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V_GaussIntegration.cpp
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V_GaussIntegration.cpp
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/*=========================================================================
Module: V_GaussIntegration.cpp
Copyright 2003,2006,2019 National Technology & Engineering Solutions of Sandia, LLC (NTESS).
Under the terms of Contract DE-NA0003525 with NTESS,
the U.S. Government retains certain rights in this software.
See LICENSE for details.
=========================================================================*/
/*
*
* GaussIntegration.cpp performs Gauss Integrations
*
* This file is part of VERDICT
*
*/
#include "V_GaussIntegration.hpp"
#include "verdict.h"
namespace VERDICT_NAMESPACE
{
void GaussIntegration::initialize(int n, int m, int dim, int tri)
{
numberGaussPoints = n;
numberNodes = m;
numberDims = dim;
if (tri == 1)
// triangular element
{
if (numberDims == 2)
{
totalNumberGaussPts = numberGaussPoints;
}
else if (numberDims == 3)
{
totalNumberGaussPts = numberGaussPoints;
}
}
else if (tri == 0)
{
if (numberDims == 2)
{
totalNumberGaussPts = numberGaussPoints * numberGaussPoints;
}
else if (numberDims == 3)
{
totalNumberGaussPts = numberGaussPoints * numberGaussPoints * numberGaussPoints;
}
}
}
void GaussIntegration::get_shape_func(double shape_function[], double dndy1_at_gauss_pts[],
double dndy2_at_gauss_pts[], double gauss_weight[])
{
int i, j;
for (i = 0; i < totalNumberGaussPts; i++)
{
for (j = 0; j < numberNodes; j++)
{
shape_function[i * maxNumberNodes + j] = shapeFunction[i][j];
dndy1_at_gauss_pts[i * maxNumberNodes + j] = dndy1GaussPts[i][j];
dndy2_at_gauss_pts[i * maxNumberNodes + j] = dndy2GaussPts[i][j];
}
}
for (i = 0; i < totalNumberGaussPts; i++)
{
gauss_weight[i] = totalGaussWeight[i];
}
}
void GaussIntegration::get_shape_func(double shape_function[], double dndy1_at_gauss_pts[],
double dndy2_at_gauss_pts[], double dndy3_at_gauss_pts[], double gauss_weight[])
{
int i, j;
for (i = 0; i < totalNumberGaussPts; i++)
{
for (j = 0; j < numberNodes; j++)
{
shape_function[i * maxNumberNodes + j] = shapeFunction[i][j];
dndy1_at_gauss_pts[i * maxNumberNodes + j] = dndy1GaussPts[i][j];
dndy2_at_gauss_pts[i * maxNumberNodes + j] = dndy2GaussPts[i][j];
dndy3_at_gauss_pts[i * maxNumberNodes + j] = dndy3GaussPts[i][j];
}
}
for (i = 0; i < totalNumberGaussPts; i++)
{
gauss_weight[i] = totalGaussWeight[i];
}
}
void GaussIntegration::get_gauss_pts_and_weight()
{
switch (numberGaussPoints)
{
case 1:
gaussPointY[0] = 0.0;
gaussWeight[0] = 2.0;
break;
case 2:
gaussPointY[0] = -0.577350269189626;
gaussPointY[1] = 0.577350269189626;
gaussWeight[0] = 1.0;
gaussWeight[1] = 1.0;
break;
case 3:
gaussPointY[0] = -0.774596669241483;
gaussPointY[1] = 0.0;
gaussPointY[2] = 0.774596669241483;
gaussWeight[0] = 0.555555555555555;
gaussWeight[1] = 0.888888888888889;
gaussWeight[2] = 0.555555555555555;
break;
}
}
void GaussIntegration::calculate_shape_function_2d_quad()
{
int ife = 0, i, j;
double y1, y2;
get_gauss_pts_and_weight();
switch (numberNodes)
{
case 4:
for (i = 0; i < numberGaussPoints; i++)
{
for (j = 0; j < numberGaussPoints; j++)
{
y1 = gaussPointY[i];
y2 = gaussPointY[j];
shapeFunction[ife][0] = 0.25 * (1 - y1) * (1 - y2);
shapeFunction[ife][1] = 0.25 * (1 + y1) * (1 - y2);
shapeFunction[ife][2] = 0.25 * (1 + y1) * (1 + y2);
shapeFunction[ife][3] = 0.25 * (1 - y1) * (1 + y2);
dndy1GaussPts[ife][0] = -0.25 * (1 - y2);
dndy1GaussPts[ife][1] = 0.25 * (1 - y2);
dndy1GaussPts[ife][2] = 0.25 * (1 + y2);
dndy1GaussPts[ife][3] = -0.25 * (1 + y2);
dndy2GaussPts[ife][0] = -0.25 * (1 - y1);
dndy2GaussPts[ife][1] = -0.25 * (1 + y1);
dndy2GaussPts[ife][2] = 0.25 * (1 + y1);
dndy2GaussPts[ife][3] = 0.25 * (1 - y1);
totalGaussWeight[ife] = gaussWeight[i] * gaussWeight[j];
ife++;
}
}
break;
case 8:
for (i = 0; i < numberGaussPoints; i++)
{
for (j = 0; j < numberGaussPoints; j++)
{
y1 = gaussPointY[i];
y2 = gaussPointY[j];
shapeFunction[ife][0] = 0.25 * (1 - y1) * (1 - y2) * (-y1 - y2 - 1);
shapeFunction[ife][1] = 0.25 * (1 + y1) * (1 - y2) * (y1 - y2 - 1);
shapeFunction[ife][2] = 0.25 * (1 + y1) * (1 + y2) * (y1 + y2 - 1);
shapeFunction[ife][3] = 0.25 * (1 - y1) * (1 + y2) * (-y1 + y2 - 1);
shapeFunction[ife][4] = 0.5 * (1 - y1 * y1) * (1 - y2);
shapeFunction[ife][5] = 0.5 * (1 - y2 * y2) * (1 + y1);
shapeFunction[ife][6] = 0.5 * (1 - y1 * y1) * (1 + y2);
shapeFunction[ife][7] = 0.5 * (1 - y2 * y2) * (1 - y1);
dndy1GaussPts[ife][0] = 0.25 * (1 - y2) * (2.0 * y1 + y2);
dndy1GaussPts[ife][1] = 0.25 * (1 - y2) * (2.0 * y1 - y2);
dndy1GaussPts[ife][2] = 0.25 * (1 + y2) * (2.0 * y1 + y2);
dndy1GaussPts[ife][3] = 0.25 * (1 + y2) * (2.0 * y1 - y2);
dndy1GaussPts[ife][4] = -y1 * (1 - y2);
dndy1GaussPts[ife][5] = 0.5 * (1 - y2 * y2);
dndy1GaussPts[ife][6] = -y1 * (1 + y2);
dndy1GaussPts[ife][7] = -0.5 * (1 - y2 * y2);
dndy2GaussPts[ife][0] = 0.25 * (1 - y1) * (2.0 * y2 + y1);
dndy2GaussPts[ife][1] = 0.25 * (1 + y1) * (2.0 * y2 - y1);
dndy2GaussPts[ife][2] = 0.25 * (1 + y1) * (2.0 * y2 + y1);
dndy2GaussPts[ife][3] = 0.25 * (1 - y1) * (2.0 * y2 - y1);
dndy2GaussPts[ife][4] = -0.5 * (1 - y1 * y1);
dndy2GaussPts[ife][5] = -y2 * (1 + y1);
dndy2GaussPts[ife][6] = 0.5 * (1 - y1 * y1);
dndy2GaussPts[ife][7] = -y2 * (1 - y1);
totalGaussWeight[ife] = gaussWeight[i] * gaussWeight[j];
ife++;
}
}
break;
}
}
void GaussIntegration::calculate_shape_function_3d_hex()
{
int ife = 0, i, j, k, node_id;
double y1, y2, y3, sign_node_y1, sign_node_y2, sign_node_y3;
double y1_term, y2_term, y3_term, y123_temp;
get_gauss_pts_and_weight();
switch (numberNodes)
{
case 8:
for (i = 0; i < numberGaussPoints; i++)
{
for (j = 0; j < numberGaussPoints; j++)
{
for (k = 0; k < numberGaussPoints; k++)
{
y1 = gaussPointY[i];
y2 = gaussPointY[j];
y3 = gaussPointY[k];
for (node_id = 0; node_id < numberNodes; node_id++)
{
get_signs_for_node_local_coord_hex(node_id, sign_node_y1, sign_node_y2, sign_node_y3);
y1_term = 1 + sign_node_y1 * y1;
y2_term = 1 + sign_node_y2 * y2;
y3_term = 1 + sign_node_y3 * y3;
shapeFunction[ife][node_id] = 0.125 * y1_term * y2_term * y3_term;
dndy1GaussPts[ife][node_id] = 0.125 * sign_node_y1 * y2_term * y3_term;
dndy2GaussPts[ife][node_id] = 0.125 * sign_node_y2 * y1_term * y3_term;
dndy3GaussPts[ife][node_id] = 0.125 * sign_node_y3 * y1_term * y2_term;
}
totalGaussWeight[ife] = gaussWeight[i] * gaussWeight[j] * gaussWeight[k];
ife++;
}
}
}
break;
case 20:
for (i = 0; i < numberGaussPoints; i++)
{
for (j = 0; j < numberGaussPoints; j++)
{
for (k = 0; k < numberGaussPoints; k++)
{
y1 = gaussPointY[i];
y2 = gaussPointY[j];
y3 = gaussPointY[k];
for (node_id = 0; node_id < numberNodes; node_id++)
{
get_signs_for_node_local_coord_hex(node_id, sign_node_y1, sign_node_y2, sign_node_y3);
y1_term = 1 + sign_node_y1 * y1;
y2_term = 1 + sign_node_y2 * y2;
y3_term = 1 + sign_node_y3 * y3;
y123_temp = sign_node_y1 * y1 + sign_node_y2 * y2 + sign_node_y3 * y3 - 2.;
switch (node_id)
{
case 0:
case 1:
case 2:
case 3:
case 4:
case 5:
case 6:
case 7:
{
shapeFunction[ife][node_id] = 0.125 * y1_term * y2_term * y3_term * y123_temp;
dndy1GaussPts[ife][node_id] =
0.125 * sign_node_y1 * y123_temp * y2_term * y3_term +
0.125 * y1_term * y2_term * y3_term * sign_node_y1;
dndy2GaussPts[ife][node_id] =
0.125 * sign_node_y2 * y1_term * y3_term * y123_temp +
0.125 * y1_term * y2_term * y3_term * sign_node_y2;
dndy3GaussPts[ife][node_id] =
0.125 * sign_node_y3 * y1_term * y2_term * y123_temp +
0.125 * y1_term * y2_term * y3_term * sign_node_y3;
break;
}
case 8:
case 10:
case 16:
case 18:
{
shapeFunction[ife][node_id] = 0.25 * (1 - y1 * y1) * y2_term * y3_term;
dndy1GaussPts[ife][node_id] = -0.5 * y1 * y2_term * y3_term;
dndy2GaussPts[ife][node_id] = 0.25 * (1 - y1 * y1) * sign_node_y2 * y3_term;
dndy3GaussPts[ife][node_id] = 0.25 * (1 - y1 * y1) * y2_term * sign_node_y3;
break;
}
case 9:
case 11:
case 17:
case 19:
{
shapeFunction[ife][node_id] = 0.25 * (1 - y2 * y2) * y1_term * y3_term;
dndy1GaussPts[ife][node_id] = 0.25 * (1 - y2 * y2) * sign_node_y1 * y3_term;
dndy2GaussPts[ife][node_id] = -0.5 * y2 * y1_term * y3_term;
dndy3GaussPts[ife][node_id] = 0.25 * (1 - y2 * y2) * y1_term * sign_node_y3;
break;
}
case 12:
case 13:
case 14:
case 15:
{
shapeFunction[ife][node_id] = 0.25 * (1 - y3 * y3) * y1_term * y2_term;
dndy1GaussPts[ife][node_id] = 0.25 * (1 - y3 * y3) * sign_node_y1 * y2_term;
dndy2GaussPts[ife][node_id] = 0.25 * (1 - y3 * y3) * y1_term * sign_node_y2;
dndy3GaussPts[ife][node_id] = -0.5 * y3 * y1_term * y2_term;
break;
}
}
}
totalGaussWeight[ife] = gaussWeight[i] * gaussWeight[j] * gaussWeight[k];
ife++;
}
}
}
break;
}
}
void GaussIntegration::calculate_derivative_at_nodes(
double dndy1_at_nodes[][maxNumberNodes], double dndy2_at_nodes[][maxNumberNodes])
{
double y1 = 0., y2 = 0.;
int i;
for (i = 0; i < numberNodes; i++)
{
switch (i)
{
case 0:
y1 = -1.;
y2 = -1.;
break;
case 1:
y1 = 1.;
y2 = -1.;
break;
case 2:
y1 = 1.;
y2 = 1.;
break;
case 3:
y1 = -1.;
y2 = 1.;
break;
// mid-side nodes if there is any
case 4:
y1 = 0.;
y2 = -1.;
break;
case 5:
y1 = 1.;
y2 = 0.;
break;
case 6:
y1 = 0.;
y2 = 1.;
break;
case 7:
y1 = -1.;
y2 = 0.;
break;
}
switch (numberNodes)
{
case 4:
// dn_i/dy1 evaluated at node i
dndy1_at_nodes[i][0] = -0.25 * (1 - y2);
dndy1_at_nodes[i][1] = 0.25 * (1 - y2);
dndy1_at_nodes[i][2] = 0.25 * (1 + y2);
dndy1_at_nodes[i][3] = -0.25 * (1 + y2);
// dn_i/dy2 evaluated at node i
dndy2_at_nodes[i][0] = -0.25 * (1 - y1);
dndy2_at_nodes[i][1] = -0.25 * (1 + y1);
dndy2_at_nodes[i][2] = 0.25 * (1 + y1);
dndy2_at_nodes[i][3] = 0.25 * (1 - y1);
break;
case 8:
dndy1_at_nodes[i][0] = 0.25 * (1 - y2) * (2.0 * y1 + y2);
dndy1_at_nodes[i][1] = 0.25 * (1 - y2) * (2.0 * y1 - y2);
dndy1_at_nodes[i][2] = 0.25 * (1 + y2) * (2.0 * y1 + y2);
dndy1_at_nodes[i][3] = 0.25 * (1 + y2) * (2.0 * y1 - y2);
dndy1_at_nodes[i][4] = -y1 * (1 - y2);
dndy1_at_nodes[i][5] = 0.5 * (1 - y2 * y2);
dndy1_at_nodes[i][6] = -y1 * (1 + y2);
dndy1_at_nodes[i][7] = -0.5 * (1 - y2 * y2);
dndy2_at_nodes[i][0] = 0.25 * (1 - y1) * (2.0 * y2 + y1);
dndy2_at_nodes[i][1] = 0.25 * (1 + y1) * (2.0 * y2 - y1);
dndy2_at_nodes[i][2] = 0.25 * (1 + y1) * (2.0 * y2 + y1);
dndy2_at_nodes[i][3] = 0.25 * (1 - y1) * (2.0 * y2 - y1);
dndy2_at_nodes[i][4] = -0.5 * (1 - y1 * y1);
dndy2_at_nodes[i][5] = -y2 * (1 + y1);
dndy2_at_nodes[i][6] = 0.5 * (1 - y1 * y1);
dndy2_at_nodes[i][7] = -y2 * (1 - y1);
break;
}
}
}
void GaussIntegration::calculate_derivative_at_nodes_3d(double dndy1_at_nodes[][maxNumberNodes],
double dndy2_at_nodes[][maxNumberNodes], double dndy3_at_nodes[][maxNumberNodes])
{
double y1, y2, y3, sign_node_y1, sign_node_y2, sign_node_y3;
double y1_term, y2_term, y3_term, y123_temp;
int node_id, node_id_2;
for (node_id = 0; node_id < numberNodes; node_id++)
{
get_signs_for_node_local_coord_hex(node_id, y1, y2, y3);
switch (numberNodes)
{
case 8:
for (node_id_2 = 0; node_id_2 < numberNodes; node_id_2++)
{
get_signs_for_node_local_coord_hex(node_id_2, sign_node_y1, sign_node_y2, sign_node_y3);
y1_term = 1 + sign_node_y1 * y1;
y2_term = 1 + sign_node_y2 * y2;
y3_term = 1 + sign_node_y3 * y3;
dndy1_at_nodes[node_id][node_id_2] = 0.125 * sign_node_y1 * y2_term * y3_term;
dndy2_at_nodes[node_id][node_id_2] = 0.125 * sign_node_y2 * y1_term * y3_term;
dndy3_at_nodes[node_id][node_id_2] = 0.125 * sign_node_y3 * y1_term * y2_term;
}
break;
case 20:
for (node_id_2 = 0; node_id_2 < numberNodes; node_id_2++)
{
get_signs_for_node_local_coord_hex(node_id_2, sign_node_y1, sign_node_y2, sign_node_y3);
y1_term = 1 + sign_node_y1 * y1;
y2_term = 1 + sign_node_y2 * y2;
y3_term = 1 + sign_node_y3 * y3;
y123_temp = sign_node_y1 * y1 + sign_node_y2 * y2 + sign_node_y3 * y3 - 2.;
switch (node_id_2)
{
case 0:
case 1:
case 2:
case 3:
case 4:
case 5:
case 6:
case 7:
{
dndy1_at_nodes[node_id][node_id_2] =
0.125 * sign_node_y1 * y2_term * y3_term * y123_temp +
0.125 * y1_term * y2_term * y3_term * sign_node_y1;
dndy2_at_nodes[node_id][node_id_2] =
0.125 * sign_node_y2 * y1_term * y3_term * y123_temp +
0.125 * y1_term * y2_term * y3_term * sign_node_y2;
dndy3_at_nodes[node_id][node_id_2] =
0.125 * sign_node_y3 * y1_term * y2_term * y123_temp +
0.125 * y1_term * y2_term * y3_term * sign_node_y3;
break;
}
case 8:
case 10:
case 16:
case 18:
{
dndy1_at_nodes[node_id][node_id_2] = -0.5 * y1 * y2_term * y3_term;
dndy2_at_nodes[node_id][node_id_2] = 0.25 * (1 - y1 * y1) * sign_node_y2 * y3_term;
dndy3_at_nodes[node_id][node_id_2] = 0.25 * (1 - y1 * y1) * y2_term * sign_node_y3;
break;
}
case 9:
case 11:
case 17:
case 19:
{
dndy1_at_nodes[node_id][node_id_2] = 0.25 * (1 - y2 * y2) * sign_node_y1 * y3_term;
dndy2_at_nodes[node_id][node_id_2] = -0.5 * y2 * y1_term * y3_term;
dndy3_at_nodes[node_id][node_id_2] = 0.25 * (1 - y2 * y2) * y1_term * sign_node_y3;
break;
}
case 12:
case 13:
case 14:
case 15:
{
dndy1_at_nodes[node_id][node_id_2] = 0.25 * (1 - y3 * y3) * sign_node_y1 * y2_term;
dndy2_at_nodes[node_id][node_id_2] = 0.25 * (1 - y3 * y3) * y1_term * sign_node_y2;
dndy3_at_nodes[node_id][node_id_2] = -0.5 * y3 * y1_term * y2_term;
break;
}
}
}
break;
}
}
}
void GaussIntegration::get_signs_for_node_local_coord_hex(
int node_id, double& sign_node_y1, double& sign_node_y2, double& sign_node_y3)
{
switch (node_id)
{
case 0:
sign_node_y1 = -1.;
sign_node_y2 = -1.;
sign_node_y3 = -1.;
break;
case 1:
sign_node_y1 = 1.;
sign_node_y2 = -1.;
sign_node_y3 = -1.;
break;
case 2:
sign_node_y1 = 1.;
sign_node_y2 = 1.;
sign_node_y3 = -1.;
break;
case 3:
sign_node_y1 = -1.;
sign_node_y2 = 1.;
sign_node_y3 = -1.;
break;
case 4:
sign_node_y1 = -1.;
sign_node_y2 = -1.;
sign_node_y3 = 1.;
break;
case 5:
sign_node_y1 = 1.;
sign_node_y2 = -1.;
sign_node_y3 = 1.;
break;
case 6:
sign_node_y1 = 1.;
sign_node_y2 = 1.;
sign_node_y3 = 1.;
break;
case 7:
sign_node_y1 = -1.;
sign_node_y2 = 1.;
sign_node_y3 = 1.;
break;
case 8:
sign_node_y1 = 0;
sign_node_y2 = -1.;
sign_node_y3 = -1.;
break;
case 9:
sign_node_y1 = 1.;
sign_node_y2 = 0;
sign_node_y3 = -1.;
break;
case 10:
sign_node_y1 = 0;
sign_node_y2 = 1.;
sign_node_y3 = -1.;
break;
case 11:
sign_node_y1 = -1.;
sign_node_y2 = 0.;
sign_node_y3 = -1.;
break;
case 12:
sign_node_y1 = -1.;
sign_node_y2 = -1.;
sign_node_y3 = 0.;
break;
case 13:
sign_node_y1 = 1.;
sign_node_y2 = -1.;
sign_node_y3 = 0.;
break;
case 14:
sign_node_y1 = 1.;
sign_node_y2 = 1.;
sign_node_y3 = 0.;
break;
case 15:
sign_node_y1 = -1.;
sign_node_y2 = 1.;
sign_node_y3 = 0.;
break;
case 16:
sign_node_y1 = 0;
sign_node_y2 = -1.;
sign_node_y3 = 1.;
break;
case 17:
sign_node_y1 = 1.;
sign_node_y2 = 0;
sign_node_y3 = 1.;
break;
case 18:
sign_node_y1 = 0;
sign_node_y2 = 1.;
sign_node_y3 = 1.;
break;
case 19:
sign_node_y1 = -1.;
sign_node_y2 = 0.;
sign_node_y3 = 1.;
break;
default:
// Should not be possible to get here, but if we do, at least results will be consistent, not
// random
sign_node_y1 = 0.;
sign_node_y2 = 0.;
sign_node_y3 = 0.;
break;
}
}
void GaussIntegration::get_tri_rule_pts_and_weight()
{
// get triangular rule integration points and weight
switch (numberGaussPoints)
{
case 6:
y1Area[0] = 0.09157621;
y2Area[0] = 0.09157621;
y1Area[1] = 0.09157621;
y2Area[1] = 0.8168476;
y1Area[2] = 0.8168476;
y2Area[2] = 0.09157621;
y1Area[3] = 0.4459485;
y2Area[3] = 0.4459485;
y1Area[4] = 0.4459485;
y2Area[4] = 0.1081030;
y1Area[5] = 0.1081030;
y2Area[5] = 0.4459485;
int i;
for (i = 0; i < 3; i++)
{
totalGaussWeight[i] = 0.06348067;
}
for (i = 3; i < 6; i++)
{
totalGaussWeight[i] = 0.1289694;
}
break;
}
}
void GaussIntegration::calculate_shape_function_2d_tri()
{
int ife;
double y1, y2, y3;
get_tri_rule_pts_and_weight();
for (ife = 0; ife < totalNumberGaussPts; ife++)
{
y1 = y1Area[ife];
y2 = y2Area[ife];
y3 = 1.0 - y1 - y2;
shapeFunction[ife][0] = y1 * (2. * y1 - 1.);
shapeFunction[ife][1] = y2 * (2. * y2 - 1.);
shapeFunction[ife][2] = y3 * (2. * y3 - 1.);
shapeFunction[ife][3] = 4. * y1 * y2;
shapeFunction[ife][4] = 4. * y2 * y3;
shapeFunction[ife][5] = 4. * y1 * y3;
dndy1GaussPts[ife][0] = 4 * y1 - 1.;
dndy1GaussPts[ife][1] = 0;
dndy1GaussPts[ife][2] = 1 - 4. * y3;
dndy1GaussPts[ife][3] = 4. * y2;
dndy1GaussPts[ife][4] = -4. * y2;
dndy1GaussPts[ife][5] = 4. * (1 - 2 * y1 - y2);
dndy2GaussPts[ife][0] = 0.0;
dndy2GaussPts[ife][1] = 4. * y2 - 1.;
dndy2GaussPts[ife][2] = 1 - 4. * y3;
dndy2GaussPts[ife][3] = 4. * y1;
dndy2GaussPts[ife][4] = 4. * (1 - y1 - 2. * y2);
dndy2GaussPts[ife][5] = -4. * y1;
}
}
void GaussIntegration::calculate_derivative_at_nodes_2d_tri(
double dndy1_at_nodes[][maxNumberNodes], double dndy2_at_nodes[][maxNumberNodes])
{
double y1 = 0., y2 = 0., y3;
int i;
for (i = 0; i < numberNodes; i++)
{
switch (i)
{
case 0:
y1 = 1.;
y2 = 0.;
break;
case 1:
y1 = 0.;
y2 = 1.;
break;
case 2:
y1 = 0.;
y2 = 0.;
break;
case 3:
y1 = 0.5;
y2 = 0.5;
break;
case 4:
y1 = 0.;
y2 = 0.5;
break;
case 5:
y1 = 0.5;
y2 = 0.0;
break;
}
y3 = 1. - y1 - y2;
dndy1_at_nodes[i][0] = 4 * y1 - 1.;
dndy1_at_nodes[i][1] = 0;
dndy1_at_nodes[i][2] = 1 - 4. * y3;
dndy1_at_nodes[i][3] = 4. * y2;
dndy1_at_nodes[i][4] = -4. * y2;
dndy1_at_nodes[i][5] = 4. * (1 - 2 * y1 - y2);
dndy2_at_nodes[i][0] = 0.0;
dndy2_at_nodes[i][1] = 4. * y2 - 1.;
dndy2_at_nodes[i][2] = 1 - 4. * y3;
dndy2_at_nodes[i][3] = 4. * y1;
dndy2_at_nodes[i][4] = 4. * (1 - y1 - 2. * y2);
dndy2_at_nodes[i][5] = -4. * y1;
}
}
void GaussIntegration::get_tet_rule_pts_and_weight()
{
// get tetrahedron rule integration points and weight
double a, b;
switch (numberGaussPoints)
{
case 1:
// 1 integration point formula, degree of precision 1
y1Volume[0] = 0.25;
y2Volume[0] = 0.25;
y3Volume[0] = 0.25;
y4Volume[0] = 0.25;
totalGaussWeight[0] = 1.;
break;
case 4:
// 4 integration points formula, degree of precision 2
a = 0.58541020;
b = 0.13819660;
y1Volume[0] = a;
y2Volume[0] = b;
y3Volume[0] = b;
y4Volume[0] = b;
y1Volume[1] = b;
y2Volume[1] = a;
y3Volume[1] = b;
y4Volume[1] = b;
y1Volume[2] = b;
y2Volume[2] = b;
y3Volume[2] = a;
y4Volume[2] = b;
y1Volume[3] = b;
y2Volume[3] = b;
y3Volume[3] = b;
y4Volume[3] = a;
int i;
for (i = 0; i < 4; i++)
{
totalGaussWeight[i] = 0.25;
}
break;
}
}
void GaussIntegration::calculate_shape_function_3d_tet()
{
int ife;
double y1, y2, y3, y4;
get_tet_rule_pts_and_weight();
switch (numberNodes)
{
case 10: // 10 nodes quadratic tet
{
for (ife = 0; ife < totalNumberGaussPts; ife++)
{
// y1,y2,y3,y4 are the volume coordinates
y1 = y1Volume[ife];
y2 = y2Volume[ife];
y3 = y3Volume[ife];
y4 = y4Volume[ife];
// shape function is the same as in ABAQUS
// it is different from that in all the FEA book
// in which node is the first node
// here at node 1 y4=1
shapeFunction[ife][0] = y4 * (2. * y4 - 1.);
shapeFunction[ife][1] = y1 * (2. * y1 - 1.);
shapeFunction[ife][2] = y2 * (2. * y2 - 1.);
shapeFunction[ife][3] = y3 * (2. * y3 - 1.);
shapeFunction[ife][4] = 4. * y1 * y4;
shapeFunction[ife][5] = 4. * y1 * y2;
shapeFunction[ife][6] = 4. * y2 * y4;
shapeFunction[ife][7] = 4. * y3 * y4;
shapeFunction[ife][8] = 4. * y1 * y3;
shapeFunction[ife][9] = 4. * y2 * y3;
dndy1GaussPts[ife][0] = 1 - 4 * y4;
dndy1GaussPts[ife][1] = 4 * y1 - 1.;
dndy1GaussPts[ife][2] = 0;
dndy1GaussPts[ife][3] = 0;
dndy1GaussPts[ife][4] = 4. * (y4 - y1);
dndy1GaussPts[ife][5] = 4. * y2;
dndy1GaussPts[ife][6] = -4. * y2;
dndy1GaussPts[ife][7] = -4. * y3;
dndy1GaussPts[ife][8] = 4. * y3;
dndy1GaussPts[ife][9] = 0;
dndy2GaussPts[ife][0] = 1 - 4 * y4;
dndy2GaussPts[ife][1] = 0;
dndy2GaussPts[ife][2] = 4. * y2 - 1.;
dndy2GaussPts[ife][3] = 0;
dndy2GaussPts[ife][4] = -4. * y1;
dndy2GaussPts[ife][5] = 4. * y1;
dndy2GaussPts[ife][6] = 4. * (y4 - y2);
dndy2GaussPts[ife][7] = -4. * y3;
dndy2GaussPts[ife][8] = 0.;
dndy2GaussPts[ife][9] = 4. * y3;
dndy3GaussPts[ife][0] = 1 - 4 * y4;
dndy3GaussPts[ife][1] = 0;
dndy3GaussPts[ife][2] = 0;
dndy3GaussPts[ife][3] = 4. * y3 - 1.;
dndy3GaussPts[ife][4] = -4. * y1;
dndy3GaussPts[ife][5] = 0;
dndy3GaussPts[ife][6] = -4. * y2;
dndy3GaussPts[ife][7] = 4. * (y4 - y3);
dndy3GaussPts[ife][8] = 4. * y1;
dndy3GaussPts[ife][9] = 4. * y2;
}
break;
}
case 4: // four node linear tet for debug purpose
{
for (ife = 0; ife < totalNumberGaussPts; ife++)
{
y1 = y1Volume[ife];
y2 = y2Volume[ife];
y3 = y3Volume[ife];
y4 = y4Volume[ife];
shapeFunction[ife][0] = y4;
shapeFunction[ife][1] = y1;
shapeFunction[ife][2] = y2;
shapeFunction[ife][3] = y3;
dndy1GaussPts[ife][0] = -1.;
dndy1GaussPts[ife][1] = 1;
dndy1GaussPts[ife][2] = 0;
dndy1GaussPts[ife][3] = 0;
dndy2GaussPts[ife][0] = -1.;
dndy2GaussPts[ife][1] = 0;
dndy2GaussPts[ife][2] = 1;
dndy2GaussPts[ife][3] = 0;
dndy3GaussPts[ife][0] = -1.;
dndy3GaussPts[ife][1] = 0;
dndy3GaussPts[ife][2] = 0;
dndy3GaussPts[ife][3] = 1;
}
break;
}
}
}
void GaussIntegration::calculate_derivative_at_nodes_3d_tet(double dndy1_at_nodes[][maxNumberNodes],
double dndy2_at_nodes[][maxNumberNodes], double dndy3_at_nodes[][maxNumberNodes])
{
double y1, y2, y3, y4;
int i;
switch (numberNodes)
{
case 10:
{
for (i = 0; i < numberNodes; i++)
{
get_node_local_coord_tet(i, y1, y2, y3, y4);
dndy1_at_nodes[i][0] = 1 - 4 * y4;
dndy1_at_nodes[i][1] = 4 * y1 - 1.;
dndy1_at_nodes[i][2] = 0;
dndy1_at_nodes[i][3] = 0;
dndy1_at_nodes[i][4] = 4. * (y4 - y1);
dndy1_at_nodes[i][5] = 4. * y2;
dndy1_at_nodes[i][6] = -4. * y2;
dndy1_at_nodes[i][7] = -4. * y3;
dndy1_at_nodes[i][8] = 4. * y3;
dndy1_at_nodes[i][9] = 0;
dndy2_at_nodes[i][0] = 1 - 4 * y4;
dndy2_at_nodes[i][1] = 0;
dndy2_at_nodes[i][2] = 4. * y2 - 1.;
dndy2_at_nodes[i][3] = 0;
dndy2_at_nodes[i][4] = -4. * y1;
dndy2_at_nodes[i][5] = 4. * y1;
dndy2_at_nodes[i][6] = 4. * (y4 - y2);
dndy2_at_nodes[i][7] = -4. * y3;
dndy2_at_nodes[i][8] = 0.;
dndy2_at_nodes[i][9] = 4. * y3;
dndy3_at_nodes[i][0] = 1 - 4 * y4;
dndy3_at_nodes[i][1] = 0;
dndy3_at_nodes[i][2] = 0;
dndy3_at_nodes[i][3] = 4. * y3 - 1.;
dndy3_at_nodes[i][4] = -4. * y1;
dndy3_at_nodes[i][5] = 0;
dndy3_at_nodes[i][6] = -4. * y2;
dndy3_at_nodes[i][7] = 4. * (y4 - y3);
dndy3_at_nodes[i][8] = 4. * y1;
dndy3_at_nodes[i][9] = 4. * y2;
}
break;
}
case 4:
{
for (i = 0; i < numberNodes; i++)
{
get_node_local_coord_tet(i, y1, y2, y3, y4);
dndy1_at_nodes[i][0] = -1.;
dndy1_at_nodes[i][1] = 1;
dndy1_at_nodes[i][2] = 0;
dndy1_at_nodes[i][3] = 0;
dndy2_at_nodes[i][0] = -1.;
dndy2_at_nodes[i][1] = 0;
dndy2_at_nodes[i][2] = 1;
dndy2_at_nodes[i][3] = 0;
dndy3_at_nodes[i][0] = -1.;
dndy3_at_nodes[i][1] = 0;
dndy3_at_nodes[i][2] = 0;
dndy3_at_nodes[i][3] = 1;
}
break;
}
}
}
void GaussIntegration::get_node_local_coord_tet(
int node_id, double& y1, double& y2, double& y3, double& y4)
{
switch (node_id)
{
case 0:
y1 = 0.;
y2 = 0.;
y3 = 0.;