobian.
    inline double dshape_and_dtest_eulerian_fvk(const Vector<double>& s,
                                                Shape& psi,
                                                DShape& dpsidx,
                                                Shape& test,
                                                DShape& dtestdx) const;
 
 
    /// Shape, test functions & derivs. w.r.t. to global coords. Return
    /// Jacobian.
    inline double dshape_and_dtest_eulerian_at_knot_fvk(const unsigned& ipt,
                                                        Shape& psi,
                                                        DShape& dpsidx,
                                                        Shape& test,
                                                        DShape& dtestdx) const;
 
    /// Order of recovery shape functions for Z2 error estimation:
    /// Same order as shape functions.
    unsigned nrecovery_order()
    {
      return (NNODE_1D - 1);
    }
 
    /// Number of 'flux' terms for Z2 error estimation
    unsigned num_Z2_flux_terms()
    {
      return 2;
    } // The dimension
 
    /// Get 'flux' for Z2 error recovery:  Standard flux.from FvK equations
    void get_Z2_flux(const Vector<double>& s, Vector<double>& flux)
    {
      this->get_gradient_of_deflection(s, flux);
    }
 
    /// Number of vertex nodes in the element
    unsigned nvertex_node() const
    {
      return TElement<2, NNODE_1D>::nvertex_node();
    }
 
    /// Pointer to the j-th vertex node in the element
    Node* vertex_node_pt(const unsigned& j) const
    {
      return TElement<2, NNODE_1D>::vertex_node_pt(j);
    }
 
  private:
    /// Static unsigned that holds the (same) number of variables at every node
    static const unsigned Initial_Nvalue;
  };
 
 
  // Inline functions:
 
 
  //======================================================================
  /// Define the shape functions and test functions and derivatives
  /// w.r.t. global coordinates and return Jacobian of mapping.
  ///
  /// Galerkin: Test functions = shape functions
  //======================================================================
  template<unsigned NNODE_1D>
  double TDisplacementBasedFoepplvonKarmanElement<
    NNODE_1D>::dshape_and_dtest_eulerian_fvk(const Vector<double>& s,
                                             Shape& psi,
                                             DShape& dpsidx,
                                             Shape& test,
                                             DShape& dtestdx) const
  {
    unsigned n_node = this->nnode();
 
    // Call the geometrical shape functions and derivatives
    double J = this->dshape_eulerian(s, psi, dpsidx);
 
    // Loop over the test functions and derivatives and set them equal to the
    // shape functions
    for (unsigned i = 0; i < n_node; i++)
    {
      test[i] = psi[i];
      dtestdx(i, 0) = dpsidx(i, 0);
      dtestdx(i, 1) = dpsidx(i, 1);
    }
 
    // Return the jacobian
    return J;
  }
 
 
  //======================================================================
  /// Define the shape functions and test functions and derivatives
  /// w.r.t. global coordinates and return Jacobian of mapping.
  ///
  /// Galerkin: Test functions = shape functions
  //======================================================================
  template<unsigned NNODE_1D>
  double TDisplacementBasedFoepplvonKarmanElement<
    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
    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;
  }
 
 
  //=======================================================================
  /// Face geometry for the TDisplacementBasedFoepplvonKarmanElement
  //  elements:The spatial / dimension of the face elements is one lower
  //  than that of the / bulk element but they have the same number of
  //  points / along their 1D edges.
  //=======================================================================
  template<unsigned NNODE_1D>
  class FaceGeometry<TDisplacementBasedFoepplvonKarmanElement<NNODE_1D>>
    : public virtual TElement<1, NNODE_1D>
  {
  public:
    /// Constructor: Call the constructor for the
    /// appropriate lower-dimensional TElement
    FaceGeometry() : TElement<1, NNODE_1D>() {}
  };
 
} // namespace oomph
 
#endif