jive::geom::QuadraticTriangle Class Reference

Constructs shape objects that encapsulate the geometrical properties of quadratic triangle elements. More...

Inheritance diagram for jive::geom::QuadraticTriangle:

Static Public Member Functions
static jem::Ref< InternalShape >	getShape (int ipCount=7, 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/Triangle.h>

The QuadraticTriangle class provides functions for constructing InternalShape objects that encapsulate the geometrical properties of triangle elements with six nodes and 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 quadratic triangle are identical to the node coordinates of a standard quadratic triangle.

A quadratic triangle has three 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, 0

The normals on the boundaries point away from the interior of the triangle. 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 QuadraticTriangle class has only static members; it should be used as a mini name space.

See also

LinearTriangle

Member Function Documentation

static jem::Ref<InternalShape> jive::geom::QuadraticTriangle::getShape ( int  ipCount = 7, int  bndIpCount = 3  )

static

Returns an InternalShape object that encapsulates the geometrical properties of a quadratic triangle element. This function is similar to LinearTriangle::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 quadratic triangle element.

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

static

Returns an InternalShape object that represents a quadratic triangle element with a specific set of integration points. This function is similar to LinearTriangle::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 quadratic triangle element.

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

static

Returns an InternalShape object that represents a quadratic triangle element with a specific set of integration points and boundaries. This function is similar to LinearTriangle::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.
boundary	- the boundaries of the shape object that is to be constructed.

Precondition

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

Returns

An InternalShape object that encapsulates the geometrical properties of a quadratic triangle element.