NumLib::ShapeQuad4 Class Reference

Detailed Description

Shape function for a quadrilateral element of four nodes in natural coordinates

*  2 (-1,1)     1 (1,1)
*     *--------*
*     |        |
*     |        |
*     |        |
*     *--------*
*  3 (-1,-1)    4 (1,-1)
* 

Definition at line 34 of file ShapeQuad4.h.

#include <ShapeQuad4.h>

Public Types
using	MeshElement = MeshLib::Quad

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 constexpr std::array	reference_element_centre = {0.0, 0.0}
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::ShapeQuad4::MeshElement = MeshLib::Quad

Definition at line 57 of file ShapeQuad4.h.

Member Function Documentation

computeGradShapeFunction()

template<class T_X , class T_N >

void NumLib::ShapeQuad4::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 25 of file ShapeQuad4-impl.h.

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

computeShapeFunction()

template<class T_X , class T_N >

void NumLib::ShapeQuad4::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 16 of file ShapeQuad4-impl.h.

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

References NumLib::N.

Member Data Documentation

DIM

const unsigned NumLib::ShapeQuad4::DIM = MeshElement::dimension

static

Definition at line 58 of file ShapeQuad4.h.

NPOINTS

const unsigned NumLib::ShapeQuad4::NPOINTS = MeshElement::n_all_nodes

static

Definition at line 59 of file ShapeQuad4.h.

ORDER

int NumLib::ShapeQuad4::ORDER = 1

staticconstexpr

Definition at line 60 of file ShapeQuad4.h.

reference_element_centre

std::array NumLib::ShapeQuad4::reference_element_centre = {0.0, 0.0}

staticconstexpr

Definition at line 55 of file ShapeQuad4.h.

{0.0, 0.0};

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

• NumLib/Fem/ShapeFunction/ShapeQuad4.h
• NumLib/Fem/ShapeFunction/ShapeQuad4-impl.h
• NumLib/Fem/ShapeFunction/ShapeStaticConsts.cpp