Defines a 6-node pentahedral finite element using P₁ interpolation in local coordinates (s.x,s.y) and Q₁ isoparametric interpolation in local coordinates (s.x,s.z) and (s.y,s.z). More...

#include <Penta6.h>

Inheritance diagram for Penta6:

Public Member Functions
	Penta6 ()
	Default Constructor.

	Penta6 (const Element *element)
	Constructor when data of Element `el` are given.

	~Penta6 ()
	Destructor.

void	set (const Element *el)
	Choose element by giving its pointer.

void	setLocal (const Point< real_t > &s)
	Initialize local point coordinates in element.

vector< Point< real_t > >	DSh () const
	Return partial derivatives of shape functions of element nodes.

real_t	getMaxEdgeLength () const
	Return Maximum length of pentahedron edges.

real_t	getMinEdgeLength () const
	Return Mimimum length of pentahedron edges.

Public Member Functions inherited from FEShape
	FEShape ()
	Default Constructor.

	FEShape (const Element *el)
	Constructor for an element.

	FEShape (const Side *sd)
	Constructor for a side.

virtual	~FEShape ()
	Destructor.

real_t	Sh (size_t i) const
	Return shape function of node `i` at given point.

real_t	Sh (size_t i, Point< real_t > s) const
	Calculate shape function of node `i` at a given point `s`.

real_t	getDet () const
	Return determinant of jacobian.

Point< real_t >	getCenter () const
	Return coordinates of center of element.

Point< real_t >	getLocalPoint () const
	Localize a point in the element.

Point< real_t >	getLocalPoint (const Point< real_t > &s) const
	Localize a point in the element.

Detailed Description

Defines a 6-node pentahedral finite element using P₁ interpolation in local coordinates (s.x,s.y) and Q₁ isoparametric interpolation in local coordinates (s.x,s.z) and (s.y,s.z).

The reference element is the cartesian product of the standard reference triangle with the line [-1,1]. The nodes are ordered as follows: Node 1 in reference element is at s=(1,0,0) Node 2 in reference element is at s=(0,1,0) Node 3 in reference element is at s=(0,0,0) Node 4 in reference element is at s=(1,0,1) Node 5 in reference element is at s=(0,1,1) Node 6 in reference element is at s=(0,0,1)

The user must take care to the fact that determinant of jacobian and other quantities depend on the point in the reference element where they are calculated. For this, before any utilization of shape functions or jacobian, function setLocal() must be invoked.

Author: Rachid Touzani

Copyright: GNU Lesser Public License

Constructor & Destructor Documentation

◆ Penta6()

Penta6 ( const Element * element )

Constructor when data of Element el are given.

Parameters

[in] element Pointer to Element

Member Function Documentation

◆ DSh()

vector< Point< real_t > > DSh ( ) const

Return partial derivatives of shape functions of element nodes.

Returns: LocalVect instance of partial derivatives of shape functions e.g. dsh(i).x, dsh(i).y, are partial derivatives of the i-th shape function.

Note: The local point at which the derivatives are computed must be chosen before by using the member function setLocal

◆ setLocal()

void setLocal ( const Point< real_t > & s )

Initialize local point coordinates in element.