J:/Tecgraf/prj/femoop/trunk/shp/shpline.h

// -------------------------------------------------------------------------
// ShpLine.h  -  This header file contains the definitions of :
//               Line2D and Line3D shape class.
// -------------------------------------------------------------------------
// Public methods:
// -------------------------------------------------------------------------
//
// void DerivXYZ (   double    **invjac,
//                   sDerivNat  *derivshp_rst,
//                   sDerivCart *deriv_xyz )
//
//      invjac         -   inverse of the jacobian matrix     (  in )
//      derivshp_rst   -   local shape functions derivatives  (  in )
//      deriv_xyz      -   global shape functions derivatives ( out )
//
//
//                 -     -                     -     -
//                | dN/dx |                   | dN/dr |
//                |       |                   |       |
//                | dN/dy |  =  [jac_inv]  *  |   0   | , where dN/ds = 0
//                |       |                   |       |
//                | dN/dz |                   |   0   |         dN/dt = 0.
//                 -     -                     -     -
//
//      This method  evaluates the global shape  functions derivatives
//      at a given integration point, for line elements.
//
// -------------------------------------------------------------------------
//
// void Jacobian ( sDerivNat  *derivmap_rst,
//                 sNodeCoord *coord,
//                 double     *detjac,
//                 double    **invjac )
//
//      derivmap_rst   -   local map functions derivatives    (  in )
//      mapfunc        -   map functions                      (  in )
//      coord          -   element coordinates                (  in )
//      detjac         -   determinant of jacobian matrix     ( out )
//      jac            -   jacobian matrix                    ( out )
//      invjac         -   inverse of the jacobian matrix     ( out )
//
//
//      Line2D
//
//      This method evaluates the jacobian matrix, its inverse and its
//      determinant for  line  element shape.  The jacobian  matrix is 
//      defined as follows:
//      The first row is formed by the derivatives of the position
//      vector with respect to the line parametric coordinate, i.e.,
//      the line tangent direction.
//      The second row is a direction in the plane which is
//      normal to the line tangent direction, i.e., a 
//      direction perpendicular to the first Jacobian matrix row.
//      The third row is the unity vector in the z-direction.
//      The size of the vector (dx/dr,dy/dr) is returned as the
//      determinant of the jacobian matrix.
//
//                -                   -
//               |  dx/dr   dy/dr   0  |
//               |                     |
//       [jac] = | -dy/dr   dx/dr   0  |
//               |                     |
//               |    0       0     1  |
//                -                   -
//
//                                 2           2
//          det_jac = sqrt( (dx/dr)  +  (dy/dr)  )
//
//
//      Line3D
//
//      This method evaluates the jacobian matrix, its inverse and its
//      determinant for  line  element shape.  The jacobian  matrix is 
//      defined as follows:
//      The first row is formed by the derivatives of the position
//      vector with respect to the line parametric coordinate, i.e.,
//      the line tangent direction.
//      The second row is any direction which is found perdendicular
//      to the first row.  The first choice is a direction which
//      also perpendicular to the z-axis, the second is a direction
//      perpendicular to the y-axis, and the third choice is a
//      direction perpendicular to the x-axis.
//      The third row is obtained by the cross product of the
//      first two rows.
//      The size of the vector (dx/dr,dy/dr,dz/dr) is returned as the
//      determinant of the jacobian matrix.
//
//                                 2           2           2
//          det_jac = sqrt( (dx/dr)  +  (dy/dr)  +  (dz/dr)  )
//
// -------------------------------------------------------------------------
//
// void LocalSys  ( sDerivNat  *derivmap_rst,
//                  sNodeCoord *coord,
//                  double    **rot )
//
//      derivmap_rst    -   local map functions derivatives    (  in )
//      coord           -   element coordinates                (  in )
//      rot[3][3]       -   rotation matrix                    ( out )
//
//      This method computes the rotation matrix of a local system  of
//      coordinates evaluated at a point on the line.     The rotation 
//      matrix is  formed as follows:
//      Each column of the rotation matrix is formed by the coordinates 
//      of each local system unity vector in the global system.
//      The non-normalized coordinates of the local system directions
//      are considered as:
//      The first column is formed by the derivatives of the position
//      vector with respect to the line parametric coordinate, i.e.,
//      the line tangent direction.
//      The second column is any direction which is found perdendicular
//      to the first row.  The first choice is a direction which
//      also perpendicular to the z-axis, the second is a direction
//      perpendicular to the y-axis, and the third choice is a
//      direction perpendicular to the x-axis.
//      The third column is obtained by the cross product of the
//      first two rows.
//
// -------------------------------------------------------------------------
//
// $Author: joaquim $
// $Revision: 1.2 $
// $Date: 1998/02/16 20:21:11 $
// $State: Exp $
//
// -------------------------------------------------------------------------

#ifndef  _SHPLINE_H
#define  _SHPLINE_H

#include "gbldefs.h"
#include "shape.h"

// -------------------------------------------------------------------------
// Line2D Shape class:
//
class cLine2D : public cShape
{
 public:
               cLine2D     ( void );
  virtual     ~cLine2D     ( void );
          int  GetDimShape ( void ) { return 1; }
  virtual void Jacobian    ( sDerivNat *, double *, sNodeCoord *,
                             double *, double **, double ** );
  virtual void DerivXYZ    ( double **, sDerivNat *,sDerivCart * );
  virtual void LocalSys    ( sDerivNat *, sNodeCoord *, double ** );
  virtual void GetTangent  ( sNodeCoord *, sDerivNat *, sVector *, 
                             double *);
  virtual void DsaDerivXYZ ( sNodeCoord *, sDerivNat *, sDerivNat *,
                             double *, sDerivCart *, sNodeCoord *,
                             double *, sDerivCart *);
};


// -------------------------------------------------------------------------
// Line3D Shape class:
//
class cLine3D : public virtual cLine2D
{
 public:
               cLine3D     ( void );
  virtual     ~cLine3D     ( void );
  virtual void Jacobian    ( sDerivNat *, double *, sNodeCoord *,
                             double *, double **, double ** );
  virtual void DerivXYZ    ( double **, sDerivNat *,sDerivCart * );
  virtual void LocalSys    ( sDerivNat *, sNodeCoord *, double ** );
  virtual void GetTangent  ( sNodeCoord *, sDerivNat *, sVector *, 
                             double *);
  virtual void DsaDerivXYZ ( sNodeCoord *, sDerivNat *, sDerivNat *,
                             double *, sDerivCart *, sNodeCoord *,
                             double *, sDerivCart *);
};

#endif

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