NumLib::ShapePyra5 Class Reference

Detailed Description

Shape function for a 5-nodes pyramid element in natural coordinates

Definition at line 21 of file ShapePyra5.h.

#include <ShapePyra5.h>

Public Types
using	MeshElement = MeshLib::Pyramid

Static Public Member Functions
template<class T_X , class T_N >
static void	computeShapeFunction (const T_X &x, T_N &N)
template<class T_X , class T_N >
static void	computeGradShapeFunction (const T_X &x, T_N &dN)

Static Public Attributes
static const unsigned	DIM = MeshElement::dimension
static const unsigned	NPOINTS = MeshElement::n_all_nodes
static constexpr int	ORDER = 1

Member Typedef Documentation

MeshElement

using NumLib::ShapePyra5::MeshElement = MeshLib::Pyramid

Definition at line 42 of file ShapePyra5.h.

Member Function Documentation

computeGradShapeFunction()

template<class T_X , class T_N >

void NumLib::ShapePyra5::computeGradShapeFunction ( const T_X & x, T_N & dN )

static

Evaluate derivatives of the shape function at the given point

Parameters

[in]	x	natural coordinates (r,s,t)
[out]	dN	a matrix of the derivatives

Definition at line 28 of file ShapePyra5-impl.h.

{
    const double r = x[0];
    const double s = x[1];
    const double t = x[2];
    //  dN/dL1
    dN[0] = -0.125 * (1.0 - s) * (1.0 - t);
    dN[1] = -dN[0];
    dN[2] = 0.125 * (1.0 + s) * (1.0 - t);
    dN[3] = -dN[2];
    dN[4] = 0.0;
    //  dN/dL2
    dN[5] = -0.125 * (1.0 - r) * (1.0 - t);
    dN[6] = -0.125 * (1.0 + r) * (1.0 - t);
    dN[7] = -dN[6];
    dN[8] = -dN[5];
    dN[9] = 0.0;
    //  dN/dt
    dN[10] = -0.125 * (1.0 - r) * (1.0 - s);
    dN[11] = -0.125 * (1.0 + r) * (1.0 - s);
    dN[12] = -0.125 * (1.0 + r) * (1.0 + s);
    dN[13] = -0.125 * (1.0 - r) * (1.0 + s);
    dN[14] = 0.5;
}

computeShapeFunction()

template<class T_X , class T_N >

void NumLib::ShapePyra5::computeShapeFunction ( const T_X & x, T_N & N )

static

Evaluate the shape function at the given point

Parameters

[in]	x	natural coordinates (r,s,t)
[out]	N	a vector of calculated shape functions

Definition at line 14 of file ShapePyra5-impl.h.

{
    const double r = x[0];
    const double s = x[1];
    const double t = x[2];
 
    N[0] = 0.125 * (1 - r) * (1 - s) * (1 - t);
    N[1] = 0.125 * (1 + r) * (1 - s) * (1 - t);
    N[2] = 0.125 * (1 + r) * (1 + s) * (1 - t);
    N[3] = 0.125 * (1 - r) * (1 + s) * (1 - t);
    N[4] = 0.5 * (1 + t);
}

References NumLib::N.

Member Data Documentation

DIM

const unsigned NumLib::ShapePyra5::DIM = MeshElement::dimension

static

Definition at line 43 of file ShapePyra5.h.

NPOINTS

const unsigned NumLib::ShapePyra5::NPOINTS = MeshElement::n_all_nodes

static

Definition at line 44 of file ShapePyra5.h.

ORDER

constexpr int NumLib::ShapePyra5::ORDER = 1

staticconstexpr

Definition at line 45 of file ShapePyra5.h.

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The documentation for this class was generated from the following files:

• NumLib/Fem/ShapeFunction/ShapePyra5.h
• NumLib/Fem/ShapeFunction/ShapePyra5-impl.h
• NumLib/Fem/ShapeFunction/ShapeStaticConsts.cpp