 |
GemaCoreLib
The GeMA Core library
|
|
GemaCoreLib
The GeMA Core library
|
GmShape specialization for a 3D cohesive element with 8 nodes object. More...
#include <gmInt3DQFaceShape.h>
Public Member Functions | |
| virtual GmCellType | elemType () const |
| Returns the type of this element. | |
| virtual int | numFunctions () const |
| Returns the number of shape functions of this element type (equal to the number of nodes) | |
| virtual void | nodeNaturalCoord (int node, GmVector &coord) const |
| Fills the coord vector with the set of natural coordinates for the reference shape function node. Node should be a value between 0 and numFunctions(). This is generally equal to the number of nodes but can be different for interface elements. More... | |
| virtual void | shapeValues (const GmVector &ncoord, GmVector &N) const |
| Returns the shape function evaluated at (Xi, Eta). More... | |
| virtual void | shapePartials (const GmVector &ncoord, GmMatrix &dN, bool transposed=false) const |
| Returns shape function partial derivatives with respect to Xi and Eta, evaluated at the point (Xi, Eta). More... | |
 Public Member Functions inherited from GmInt3DShape | |
| virtual int | numNaturalCoord () const |
| Returns the number of natural coordinates used by this element type. | |
| virtual int | numCartesianCoord () const |
| Returns the number of cartesian coordinates expected by this element type. | |
| virtual void | naturalCoordLimits (int coord, double *min, double *max) const |
| Fills min and max with the domain limits for the given natural coordinate (between 0 and numNaturalCoord() - 1) | |
| virtual void | naturalCenter (GmVector &coord) const |
| Fills the coord vector with the set of natural coordinates for the element center. More... | |
| virtual bool | translateEdgePoint (int edge, const GmVector &srcEdgeCoord, GmVector &elementCoord) const |
| Given a "bar like" edge coordinate (from -1 to 1), at the given edge, fills elementCoord with the equivalent element natural coordinate. Should be implemented for 2D & 3D elements. More... | |
| virtual bool | translateFacePoint (int face, const GmVector &srcFaceCoord, GmVector &elementCoord) const |
| Given a "quad like" or "tri like" face coordinate (-1 to 1 pair for quad faces and 0 to 1 barycentric triple for tri faces), at the given face, fills elementCoord with the equivalent element natural coordinate. Should be implemented for 3D elements. More... | |
| virtual double | shapeCartesianPartialsFromPJ (const GmMatrix &P, const GmMatrix &J, GmMatrix &dN, bool transposed=false) const |
| Alternative version of shapeCartesianPartialsXxxx() to calculate shape function partial derivatives with respect to its cartesian coordinates, given a previously calculated Jacobian matrix and a previously calculated shape function partial matrix. More... | |
| virtual double | scaledJacobianDet (const GmMatrix &J) const |
| Returns the Jacobian determinant multiplied by the scaling factor needed for transforming the differential area element. dOmega = dx.dy = J.dXi.dEta where J is the scaled Jacobian determinant. More... | |
| virtual void | jacobianAndPartials (const GmVector &ncoord, const GmMatrix &MX, GmMatrix &J, GmMatrix &P, bool transposed=false) const |
| This function does the same calculations as the jacobian() call, but also filling the extra parameter P with the matrix of shape function partials. More... | |
| virtual double | borderScalingFactor (int border, const GmVector &borderCoord, const GmVector &elementCoord, const GmMatrix &X, bool transposed=false) const |
| Returns the scaling factor needed when calculating integrals over borders (edges or faces). This has the same effect as the jacobian determinant when integrating over the whole element. It can be used to treat 2D and 3D edge / face boundary conditions in a single code. More... | |
| virtual double | edgeScalingFactor (int border, const GmVector &borderCoord, const GmVector &elementCoord, const GmMatrix &X, bool transposed=false) const |
| Returns the scaling factor needed when calculating integrals over element edges. This has the same effect as the jacobian determinant when integrating over the whole element. More... | |
| virtual double | faceScalingFactor (int border, const GmVector &borderCoord, const GmVector &elementCoord, const GmMatrix &X, bool transposed=false) const |
| Returns the scaling factor needed when calculating integrals over element faces. This has the same effect as the jacobian determinant when integrating over the whole element. More... | |
| void | naturalToCartesian (const GmVector &ncoord, const GmMatrix &X, GmVector &coord) const |
| Given a set of natural coordinates 'ncoord' and a matrix with node coordinates 'X', calculates the corresponding cartesian coordinates filling 'coord'. More... | |
| Public Member Functions inherited from GmShape | |
| void | fillNaturalCoordinates (GmMatrix &coord, bool transposed=false) const |
| Fills the coord matrix with the set of natural coordinates for the shape nodes. More... | |
| virtual bool | cartesianToNatural (const GmVector &coord, const GmMatrix &X, GmVector &ncoord, bool *inside) const |
| Given a set of cartesian coordinates 'coord' and a matrix with node coordinates 'X', calculates the corresponding natural coordinate filling 'ncoord'. The inside parameter is filled with true if the given cartesian coordinate is inside the element, false otherwise. More... | |
| virtual bool | cartesianToNatural (const GmVector &coord, const GmMatrix &X, bool preferGeometric, double gradTol, int maxGradIter, double outsideNatTol, GmVector &ncoord, bool *inside) const |
| Given a set of cartesian coordinates 'coord' and a matrix with node coordinates 'X', calculates the corresponding natural coordinate filling 'ncoord'. The inside parameter is filled with true if the given cartesian coordinate is inside the element, false otherwise. More... | |
| virtual double | shapeCartesianPartialsFromCoord (const GmVector &ncoord, const GmMatrix &X, GmMatrix &dN, bool transposed=false) const |
| Function used to calculate shape function partial derivatives with respect to its cartesian coordinates, evaluated at the given point. More... | |
| virtual double | shapeCartesianPartialsFromJacobian (const GmVector &ncoord, const GmMatrix &J, GmMatrix &dN, bool transposed=false) const |
| Alternative version of shapeCartesianPartials() to calculate shape function partial derivatives with respect to its cartesian coordinates, given a previously calculated Jacobian matrix. More... | |
| virtual void | jacobian (const GmVector &ncoord, const GmMatrix &X, GmMatrix &J, bool transposed=false) const |
| Calculates the jacobian matrix, relating cartesian coordinates to natural coordinates. More... | |
| virtual const GmMatrix & | gaussExtrapolationMatrix (const GmIntegrationRule *ir) const |
| Given an integration rule, compatible with the current element type, constructs an extrapolation matrix to calculate node values from integration point values. More... | |
| virtual bool | pointExtrapolationMatrix (const GmMatrix &points, GmMatrix &em) const |
| Given the set of 'm' natural coordinates in points, builds an 'n x m' extrapolation matrix that can be used to extrapolate values from an 'm' sized value vector to the 'n' elements nodes. More... | |
| double | interpolate (const GmVector &nodeValues, const GmVector &ncoord) const |
| Given a set of node values and a set of natural coordinates, interpolates the node values on the given coordinate. More... | |
Additional Inherited Members | |
| Static Public Member Functions inherited from GmShape | |
| static bool | initShapeFunctions () |
| Initializes the shape function module. Must be called BEFORE any calls to shapeFromElementType() or linearShapeFromElementType(), but AFTER the static initialization of the geometry objects. More... | |
| static void | setConfigOptions (const GmSimulationData *simData) |
| Updates the default config options used by the "simple" cartesianToNatural() call. | |
| static const GmShape * | shapeFromElementType (GmCellType etype, int P, int Q) |
| Returns a shape object suitable for handling elements of type etype. Parameters P and Q are needed only when working with hierarchical element types, such as GM_HQUADP or GM_HHEXP. They can be set to 0 for "common" element types. | |
| static const GmShape * | linearShapeFromElementType (GmCellType etype, int P, int Q) |
| Returns a linear shape object suitable for handling elements of type etype. Parameters P and Q are needed only when working with hierarchical element types, such as GM_HQUADP or GM_HHEXP. They can be set to 0 for "common" element types. | |
| Protected Member Functions inherited from GmInt3DShape | |
| virtual bool | gradientBasedCartesianToNatural (const GmVector &coord, const GmMatrix &X, double tol, int maxIter, double natTol, GmVector &ncoord, bool *inside) const |
| Protected Member Functions inherited from GmShape | |
| virtual void | jacIndependentNatCoord (const GmVector &ncoord, const GmMatrix &X, GmMatrix &J, GmMatrix &P, bool transposed) const |
| A generic implementation of jacobianAndPartials() for the case where all natural coordinates are independent, such as in line segments, quads and hexahedrons. More... | |
| virtual void | jacDependentNatCoord (const GmVector &ncoord, const GmMatrix &X, GmMatrix &J, GmMatrix &P, bool transposed) const |
| A generic implementation of jacobianAndPartials() for the case where all natural coordinates are NOT independent, such as in triangles and tetrahedrons. More... | |
| bool | ginv (const GmMatrix &A, GmMatrix &inv) const |
| Calculates the Moore-Penrose generalized matrix inverse for the 'm x n' matrix A, filling inv. More... | |
| bool | gradientBasedCartesianToNaturalQuadHex (const GmVector &coord, const GmMatrix &X, double tol, int maxIter, double natTol, GmVector &ncoord, bool *inside) const |
| Given a set of cartesian coordinates 'coord' and a matrix with node coordinates 'X', calculates the corresponding natural coordinate filling 'ncoord'. Returns true if the calculation succeeded, false otherwise. More... | |
| bool | gradientBasedCartesianToNaturalTriTet (const GmVector &coord, const GmMatrix &X, double tol, int maxIter, double natTol, GmVector &ncoord, bool *inside) const |
| An implementation of the gradient based cartesian to natural algorithm specific to Tri and Tet elements. For a description of the algorithm and function parameters, see gradientBasedCartesianToNaturalQuadHex(). | |
| bool | gradientBasedCartesianToNaturalBar (const GmVector &coord, const GmMatrix &X, double tol, int maxIter, double natTol, GmVector &ncoord, bool *inside) const |
| An implementation of the gradient based cartesian to natural algorithm specific to Bar elements. For a description of the algorithm and function parameters, see gradientBasedCartesianToNaturalQuadHex(). | |
| bool | gradientBasedCartesianToNaturalWedge (const GmVector &coord, const GmMatrix &X, double tol, int maxIter, double natTol, GmVector &ncoord, bool *inside) const |
| An implementation of the gradient based cartesian to natural algorithm specific to Wedge elements. For a description of the algorithm and function parameters, see gradientBasedCartesianToNaturalQuadHex(). | |
| virtual bool | hasGeometryBasedCartesianToNatural () const |
| A virtual function that should be replaced to return true if the shape implements a geometry based algorithm for converting cartesian coordinates to natural coordinates. In that case, geometryBasedCartesianToNatural() must also be reimplemented. | |
| virtual bool | geometryBasedCartesianToNatural (const GmVector &coord, const GmMatrix &X, double natTol, GmVector &ncoord, bool *inside) const |
| Virtual function that should be implemented if a shape can provide a geometric algorithm for converting cartesian coordinates to natural coordinates. See the cartesianToNatural() description for the arguments description. | |
| bool | checkAndClampNaturalCoordinate (double &ncoord, double min, double max, double natTol) const |
| An utilitary function that given a natural coordinate component and its domain (given by min and max), checks that coord is inside the interval, possibly clamping it to the domain if outside by a little bit, controled by the given tolerance. More... | |
| bool | checkAndClampBarycentricNaturalCoordinates (GmVector &ncoord, double natTol) const |
| An utilitary function that given a set of 3 or 4 barycentric natural coordinates, checks for out of the triangle/tetrahedron values, possibly clamping it to the domain if outside by a little bit, controled by the given tolerance. More... | |
GmShape specialization for a 3D cohesive element with 8 nodes object.
Natural coordinates: Xi, Ni Natural coordinates domain: [-1, 1]
Node ordering: Node list formed by the four nodes defining the quad in CCW order. Vertex: 0-1, 1-2, 2-3 and 3-0 See schema in the documentation of the GmCellGeometry class.
|
virtual |
Fills the coord vector with the set of natural coordinates for the reference shape function node. Node should be a value between 0 and numFunctions(). This is generally equal to the number of nodes but can be different for interface elements.
The resulting vector will have size equal to numNaturalCoord(). If coord holds a vector created by DECLARE_REF_VECTOR(), its size MUST already be equal to the expected result size.
Implements GmShape.
|
virtual |
Returns shape function partial derivatives with respect to Xi and Eta, evaluated at the point (Xi, Eta).
See comments on the base class for function behaviour and on the class for coordinate assumptions and node ordering
Int3q16 shape functions:
N1 = 1/4 * (1 - Xi)(1 - Eta)(-1 - Xi - Eta) N2 = 1/4 * (1 + Xi)(1 - Eta)(-1 + Xi - Eta) N3 = 1/4 * (1 + Xi)(1 + Eta)(-1 + Xi + Eta) N4 = 1/4 * (1 - Xi)(1 + Eta)(-1 - Xi + Eta) N5 = 1/2 * (1 - Eta)(1 - Xi*Xi) N6 = 1/2 * (1 + Xi)(1 - Eta*Eta) N7 = 1/2 * (1 + Eta)(1 - Xi*Xi) N8 = 1/2 * (1 - Xi)(1 - Eta*Eta)
Partial derivatives with respect to Xi: dN1/dXi = 1/4 * ( 1 - Eta)*(2*Xi + Eta) dN2/dXi = 1/4 * ( 1 - Eta)*(2*Xi - Eta) dN3/dXi = 1/4 * ( 1 + Eta)*(2*Xi + Eta) dN4/dXi = 1/4 * ( 1 + Eta)*(2*Xi - Eta) dN5/dXi = -Xi * ( 1 - Eta) dN6/dXi = 1/2 * ( 1 - Eta*Eta) dN7/dXi = -Xi * ( 1 + Eta) dN8/dXi = -1/2 * (1 - Eta*Eta)
Partial derivatives with respect to Eta: dN1/dEta = 1/4 * ( 1 - Xi)*(2*Eta + Xi) dN2/dEta = 1/4 * ( 1 + Xi)*(2*Eta - Xi) dN3/dEta = 1/4 * ( 1 + Xi)*(2*Eta + Xi) dN4/dEta = 1/4 * ( 1 - Xi)*(2*Eta - Xi) dN5/dEta = -1/2 * (1 - Xi*Xi) dN6/dEta = -Eta * (1 + Xi) dN7/dEta = 1/2 * (1 - Xi*Xi) dN8/dEta = -Eta * (1 - Xi)
Implements GmShape.
Returns the shape function evaluated at (Xi, Eta).
See comments on the base class for function behaviour and on the class for coordinate assumptions and node ordering
Int3dq16 using 8 shape functions: 4 7 3 o------—o | *4 *3 | 8| |6 at middle plane | *1 *2 | o------—o 1 5 2 N1 = 1/4 * (1 - Xi)(1 - Eta)(-1 - Xi - Eta) N2 = 1/4 * (1 + Xi)(1 - Eta)(-1 + Xi - Eta) N3 = 1/4 * (1 + Xi)(1 + Eta)(-1 + Xi + Eta) N4 = 1/4 * (1 - Xi)(1 + Eta)(-1 - Xi + Eta)
N5 = 1/2 * (1 - Eta)(1 - Xi*Xi) N6 = 1/2 * (1 + Xi)(1 - Eta*Eta) N7 = 1/2 * (1 + Eta)(1 - Xi*Xi) N8 = 1/2 * (1 - Xi)(1 - Eta*Eta)
Implements GmShape.
1.8.15