NumLib::ShapeTet10 Class Reference

Detailed Description

Shape function for a 10-nodes tetrahedral element

Definition at line 21 of file ShapeTet10.h.

#include <ShapeTet10.h>

Public Types
using	MeshElement = MeshLib::Tet10

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 = {0.5, 0.5, 0.5}
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::ShapeTet10::MeshElement = MeshLib::Tet10

Definition at line 45 of file ShapeTet10.h.

Member Function Documentation

computeGradShapeFunction()

template<class T_X , class T_N >

void NumLib::ShapeTet10::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 29 of file ShapeTet10-impl.h.

{
    dN[0] = 4.0 * (r[0] + r[1] + r[2]) - 3.0;
    dN[1] = 4. * r[0] - 1.;
    dN[2] = 0.0;
    dN[3] = 0.0;
    dN[4] = 4.0 * (1.0 - 2.0 * r[0] - r[1] - r[2]);
    dN[5] = 4.0 * r[1];
    dN[6] = -4.0 * r[1];
    dN[7] = -4.0 * r[2];
    dN[8] = 4.0 * r[2];
    dN[9] = 0.0;
 
    dN[10] = 4. * (r[0] + r[1] + r[2]) - 3.;
    dN[11] = 0.0;
    dN[12] = 4. * r[1] - 1.;
    dN[13] = 0.;
    dN[14] = -4.0 * r[0];
    dN[15] = 4.0 * r[0];
    dN[16] = 4.0 * (1.0 - r[0] - 2.0 * r[1] - r[2]);
    dN[17] = -4.0 * r[2];
    dN[18] = 0.0;
    dN[19] = 4.0 * r[2];
 
    dN[20] = 4. * (r[0] + r[1] + r[2]) - 3.;
    dN[21] = 0.;
    dN[22] = 0.;
    dN[23] = 4. * r[2] - 1.;
    dN[24] = -4.0 * r[0];
    dN[25] = 0.0;
    dN[26] = -4.0 * r[1];
    dN[27] = 4.0 * (1.0 - r[0] - r[1] - 2.0 * r[2]);
    dN[28] = 4.0 * r[0];
    dN[29] = 4.0 * r[1];
}

computeShapeFunction()

template<class T_X , class T_N >

void NumLib::ShapeTet10::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 ShapeTet10-impl.h.

{
    N[0] = 2. * (1 - r[0] - r[1] - r[2]) * (0.5 - r[0] - r[1] - r[2]);
    N[1] = r[0] * (2. * r[0] - 1);
    N[2] = r[1] * (2. * r[1] - 1);
    N[3] = r[2] * (2. * r[2] - 1);
    N[4] = 4.0 * r[0] * (1.0 - r[0] - r[1] - r[2]);
    N[5] = 4.0 * r[0] * r[1];
    N[6] = 4.0 * r[1] * (1.0 - r[0] - r[1] - r[2]);
    N[7] = 4.0 * r[2] * (1.0 - r[0] - r[1] - r[2]);
    N[8] = 4.0 * r[0] * r[2];
    N[9] = 4.0 * r[1] * r[2];
}

References NumLib::N.

Member Data Documentation

DIM

const unsigned NumLib::ShapeTet10::DIM = MeshElement::dimension

static

Definition at line 46 of file ShapeTet10.h.

NPOINTS

const unsigned NumLib::ShapeTet10::NPOINTS = MeshElement::n_all_nodes

static

Definition at line 47 of file ShapeTet10.h.

ORDER

int NumLib::ShapeTet10::ORDER = 2

staticconstexpr

Definition at line 48 of file ShapeTet10.h.

reference_element_centre

std::array NumLib::ShapeTet10::reference_element_centre = {0.5, 0.5, 0.5}

staticconstexpr

Definition at line 43 of file ShapeTet10.h.

{0.5, 0.5, 0.5};

---

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

• NumLib/Fem/ShapeFunction/ShapeTet10.h
• NumLib/Fem/ShapeFunction/ShapeStaticConsts.cpp
• NumLib/Fem/ShapeFunction/ShapeTet10-impl.h