NumLib::ShapeQuad8 Class Reference

Detailed Description

Shape function for a 8-nodes quadrilateral element

Definition at line 20 of file ShapeQuad8.h.

#include <ShapeQuad8.h>

Public Types
using	MeshElement = MeshLib::Quad8

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

Static Public Attributes
static const unsigned	DIM = MeshElement::dimension
static const unsigned	NPOINTS = MeshElement::n_all_nodes
static constexpr int	ORDER = 2

Member Typedef Documentation

MeshElement

using NumLib::ShapeQuad8::MeshElement = MeshLib::Quad8

Definition at line 41 of file ShapeQuad8.h.

Member Function Documentation

computeGradShapeFunction()

template<class T_X , class T_N >

void NumLib::ShapeQuad8::computeGradShapeFunction ( const T_X &  r, T_N &  dN  )

static

Evaluate derivatives of the shape function at the given point

Parameters

[in]	r	point coordinates
[out]	dN	a matrix of the derivatives

Definition at line 28 of file ShapeQuad8-impl.h.

{
    const double r = rs[0];
    const double s = rs[1];
 
    // dN/dr
    dNdr[0] = (1 + s) * (2 * r + s) * 0.25;
    dNdr[1] = (1 + s) * (2 * r - s) * 0.25;
    dNdr[2] = (1 - s) * (2 * r + s) * 0.25;
    dNdr[3] = (1 - s) * (2 * r - s) * 0.25;
 
    dNdr[4] = -r * (1 + s);
    dNdr[5] = -(1 - s * s) * 0.5;
    dNdr[6] = -r * (1 - s);
    dNdr[7] = (1 - s * s) * 0.5;
 
    // dN/ds
    dNdr[8] = (1 + r) * (r + 2 * s) * 0.25;
    dNdr[9] = -(1 - r) * (r - 2 * s) * 0.25;
    dNdr[10] = (1 - r) * (r + 2 * s) * 0.25;
    dNdr[11] = -(1 + r) * (r - 2 * s) * 0.25;
 
    dNdr[12] = (1 - r * r) * 0.5;
    dNdr[13] = -(1 - r) * s;
    dNdr[14] = -(1 - r * r) * 0.5;
    dNdr[15] = -(1 + r) * s;
}

References MathLib::r.

computeShapeFunction()

template<class T_X , class T_N >

void NumLib::ShapeQuad8::computeShapeFunction ( const T_X &  r, T_N &  N  )

static

Evaluate the shape function at the given point

Parameters

[in]	r	point coordinates
[out]	N	a vector of calculated shape function.

Definition at line 14 of file ShapeQuad8-impl.h.

{
    N[0] = 0.25 * (1.0 + r[0]) * (1.0 + r[1]) * (-1.0 + r[0] + r[1]);
    N[1] = -0.25 * (1.0 - r[0]) * (1.0 + r[1]) * (1.0 + r[0] - r[1]);
    N[2] = -0.25 * (1.0 - r[0]) * (1.0 - r[1]) * (1.0 + r[0] + r[1]);
    N[3] = 0.25 * (1.0 + r[0]) * (1.0 - r[1]) * (-1.0 + r[0] - r[1]);
    //
    N[4] = 0.5 * (1.0 - r[0] * r[0]) * (1.0 + r[1]);
    N[5] = 0.5 * (1.0 - r[1] * r[1]) * (1.0 - r[0]);
    N[6] = 0.5 * (1.0 - r[0] * r[0]) * (1.0 - r[1]);
    N[7] = 0.5 * (1.0 - r[1] * r[1]) * (1.0 + r[0]);
}

References NumLib::N, and MathLib::r.

Member Data Documentation

DIM

const unsigned NumLib::ShapeQuad8::DIM = MeshElement::dimension

static

Definition at line 42 of file ShapeQuad8.h.

NPOINTS

const unsigned NumLib::ShapeQuad8::NPOINTS = MeshElement::n_all_nodes

static

Definition at line 43 of file ShapeQuad8.h.

ORDER

constexpr int NumLib::ShapeQuad8::ORDER = 2

staticconstexpr

Definition at line 44 of file ShapeQuad8.h.

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

• NumLib/Fem/ShapeFunction/ShapeQuad8.h
• NumLib/Fem/ShapeFunction/ShapeQuad8-impl.h
• NumLib/Fem/ShapeFunction/ShapeStaticConsts.cpp