circular_shell_mesh.template.h

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//LIC// ====================================================================
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//LIC// Copyright (C) 2006-2016 Matthias Heil and Andrew Hazel
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//LIC// This library is free software; you can redistribute it and/or
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#ifndef OOMPH_CIRCULAR_SHELL_MESH_HEADER
#define OOMPH_CIRCULAR_SHELL_MESH_HEADER

// Config header generated by autoconfig
#ifdef HAVE_CONFIG_H
  #include <oomph-lib-config.h>
#endif

// OOMPH-LIB headers
#include "../generic/mesh.h"
#include "../generic/matrices.h"
#include "../generic/quadtree.h"
#include "../generic/quad_mesh.h"
#include "rectangular_quadmesh.template.h"



namespace oomph
{
 
//========================================================================
/// A 2D solid mesh for (topologically) circular cylindrical shells.
/// The shell is represented by two Lagrangian coordinates that correspond
/// to z and theta in cylindrical polars. The required mesh is therefore a
/// 2D mesh and is therefore inherited from the generic RectangularQuadMesh
//=======================================================================
 template <class ELEMENT>
  class CircularCylindricalShellMesh : 
 public virtual RectangularQuadMesh<ELEMENT>,
  public virtual SolidMesh
  {
    public:
   
   /// Typedef for fct that defines the axial stretching fct
   typedef double (*AxialBLStretchingFctPt)(const double& x);
   
   ///Constructor for the mesh -- uniformly spaced elements
   CircularCylindricalShellMesh(const unsigned &nx,
                                const unsigned &ny,
                                const double &lx,
                                const double &ly,
                                TimeStepper* time_stepper_pt=
                                &Mesh::Default_TimeStepper) :
    RectangularQuadMesh<ELEMENT>(nx,ny,lx,ly,time_stepper_pt) 
    {
     // Use default stretching fct
     Axial_bl_stretching_fct_pt=0;
     
     // Assign dummy data consistent with uniform spacing
     Nx_bl=1; 
     Delta_bl=lx/double(nx);
     
     // Build mesh
     this->build_mesh(nx,ny,lx,ly);
    }
    
    
    /// \short Constructor for the mesh -- specify fct that maps axial
    ///  Lagr. coordinates to new positions to allow for better resolution of
    /// bending boundary layer
    CircularCylindricalShellMesh(const unsigned &nx,
                                 const unsigned &ny,
                                 const double &lx,
                                 const double &ly,
                                 AxialBLStretchingFctPt
                                 axial_bl_stretching_fct_pt,
                                 TimeStepper* time_stepper_pt=
                                 &Mesh::Default_TimeStepper) :
     RectangularQuadMesh<ELEMENT>(nx,ny,lx,ly,time_stepper_pt) 
     {
      // Apply stretching fct
    Axial_bl_stretching_fct_pt=axial_bl_stretching_fct_pt;
    
    // Assign dummy data consistent with uniform spacing
    Nx_bl=1;
    Delta_bl=lx/double(nx);
    
    // Build mesh
    this->build_mesh(nx,ny,lx,ly);
   }
   
   /// \short Constructor for the mesh. nx_bl azimuthal layers of
   /// elements near the ends are squashed to that axial extent
   /// of the elements changes from lx/nx to delta_bl. 
   CircularCylindricalShellMesh(const unsigned &nx,
                                const unsigned &ny,
                                const double &lx,
                                const double &ly,
                                const unsigned& nx_bl,
                                const double& delta_bl,
                                TimeStepper* time_stepper_pt=
                                &Mesh::Default_TimeStepper) :
    RectangularQuadMesh<ELEMENT>(nx,ny,lx,ly,time_stepper_pt) 
    {
     // Use default stretching fct
     Axial_bl_stretching_fct_pt=0;
     
     // Store bl data
     Nx_bl=nx_bl;
     Delta_bl=delta_bl;
     
     // Build mesh
     this->build_mesh(nx,ny,lx,ly);
    }
    
    
    /// \short In all elastic problems, the nodes must be assigned an 
    /// undeformed, or reference, position, corresponding to the 
    /// stress-free state of the elastic body. This function assigns 
    /// the undeformed position for the nodes on the elastic tube
    void assign_undeformed_positions(GeomObject* const&
                                     undeformed_midplane_pt);
    
    
    /// Access to fct pointer to fct that defines the axial stretching fct
    AxialBLStretchingFctPt axial_bl_stretching_fct_pt() const
    {
     return Axial_bl_stretching_fct_pt;
    }
    
    
  private:
    
    
    /// Mesh build helper fct
    void build_mesh(const unsigned &nx, const unsigned &ny,
                    const double &lx, const double &ly);
    
    
    /// \short Fct that defines the axial stretching to accomodate 
    /// bending boundary layers
    double scaled_x(const double& x)
    {
     if (Axial_bl_stretching_fct_pt==0)
      {
       return piecewise_linear_axial_bl_stretching_fct(x);
      }
     else
      {
       return (*Axial_bl_stretching_fct_pt)(x);
      }
    }
    
    /// Default axial scaling fct
    double piecewise_linear_axial_bl_stretching_fct(const double& xi)
    {
     // Length of shell
     double lx=this->Xmax-this->Xmin;
     
     // Old axial extent of the elements spanning the boundary layer
     double old_delta_bl=double(Nx_bl)*lx/double(this->Nx);
     
     double tmp_xi=xi;
     if (xi<old_delta_bl)
      {
       tmp_xi=xi*Delta_bl/old_delta_bl;
      }
     else if (xi<(lx-old_delta_bl))
      {
       tmp_xi=Delta_bl+(xi-old_delta_bl)/(lx-2.0*old_delta_bl)*
        (lx-2.0*Delta_bl);
      }
     else
      {
       double end_x=lx-Delta_bl;
       tmp_xi=end_x+(xi-(lx-old_delta_bl))/old_delta_bl*Delta_bl;
      }
     return tmp_xi;
    }
    
    
    /// Fct pointer to fct that defines the axial stretching fct
    AxialBLStretchingFctPt Axial_bl_stretching_fct_pt;
    
    /// \short Number of azimuthal element layers that get squashed into
    /// each of the the two boundary layers at the ends of the tube
    unsigned Nx_bl;
    
    /// \short Axial extent of the squashed boundary layer part of the mesh
    /// occupied by Nx_bl elements (at each end of the tube)
    double Delta_bl;
 
   
    
};
 
}


#endif