NumLib::ShapeHex20 Class Reference

Detailed Description

Shape function for a 20-nodes hex element in natural coordinates

Definition at line 21 of file ShapeHex20.h.

#include <ShapeHex20.h>

Public Types
using	MeshElement = MeshLib::Hex20

Static Public Member Functions
template<class T_X , class T_N >
static void	computeShapeFunction (const T_X &rst, T_N &N)
template<class T_X , class T_N >
static void	computeGradShapeFunction (const T_X &rst, 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::ShapeHex20::MeshElement = MeshLib::Hex20

Definition at line 42 of file ShapeHex20.h.

Member Function Documentation

computeGradShapeFunction()

template<class T_X , class T_N >

void NumLib::ShapeHex20::computeGradShapeFunction ( const T_X & rst, T_N & dN )

static

Evaluate derivatives of the shape function at the given point

Parameters

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

Definition at line 92 of file ShapeHex20-impl.h.

{
    const double r = rst[0];
    const double s = rst[1];
    const double t = rst[2];
    const static double sign1[] = {-1.0, 1.0, 1.0};
    const static double sign2[] = {1.0, -1.0, 1.0};
    const static double sign3[] = {1.0, 1.0, -1.0};
    for (int i = 0; i < 3; i++)
    {
        dN[20 * i + 0] = dShapeFunctionHexHQ_Corner(r, s, t, i);
        dN[20 * i + 1] = sign1[i] * dShapeFunctionHexHQ_Corner(-r, s, t, i);
        dN[20 * i + 2] =
            sign1[i] * sign2[i] * dShapeFunctionHexHQ_Corner(-r, -s, t, i);
        dN[20 * i + 3] = sign2[i] * dShapeFunctionHexHQ_Corner(r, -s, t, i);
        dN[20 * i + 4] = sign3[i] * dShapeFunctionHexHQ_Corner(r, s, -t, i);
        dN[20 * i + 5] =
            sign1[i] * sign3[i] * dShapeFunctionHexHQ_Corner(-r, s, -t, i);
        dN[20 * i + 6] = sign1[i] * sign2[i] * sign3[i] *
                         dShapeFunctionHexHQ_Corner(-r, -s, -t, i);
        dN[20 * i + 7] =
            sign2[i] * sign3[i] * dShapeFunctionHexHQ_Corner(r, -s, -t, i);
 
        dN[20 * i + 8] = dShapeFunctionHexHQ_Middle(r, s, t, i);
        dN[20 * i + 10] = sign2[i] * dShapeFunctionHexHQ_Middle(r, -s, t, i);
        dN[20 * i + 14] =
            sign2[i] * sign3[i] * dShapeFunctionHexHQ_Middle(r, -s, -t, i);
        dN[20 * i + 12] = sign3[i] * dShapeFunctionHexHQ_Middle(r, s, -t, i);
 
        {
            int const co = (i + 2) % 3;
            dN[20 * i + 11] = dShapeFunctionHexHQ_Middle(s, t, r, co);
            dN[20 * i + 15] =
                sign3[i] * dShapeFunctionHexHQ_Middle(s, -t, r, co);
            dN[20 * i + 13] =
                sign1[i] * sign3[i] * dShapeFunctionHexHQ_Middle(s, -t, -r, co);
            dN[20 * i + 9] =
                sign1[i] * dShapeFunctionHexHQ_Middle(s, t, -r, co);
        }
 
        {
            int const co = (i + 1) % 3;
            dN[20 * i + 16] = dShapeFunctionHexHQ_Middle(t, r, s, co);
            dN[20 * i + 17] =
                sign1[i] * dShapeFunctionHexHQ_Middle(t, -r, s, co);
            dN[20 * i + 18] =
                sign1[i] * sign2[i] * dShapeFunctionHexHQ_Middle(t, -r, -s, co);
            dN[20 * i + 19] =
                sign2[i] * dShapeFunctionHexHQ_Middle(t, r, -s, co);
        }
    }
}

computeShapeFunction()

template<class T_X , class T_N >

void NumLib::ShapeHex20::computeShapeFunction ( const T_X & rst, T_N & N )

static

Evaluate the shape function at the given point

Parameters

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

Definition at line 60 of file ShapeHex20-impl.h.

{
    const double r = rst[0];
    const double s = rst[1];
    const double t = rst[2];
 
    N[0] = ShapeFunctionHexHQ_Corner(r, s, t);
    N[1] = ShapeFunctionHexHQ_Corner(-r, s, t);
    N[2] = ShapeFunctionHexHQ_Corner(-r, -s, t);
    N[3] = ShapeFunctionHexHQ_Corner(r, -s, t);
    N[4] = ShapeFunctionHexHQ_Corner(r, s, -t);
    N[5] = ShapeFunctionHexHQ_Corner(-r, s, -t);
    N[6] = ShapeFunctionHexHQ_Corner(-r, -s, -t);
    N[7] = ShapeFunctionHexHQ_Corner(r, -s, -t);
 
    N[8] = ShapeFunctionHexHQ_Middle(r, s, t);
    N[10] = ShapeFunctionHexHQ_Middle(r, -s, t);
    N[14] = ShapeFunctionHexHQ_Middle(r, -s, -t);
    N[12] = ShapeFunctionHexHQ_Middle(r, s, -t);
 
    N[11] = ShapeFunctionHexHQ_Middle(s, t, r);
    N[15] = ShapeFunctionHexHQ_Middle(s, -t, r);
    N[13] = ShapeFunctionHexHQ_Middle(s, -t, -r);
    N[9] = ShapeFunctionHexHQ_Middle(s, t, -r);
 
    N[16] = ShapeFunctionHexHQ_Middle(t, r, s);
    N[17] = ShapeFunctionHexHQ_Middle(t, -r, s);
    N[18] = ShapeFunctionHexHQ_Middle(t, -r, -s);
    N[19] = ShapeFunctionHexHQ_Middle(t, r, -s);
}

References NumLib::N.

Member Data Documentation

DIM

const unsigned NumLib::ShapeHex20::DIM = MeshElement::dimension

static

Definition at line 43 of file ShapeHex20.h.

NPOINTS

const unsigned NumLib::ShapeHex20::NPOINTS = MeshElement::n_all_nodes

static

Definition at line 44 of file ShapeHex20.h.

ORDER

int NumLib::ShapeHex20::ORDER = 2

staticconstexpr

Definition at line 45 of file ShapeHex20.h.

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

• NumLib/Fem/ShapeFunction/ShapeHex20.h
• NumLib/Fem/ShapeFunction/ShapeHex20-impl.h
• NumLib/Fem/ShapeFunction/ShapeStaticConsts.cpp