ShapeQuad8-impl.h

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// SPDX-FileCopyrightText: Copyright (c) OpenGeoSys Community (opengeosys.org)
// SPDX-License-Identifier: BSD-3-Clause
 
namespace NumLib
{
template <class T_X, class T_N>
void ShapeQuad8::computeShapeFunction(const T_X& r, T_N& N)
{
    N[0] = 0.25 * (1.0 + r[0]) * (1.0 + r[1]) * (-1.0 + r[0] + r[1]);
    N[1] = -0.25 * (1.0 - r[0]) * (1.0 + r[1]) * (1.0 + r[0] - r[1]);
    N[2] = -0.25 * (1.0 - r[0]) * (1.0 - r[1]) * (1.0 + r[0] + r[1]);
    N[3] = 0.25 * (1.0 + r[0]) * (1.0 - r[1]) * (-1.0 + r[0] - r[1]);
    //
    N[4] = 0.5 * (1.0 - r[0] * r[0]) * (1.0 + r[1]);
    N[5] = 0.5 * (1.0 - r[1] * r[1]) * (1.0 - r[0]);
    N[6] = 0.5 * (1.0 - r[0] * r[0]) * (1.0 - r[1]);
    N[7] = 0.5 * (1.0 - r[1] * r[1]) * (1.0 + r[0]);
}
 
template <class T_X, class T_N>
void ShapeQuad8::computeGradShapeFunction(const T_X& rs, T_N& dN)
{
    const double r = rs[0];
    const double s = rs[1];
 
    // dN/dr
    dN[0] = (1 + s) * (2 * r + s) * 0.25;
    dN[1] = (1 + s) * (2 * r - s) * 0.25;
    dN[2] = (1 - s) * (2 * r + s) * 0.25;
    dN[3] = (1 - s) * (2 * r - s) * 0.25;
 
    dN[4] = -r * (1 + s);
    dN[5] = -(1 - s * s) * 0.5;
    dN[6] = -r * (1 - s);
    dN[7] = (1 - s * s) * 0.5;
 
    // dN/ds
    dN[8] = (1 + r) * (r + 2 * s) * 0.25;
    dN[9] = -(1 - r) * (r - 2 * s) * 0.25;
    dN[10] = (1 - r) * (r + 2 * s) * 0.25;
    dN[11] = -(1 + r) * (r - 2 * s) * 0.25;
 
    dN[12] = (1 - r * r) * 0.5;
    dN[13] = -(1 - r) * s;
    dN[14] = -(1 - r * r) * 0.5;
    dN[15] = -(1 + r) * s;
}
 
}  // namespace NumLib