jive::geom::BiQuadraticQuad Class Reference

Constructs shape objects that encapsulate the geometrical properties of bi-quadratic quadrilateral elements. More...

Inheritance diagram for jive::geom::BiQuadraticQuad:

Static Public Member Functions
static jem::Ref< InternalShape >	getShape (int ipCount=9, int bndIpCount=3)
	Returns a shape with a specified number of integration points. More...
static jem::Ref< InternalShape >	getShape (const Matrix &intPoints, const Vector &intWeights, const Matrix &bndIntPoints, const Vector &bndIntWeights)
	Returns a shape with a specific set of integration points. More...
static jem::Ref< InternalShape >	getShape (const Matrix &intPoints, const Vector &intWeights, const ShapeBoundary &boundary)
	Returns a shape with a specific set of boundaries. More...

Additional Inherited Members
Public Types inherited from jive::geom::TypeDefs
typedef jem::util::Properties	Properties
	A type representing a set of properties. More...
typedef util::Vector	Vector
	A vector type. More...
typedef util::Matrix	Matrix
	A matrix type. More...

Detailed Description

#include <jive/geom/Quad.h>

The QuadraticQuad class provides functions for constructing InternalShape objects that encapsulate the geometrical properties of quadrilateral elements with nine nodes and bi-quadratic, isoparametric shape functions. The following figure shows how the nodes are numbered (left image) and where they are located in the local coordinate system (right image).

Note that the local node coordinates of a bi-quadratic quadrilateral are identical to the node coordinates of a standard bi-quadratic square.

A bi-quadratic quadrilateral has four boundaries. The table below indicates which boundaries are attached to which nodes.

Boundary index	Node indices
0	0, 1, 2
1	2, 3, 4
2	4, 5, 6
3	6, 7, 0

The normals on the boundaries point away from the interior of the quadrilateral. The boundaries are normally represented by BoundaryShape objects that are constructed by the QuadraticBoundaryLine class. However, you can also specify your own set of BoundaryShape objects to be used.

Note that the QuadraticQuad class has only static members; it should be used as a mini name space.

See also

LinearQuad, QuadraticQuad

Member Function Documentation

static jem::Ref<InternalShape> jive::geom::BiQuadraticQuad::getShape ( int  ipCount = 9, int  bndIpCount = 3  )

static

Returns an InternalShape object that encapsulates the geometrical properties of a bi-quadratic quadrilateral element. This function is similar to LinearQuad::getShape().

Parameters

ipCount	- the number of integration points within the element.
bndIpCount	- the number of integration points on each boundary.

Returns

An InternalShape object representing a bi-quadratic quadrilateral element.

static jem::Ref<InternalShape> jive::geom::BiQuadraticQuad::getShape ( const Matrix &  intPoints, const Vector &  intWeights, const Matrix &  bndIntPoints, const Vector &  bndIntWeights  )

static

Returns an InternalShape object that represents a bi-quadratic quadrilateral element with a specific set of integration points. This function is similar to the function LinearQuad::getShape().

Parameters

intPoints	- a matrix containing the local coordinates of the integration points within the element.
intWeights	- a vector containing the weights of the internal integration points in the local coordinate system.
bndIntPoints	- a matrix containing the local coordinates of the integration points on each boundary.
bndIntWeights	- a vector containing the weights of the boundary integration points in the local coordinate system of the boundaries.

Precondition

intPoints.size(0) == 2 &&
intPoints.size(1) == intWeights.size() &&
bndIntPoints.size(0) == 1 &&
bndIntPoints.size(1) == bndIntWeights.size()

Returns

An InternalShape object that encapsulates the geometrical properties of a bi-quadratic quadrilateral element.

static jem::Ref<InternalShape> jive::geom::BiQuadraticQuad::getShape ( const Matrix &  intPoints, const Vector &  intWeights, const ShapeBoundary &  boundary  )

static

Returns an InternalShape object that represents a bi-quadratic quadrilateral element with a specific set of integration points and boundaries. This function is similar to LinearQuad::getShape().

Parameters

intPoints	- a matrix containing the local coordinates of the integration points within the quad.
intWeights	- a vector containing the weights of the internal integration points in the local coordinate system.
boundary	- the boundaries of the shape object returned by this function.

Precondition

intPoints.size(0) == 2 &&
intPoints.size(1) == intWeights.size()

Returns

An InternalShape object that encapsulates the geometrical properties of a bi-quadratic quadrilateral element.