NumLib::ShapeTri6 Class Reference

Detailed Description

Shape function for a 6-nodes triangle element

Definition at line 15 of file ShapeTri6.h.

#include <ShapeTri6.h>

Public Types
using	MeshElement = MeshLib::Tri6

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 = {1. / 3., 1. / 3.}
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::ShapeTri6::MeshElement = MeshLib::Tri6

Definition at line 39 of file ShapeTri6.h.

Member Function Documentation

computeGradShapeFunction()

template<class T_X, class T_N>

void NumLib::ShapeTri6::computeGradShapeFunction ( const T_X & r, T_N & dN )

static

Evaluate derivatives of the shape function at the given point The point coordinates in r are not used.

Parameters

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

Definition at line 18 of file ShapeTri6-impl.h.

{
    dN[0] = 4. * (r[0] + r[1]) - 3.;  // dN1/dL1
    dN[6] = dN[0];                    // dN1/dL2
 
    dN[1] = 4. * r[0] - 1.;  // dN2/dL1
    dN[7] = 0.;              // dN2/dL2
 
    dN[2] = 0.;              // dN3/dL1
    dN[8] = 4. * r[1] - 1.;  // dN3/dL2
 
    dN[3] = 4. * (1 - 2. * r[0] - r[1]);  // dN4/dL1
    dN[9] = -4. * r[0];                   // dN4/dL2
 
    dN[4] = 4. * r[1];  // dN5/dL1
    dN[10] = -dN[9];    // dN5/dL2
 
    dN[5] = -dN[4];                        // dN6/dL1
    dN[11] = 4. * (1 - r[0] - 2. * r[1]);  // dN6/dL2
}

computeShapeFunction()

template<class T_X, class T_N>

void NumLib::ShapeTri6::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 7 of file ShapeTri6-impl.h.

{
    N[0] = 2. * (1. - r[0] - r[1]) * (0.5 - r[0] - r[1]);
    N[1] = r[0] * (2. * r[0] - 1.);
    N[2] = r[1] * (2. * r[1] - 1.);
    N[3] = 4. * r[0] * (1. - r[0] - r[1]);
    N[4] = 4. * r[0] * r[1];
    N[5] = 4. * r[1] * (1. - r[0] - r[1]);
}

References NumLib::N.

Member Data Documentation

DIM

const unsigned NumLib::ShapeTri6::DIM = MeshElement::dimension

static

Definition at line 40 of file ShapeTri6.h.

NPOINTS

const unsigned NumLib::ShapeTri6::NPOINTS = MeshElement::n_all_nodes

static

Definition at line 41 of file ShapeTri6.h.

ORDER

int NumLib::ShapeTri6::ORDER = 2

staticconstexpr

Definition at line 42 of file ShapeTri6.h.

reference_element_centre

std::array NumLib::ShapeTri6::reference_element_centre = {1. / 3., 1. / 3.}

staticconstexpr

Definition at line 37 of file ShapeTri6.h.

{1. / 3., 1. / 3.};

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

• ShapeTri6.h
• ShapeStaticConsts.cpp
• ShapeTri6-impl.h