Quad4 Class Reference

Defines a 4-node quadrilateral finite element using Q1 isoparametric interpolation. More...

#include <Quad4.h>

Inheritance diagram for Quad4:

Public Member Functions
	Quad4 ()
	Default Constructor.
	Quad4 (const Element *element)
	Constructor when data of Element el are given.
	Quad4 (const Side *side)
	Constructor when data of Side sd are given.
	~Quad4 ()
	Destructor.
void	set (const Element *el)
	Choose element by giving its pointer.
void	set (const Side *sd)
	Choose side by giving its pointer.
void	setLocal (const Point< real_t > &s)
	Initialize local point coordinates in element.
void	atGauss (int n, std::vector< real_t > &sh, std::vector< Point< real_t > > &dsh, std::vector< real_t > &w)
	Calculate shape functions and their partial derivatives and integration weights.
Point< real_t >	Grad (const LocalVect< real_t, 4 > &u, const Point< real_t > &s)
	Return gradient of a function defined at element nodes.
real_t	getMaxEdgeLength () const
	Return maximal edge length of quadrilateral.
real_t	getMinEdgeLength () const
	Return minimal edge length of quadrilateral.
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 4-node quadrilateral finite element using Q1 isoparametric interpolation.

The reference element is the square [-1,1]x[-1,1]. 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

Quad4() [1/2]

Quad4

(

const Element *

element

)

Constructor when data of Element el are given.

Parameters

[in]

element

Pointer to Element

Quad4() [2/2]

Quad4

(

const Side *

side

)

Constructor when data of Side sd are given.

Parameters

[in]

side

Pointer to Side

Member Function Documentation

atGauss()

void atGauss	(	int	n,
		std::vector< real_t > &	sh,
		std::vector< Point< real_t > > &	dsh,
		std::vector< real_t > &	w
	)

Calculate shape functions and their partial derivatives and integration weights.

Parameters

[in]	n	Number of Gauss-Legendre integration points in each direction
[in]	sh	Vector of shape functions at Gauss points
[in]	dsh	Vector of shape function derivatives at Gauss points
[in]	w	Weights of integration formula at Gauss points

Grad()

Point< real_t > Grad	(	const LocalVect< real_t, 4 > &	u,
		const Point< real_t > &	s
	)

Return gradient of a function defined at element nodes.

Parameters

[in]	u	Vector of values at nodes
[in]	s	Local coordinates (in [-1,1]*[-1,1]) of point where the gradient is evaluated

Returns

Value of gradient

Note

If the derivatives of shape functions were not computed before calling this function (by calling setLocal), this function will compute them

setLocal()

void setLocal

(

const Point< real_t > &

s

)

Initialize local point coordinates in element.

Parameters

[in]

s

Point in the reference element This function computes jacobian, shape functions and their partial derivatives at s. Other member functions only return these values.