NumLib::ShapeHex8 Class Reference

Detailed Description

Shape function for a 8-nodes hex element in natural coordinates

*       (-1, 1, 1) 7-----------6 ( 1, 1, 1)
*                 /:          /|
*                / :         / |
*               /  :        /  |
*              /   :       /   |
*             /    :      /    |
* (-1,-1, 1) 4-----------5 ( 1,-1, 1)
*            |     :     |     |
*       (-1, 1,-1) 3.....|.....2 ( 1, 1,-1)
*            |    .      |    /
*            |   .       |   /
*            |  .        |  /
*            | .         | /
*            |.          |/
* (-1,-1,-1) 0-----------1 ( 1,-1,-1)
*          0
* 

Definition at line 34 of file ShapeHex8.h.

#include <ShapeHex8.h>

Public Types
using	MeshElement = MeshLib::Hex

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, 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::ShapeHex8::MeshElement = MeshLib::Hex

Definition at line 57 of file ShapeHex8.h.

Member Function Documentation

computeGradShapeFunction()

template<class T_X, class T_N>

void NumLib::ShapeHex8::computeGradShapeFunction ( const T_X & r, T_N & dN )

static

Evaluate derivatives of the shape function at the given point

Parameters

[in]	r	natural coordinates (r,s,t)
[out]	dN	a matrix of the derivatives

Definition at line 20 of file ShapeHex8-impl.h.

{
    // dN/dx
    dN[0] = -(1.0 - r[1]) * (1.0 - r[2]) * 0.125;
    dN[1] = -dN[0];
    dN[2] = +(1.0 + r[1]) * (1.0 - r[2]) * 0.125;
    dN[3] = -dN[2];
    dN[4] = -(1.0 - r[1]) * (1.0 + r[2]) * 0.125;
    dN[5] = -dN[4];
    dN[6] = +(1.0 + r[1]) * (1.0 + r[2]) * 0.125;
    dN[7] = -dN[6];
 
    // dN/dy
    dN[8] = -(1.0 - r[0]) * (1.0 - r[2]) * 0.125;
    dN[9] = -(1.0 + r[0]) * (1.0 - r[2]) * 0.125;
    dN[10] = -dN[9];
    dN[11] = -dN[8];
    dN[12] = -(1.0 - r[0]) * (1.0 + r[2]) * 0.125;
    dN[13] = -(1.0 + r[0]) * (1.0 + r[2]) * 0.125;
    dN[14] = -dN[13];
    dN[15] = -dN[12];
 
    // dN/dz
    dN[16] = -(1.0 - r[0]) * (1.0 - r[1]) * 0.125;
    dN[17] = -(1.0 + r[0]) * (1.0 - r[1]) * 0.125;
    dN[18] = -(1.0 + r[0]) * (1.0 + r[1]) * 0.125;
    dN[19] = -(1.0 - r[0]) * (1.0 + r[1]) * 0.125;
    dN[20] = -dN[16];
    dN[21] = -dN[17];
    dN[22] = -dN[18];
    dN[23] = -dN[19];
}

computeShapeFunction()

template<class T_X, class T_N>

void NumLib::ShapeHex8::computeShapeFunction ( const T_X & r, T_N & N )

static

Evaluate the shape function at the given point

Parameters

[in]	r	natural coordinates (r,s,t)
[out]	N	a vector of calculated shape functions

Definition at line 7 of file ShapeHex8-impl.h.

{
    N[0] = (1.0 - r[0]) * (1.0 - r[1]) * (1.0 - r[2]) * 0.125;
    N[1] = (1.0 + r[0]) * (1.0 - r[1]) * (1.0 - r[2]) * 0.125;
    N[2] = (1.0 + r[0]) * (1.0 + r[1]) * (1.0 - r[2]) * 0.125;
    N[3] = (1.0 - r[0]) * (1.0 + r[1]) * (1.0 - r[2]) * 0.125;
    N[4] = (1.0 - r[0]) * (1.0 - r[1]) * (1.0 + r[2]) * 0.125;
    N[5] = (1.0 + r[0]) * (1.0 - r[1]) * (1.0 + r[2]) * 0.125;
    N[6] = (1.0 + r[0]) * (1.0 + r[1]) * (1.0 + r[2]) * 0.125;
    N[7] = (1.0 - r[0]) * (1.0 + r[1]) * (1.0 + r[2]) * 0.125;
}

References NumLib::N.

Member Data Documentation

DIM

const unsigned NumLib::ShapeHex8::DIM = MeshElement::dimension

static

Definition at line 58 of file ShapeHex8.h.

NPOINTS

const unsigned NumLib::ShapeHex8::NPOINTS = MeshElement::n_all_nodes

static

Definition at line 59 of file ShapeHex8.h.

ORDER

int NumLib::ShapeHex8::ORDER = 1

staticconstexpr

Definition at line 60 of file ShapeHex8.h.

reference_element_centre

std::array NumLib::ShapeHex8::reference_element_centre = {0.0, 0.0, 0.0}

staticconstexpr

Definition at line 55 of file ShapeHex8.h.

{0.0, 0.0, 0.0};

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

• ShapeHex8.h
• ShapeHex8-impl.h
• ShapeStaticConsts.cpp