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Jive reference manual
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Constructs shape objects that encapsulate the geometrical properties of quadratic hexahedron elements. More...
Static Public Member Functions | |
| static jem::Ref< InternalShape > | getShape (int ipCount=27, int bndIpCount=9) |
| 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... | |
#include <jive/geom/Hexahedron.h>
The QuadraticHexahedron class provides functions for constructing InternalShape objects that encapsulate the geometrical properties of hexahedron elements with eight 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 hexahedron are identical to the node coordinates of a standard quadratic hexahedron.
A quadratic hexahedron has six boundaries. The table below indicates which boundaries are attached to which nodes.
| Boundary index | Node indices |
| 0 | 0, 7, 6, 5, 4, 3, 2, 1 |
| 1 | 0, 1, 2, 9, 14, 13, 12, 8 |
| 2 | 2, 3, 4, 10, 16, 15, 14, 9 |
| 3 | 4, 5, 6, 11, 18, 17, 16, 10 |
| 4 | 0, 8, 12, 19, 18, 11, 6, 7 |
| 5 | 12, 13, 14, 15, 16, 17, 18, 19 |
The normals on the boundaries point away from the interior of the hexahedron. The boundaries are normally represented by BoundaryShape objects that are constructed by the QuadraticBoundaryQuad class. However, you can also specify your own set of BoundaryShape objects to be used.
Note that the QuadraticHexahedron class has only static members; it should be used as a mini name space.
LinearHexahedron
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Returns an InternalShape object that encapsulates the geometrical properties of a quadratic hexahedron element. This function is similar to LinearHexahedron::getShape().
| ipCount | - the number of integration points within the element. |
| bndIpCount | - the number of integration points on each boundary. |
InternalShape object representing a quadratic hexahedron element.
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Returns an InternalShape object that represents a quadratic hexahedron element with a specific set of integration points. This function is similar to LinearHexahedron::getShape().
| 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. |
intPoints.size(0) == 3 &&
intPoints.size(1) == intWeights.size() &&
bndIntPoints.size(0) == 2 &&
bndIntPoints.size(1) == bndIntWeights.size() InternalShape object that encapsulates the geometrical properties of a quadratic hexahedron element.
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Returns an InternalShape object that represents a quadratic hexahedron element with a specific set of integration points and boundaries. This function is similar to LinearHexahedron::getShape().
| 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 returned by this function. |
intPoints.size(0) == 3 &&
intPoints.size(1) == intWeights.size() InternalShape object that encapsulates the geometrical properties of a quadratic hexahedron element. 