NumLib::ShapeQuad9 Class Reference

Detailed Description

Shape function for a 9-nodes quadrilateral element

Definition at line 20 of file ShapeQuad9.h.

#include <ShapeQuad9.h>

Public Types
using	MeshElement = MeshLib::Quad9

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::ShapeQuad9::MeshElement = MeshLib::Quad9

Definition at line 41 of file ShapeQuad9.h.

Member Function Documentation

computeGradShapeFunction()

template<class T_X , class T_N >

void NumLib::ShapeQuad9::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 ShapeQuad9-impl.h.

{
    dNdr[0] = (r[0] + 0.5) * r[1] * (r[1] + 1) / 2;
    dNdr[1] = (r[0] - 0.5) * r[1] * (r[1] + 1) / 2;
    dNdr[2] = (r[0] - 0.5) * r[1] * (r[1] - 1) / 2;
    dNdr[3] = (r[0] + 0.5) * r[1] * (r[1] - 1) / 2;
    dNdr[4] = -r[0] * r[1] * (1 + r[1]);
    dNdr[5] = (1 - r[1] * r[1]) * (r[0] - 0.5);
    dNdr[6] = r[0] * r[1] * (1 - r[1]);
    dNdr[7] = (1 - r[1] * r[1]) * (r[0] + 0.5);
    dNdr[8] = 2 * r[0] * (r[1] * r[1] - 1);
 
    dNdr[10] = (r[1] + 0.5) * r[0] * (r[0] - 1) / 2;
    dNdr[11] = (r[1] - 0.5) * r[0] * (r[0] - 1) / 2;
    dNdr[12] = (r[1] - 0.5) * r[0] * (r[0] + 1) / 2;
    dNdr[13] = (1 - r[0] * r[0]) * (r[1] + 0.5);
    dNdr[14] = r[0] * r[1] * (1 - r[0]);
    dNdr[15] = (1 - r[0] * r[0]) * (r[1] - 0.5);
    dNdr[16] = -r[0] * r[1] * (1 + r[0]);
    dNdr[17] = 2 * r[1] * (r[0] * r[0] - 1);
    dNdr[9] = (r[1] + 0.5) * r[0] * (r[0] + 1) / 2;
}

References MathLib::r.

computeShapeFunction()

template<class T_X , class T_N >

void NumLib::ShapeQuad9::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 ShapeQuad9-impl.h.

{
    N[0] = r[0] * (r[0] + 1) * r[1] * (r[1] + 1) / 4;
    N[1] = r[0] * (r[0] - 1) * r[1] * (r[1] + 1) / 4;
    N[2] = r[0] * (r[0] - 1) * r[1] * (r[1] - 1) / 4;
    N[3] = r[0] * (r[0] + 1) * r[1] * (r[1] - 1) / 4;
    N[4] = r[1] * (r[1] + 1) * (1 - r[0] * r[0]) / 2;
    N[5] = r[0] * (r[0] - 1) * (1 - r[1] * r[1]) / 2;
    N[6] = r[1] * (r[1] - 1) * (1 - r[0] * r[0]) / 2;
    N[7] = r[0] * (r[0] + 1) * (1 - r[1] * r[1]) / 2;
    N[8] = (1 - r[0] * r[0]) * (1 - r[1] * r[1]);
}

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

Member Data Documentation

DIM

const unsigned NumLib::ShapeQuad9::DIM = MeshElement::dimension

static

Definition at line 42 of file ShapeQuad9.h.

NPOINTS

const unsigned NumLib::ShapeQuad9::NPOINTS = MeshElement::n_all_nodes

static

Definition at line 43 of file ShapeQuad9.h.

ORDER

constexpr int NumLib::ShapeQuad9::ORDER = 2

staticconstexpr

Definition at line 44 of file ShapeQuad9.h.

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

• NumLib/Fem/ShapeFunction/ShapeQuad9.h
• NumLib/Fem/ShapeFunction/ShapeQuad9-impl.h
• NumLib/Fem/ShapeFunction/ShapeStaticConsts.cpp