fei3dtrquad.C

Go to the documentation of this file.

/*
 *
 *                 #####    #####   ######  ######  ###   ###
 *               ##   ##  ##   ##  ##      ##      ## ### ##
 *              ##   ##  ##   ##  ####    ####    ##  #  ##
 *             ##   ##  ##   ##  ##      ##      ##     ##
 *            ##   ##  ##   ##  ##      ##      ##     ##
 *            #####    #####   ##      ######  ##     ##
 *
 *
 *             OOFEM : Object Oriented Finite Element Code
 *
 *               Copyright (C) 1993 - 2025   Borek Patzak
 *
 *
 *
 *       Czech Technical University, Faculty of Civil Engineering,
 *   Department of Structural Mechanics, 166 29 Prague, Czech Republic
 *
 *  This library is free software; you can redistribute it and/or
 *  modify it under the terms of the GNU Lesser General Public
 *  License as published by the Free Software Foundation; either
 *  version 2.1 of the License, or (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 *  Lesser General Public License for more details.
 *
 *  You should have received a copy of the GNU Lesser General Public
 *  License along with this library; if not, write to the Free Software
 *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 */
 
#include "fei3dtrquad.h"
#include "mathfem.h"
#include "floatmatrix.h"
#include "floatarray.h"
#include "gaussintegrationrule.h"
#include <stdexcept>
 
namespace oofem {
void
FEI3dTrQuad :: evalN(FloatArray &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    this->surfaceEvalN(answer, 1, lcoords, cellgeo);
}
 
double
FEI3dTrQuad :: evaldNdx(FloatMatrix &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    OOFEM_ERROR("FEI3dTrQuad :: evaldNdx - Not supported");
    //return 0.;
}
 
 
void
FEI3dTrQuad :: evaldNdxi(FloatMatrix &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    this->surfaceEvaldNdxi(answer, lcoords);
}
 
 
void
FEI3dTrQuad :: giveDerivativeXi(FloatArray &n, const FloatArray &lc) const
{
    double l1, l2, l3;
 
    l1 = lc.at(1);
    l2 = lc.at(2);
    l3 = 1.0 - l1 - l2;
 
    n.resize(6);
 
    n.at(1) = 4.0 * l1 - 1.0;
    n.at(2) = 0.0;
    n.at(3) = -1.0 * ( 4.0 * l3 - 1.0 );
    n.at(4) = 4.0 * l2;
    n.at(5) = -4.0 * l2;
    n.at(6) = 4.0 * l3 - 4.0 * l1;
}
 
void
FEI3dTrQuad :: giveDerivativeEta(FloatArray &n, const FloatArray &lc) const
{
    double l1, l2, l3;
 
    l1 = lc.at(1);
    l2 = lc.at(2);
    l3 = 1.0 - l1 - l2;
 
    n.resize(6);
 
    n.at(1) = 0.0;
    n.at(2) = 4.0 * l2 - 1.0;
    n.at(3) = -1.0 * ( 4.0 * l3 - 1.0 );
    n.at(4) = 4.0 * l1;
    n.at(5) = 4.0 * l3 - 4.0 * l2;
    n.at(6) = -4.0 * l1;
}
 
 
void
FEI3dTrQuad :: giveLocalNodeCoords(FloatMatrix &answer,const Element_Geometry_Type) const
{
 
    answer.resize(3,6);
    answer.zero();
    answer.at(1,1) = 1.0;
    answer.at(1,2) = 0.0;
    answer.at(1,3) = 0.0;
    answer.at(1,4) = 0.5;
    answer.at(1,5) = 0.0;
    answer.at(1,6) = 0.5;
 
    answer.at(2,1) = 0.0;
    answer.at(2,2) = 1.0;
    answer.at(2,3) = 0.0;
    answer.at(2,4) = 0.5;
    answer.at(2,5) = 0.5;
    answer.at(2,6) = 0.0;
 
}
 
 
void
FEI3dTrQuad :: local2global(FloatArray &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    FloatArray n;
    this->evalN(n, lcoords, cellgeo);
    answer.clear();
    for ( int i = 1; i <= 6; ++i ) {
        answer.add( n.at(i), cellgeo.giveVertexCoordinates(i) );
    }
}
 
#define POINT_TOL 1.e-3
int
FEI3dTrQuad :: global2local(FloatArray &answer, const FloatArray &gcoords, const FEICellGeometry &cellgeo) const
{
    //OOFEM_ERROR("FEI3dTrQuad :: global2local - Not supported");
    //return -1;

    int xind = 1;
    int yind = 2;
 
    double x1 = cellgeo.giveVertexCoordinates(1).at(xind);
    double x2 = cellgeo.giveVertexCoordinates(2).at(xind);
    double x3 = cellgeo.giveVertexCoordinates(3).at(xind);
 
    double y1 = cellgeo.giveVertexCoordinates(1).at(yind);
    double y2 = cellgeo.giveVertexCoordinates(2).at(yind);
    double y3 = cellgeo.giveVertexCoordinates(3).at(yind);
 
    double detJ = x1*(y2 - y3) + x2*(-y1 + y3) + x3*(y1 - y2);
 
    answer.resize(3);
    answer.at(1) = ( ( x2 * y3 - x3 * y2 ) + ( y2 - y3 ) * gcoords.at(xind) + ( x3 - x2 ) * gcoords.at(yind) ) / detJ;
    answer.at(2) = ( ( x3 * y1 - x1 * y3 ) + ( y3 - y1 ) * gcoords.at(xind) + ( x1 - x3 ) * gcoords.at(yind) ) / detJ;
    answer.at(3) = 1. - answer.at(1) - answer.at(2);
 
    // check if point is inside
    bool inside = true;
    for ( int i = 1; i <= 3; i++ ) {
        if ( answer.at(i) < ( 0. - POINT_TOL ) ) {
            answer.at(i) = 0.;
            inside = false;
        } else if ( answer.at(i) > ( 1. + POINT_TOL ) ) {
            answer.at(i) = 1.;
            inside = false;
        }
    }
 
    return inside;
 
}
 
 
void
FEI3dTrQuad :: giveJacobianMatrixAt(FloatMatrix &jacobianMatrix, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    OOFEM_ERROR("Not supported");
}
 
 
void
FEI3dTrQuad :: edgeEvalN(FloatArray &answer, int iedge, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    double xi = lcoords.at(1);
    answer.resize(3);
    answer[0] = 0.5 * ( xi - 1.0 ) * xi;
    answer[1] = 0.5 * ( xi + 1.0 ) * xi;
    answer[2] = 1.0 - xi * xi;
}
 
 
 
void
FEI3dTrQuad :: edgeEvaldNdx(FloatMatrix &answer, int iedge,
                            const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    OOFEM_ERROR("Not supported");
}
 
void
FEI3dTrQuad :: edgeEvaldNdxi(FloatArray &answer, int iedge, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    double xi = lcoords.at(1);
    answer.resize(3);
    answer[0] = xi - 0.5;
    answer[1] = xi + 0.5;
    answer[2] = -2 * xi;
}
 
void
FEI3dTrQuad :: edgeLocal2global(FloatArray &answer, int iedge,
                                const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    FloatArray N;
    const auto &edgeNodes = this->computeLocalEdgeMapping(iedge);
    this->edgeEvalN(N, iedge, lcoords, cellgeo);
 
    answer.clear();
    for ( int i = 0; i < N.giveSize(); ++i ) {
        answer.add( N[i], cellgeo.giveVertexCoordinates( edgeNodes[i] ) );
    }
}
 
 
double
FEI3dTrQuad :: edgeGiveTransformationJacobian(int iedge, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    FloatArray dNdu;
    double u = lcoords.at(1);
    const auto &eNodes = this->computeLocalEdgeMapping(iedge);
    dNdu.add( u - 0.5, cellgeo.giveVertexCoordinates( eNodes.at(1) ) );
    dNdu.add( u + 0.5, cellgeo.giveVertexCoordinates( eNodes.at(2) ) );
    dNdu.add( -2. * u, cellgeo.giveVertexCoordinates( eNodes.at(3) ) );
    return dNdu.computeNorm();
}
 
 
IntArray
FEI3dTrQuad :: computeLocalEdgeMapping(int iedge) const
{
    if ( iedge == 1 ) { // edge between nodes 1 2
        return {1, 2, 4};
    } else if ( iedge == 2 ) { // edge between nodes 2 3
        return {2, 3, 5};
    } else if ( iedge == 3 ) { // edge between nodes 2 3
        return {3, 1, 6};
    } else {
        throw std::range_error("invalid edge number");
        //return {};
    }
}
 
double
FEI3dTrQuad :: edgeComputeLength(const IntArray &edgeNodes, const FEICellGeometry &cellgeo) const
{
    OOFEM_ERROR("Not supported");
    //return -1;
}
 
void
FEI3dTrQuad :: surfaceEvalN(FloatArray &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    double l1 = lcoords.at(1);
    double l2 = lcoords.at(2);
    double l3 = 1. - l1 - l2;
 
    answer.resize(6);
 
    answer.at(1) = ( 2. * l1 - 1. ) * l1;
    answer.at(2) = ( 2. * l2 - 1. ) * l2;
    answer.at(3) = ( 2. * l3 - 1. ) * l3;
    answer.at(4) = 4. * l1 * l2;
    answer.at(5) = 4. * l2 * l3;
    answer.at(6) = 4. * l3 * l1;
}
 
void
FEI3dTrQuad :: surfaceEvaldNdxi(FloatMatrix &answer, const FloatArray &lcoords) const
{
    // Returns matrix with derivatives wrt local coordinates
    answer.resize(6, 2);
    FloatArray dndxi(6), dndeta(6);
 
    this->giveDerivativeXi(dndxi, lcoords);
    this->giveDerivativeEta(dndeta, lcoords);
    for ( int i = 1; i <= 6; ++i ) {
        answer.at(i, 1) = dndxi.at(i);
        answer.at(i, 2) = dndeta.at(i);
    }
}
 
 
 
void
FEI3dTrQuad :: surfaceLocal2global(FloatArray &answer, int isurf,
                                   const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    //Note: This gives the coordinate in the reference system
    FloatArray N;
    this->surfaceEvalN(N, isurf, lcoords, cellgeo);
 
    answer.clear();
    for ( int i = 1; i <= N.giveSize(); ++i ) {
        answer.add( N.at(i), cellgeo.giveVertexCoordinates(i) );
    }
}
 
void
FEI3dTrQuad :: surfaceEvaldNdx(FloatMatrix &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    OOFEM_ERROR("Not supported");
}
 
void
FEI3dTrQuad :: surfaceEvalBaseVectorsAt(FloatArray &G1, FloatArray &G2, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    // Note: These are not normalized. Returns the two tangent vectors to the surface.
    FloatMatrix dNdxi;
    this->surfaceEvaldNdxi(dNdxi, lcoords);
 
    G1.clear();
    G2.clear();
    for ( int i = 0; i < 6; ++i ) {
        G1.add( dNdxi(i, 1), cellgeo.giveVertexCoordinates(i) );
        G2.add( dNdxi(i, 2), cellgeo.giveVertexCoordinates(i) );
    }
}
 
double
FEI3dTrQuad :: surfaceEvalNormal(FloatArray &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    FloatArray G1, G2; // local curvilinear base vectors
    this->surfaceEvalBaseVectorsAt(G1, G2, lcoords, cellgeo);
    answer.beVectorProductOf(G1, G2);
    double J = answer.computeNorm();
    answer.times(1 / J);
    return J;
}
 
void
FEI3dTrQuad :: surfaceGiveJacobianMatrixAt(FloatMatrix &jacobianMatrix, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    // Jacobian matrix consists of the three curvilinear base vectors. The third is taken as the normal to the surface.
    // Note! The base vectors are not normalized except the third (normal)
    FloatArray G1, G2, G3;
    this->surfaceEvalBaseVectorsAt(G1, G2, lcoords, cellgeo);
    G3.beVectorProductOf(G1, G2);
 
    jacobianMatrix.resize(3, 3);
    jacobianMatrix.at(1, 1) = G1.at(1);
    jacobianMatrix.at(1, 2) = G2.at(1);
    jacobianMatrix.at(1, 3) = G3.at(1);
    jacobianMatrix.at(2, 1) = G1.at(2);
    jacobianMatrix.at(2, 2) = G2.at(2);
    jacobianMatrix.at(2, 3) = G3.at(2);
    jacobianMatrix.at(3, 1) = G1.at(3);
    jacobianMatrix.at(3, 2) = G2.at(3);
    jacobianMatrix.at(3, 3) = G3.at(3);
}
 
double
FEI3dTrQuad :: surfaceGiveTransformationJacobian(int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    OOFEM_ERROR("Not supported yet");
    //return 0;
}
 
IntArray
FEI3dTrQuad :: computeLocalSurfaceMapping(int isurf) const
{
    //surfNodes.setValues(6, 1, 2, 3, 4, 5, 6);
    //surfNodes = {1, 2, 3, 4, 5, 6};
    return computeLocalEdgeMapping(isurf);
 
}
 
std::unique_ptr<IntegrationRule>
FEI3dTrQuad :: giveIntegrationRule(int order, Element_Geometry_Type egt) const
{
    auto iRule = std::make_unique<GaussIntegrationRule>(1, nullptr);
    int points = iRule->getRequiredNumberOfIntegrationPoints(_Triangle, order);
    iRule->SetUpPointsOnTriangle(points, _Unknown);
    return std::move(iRule);
}
 
std::unique_ptr<IntegrationRule>
FEI3dTrQuad :: giveBoundaryIntegrationRule(int order, int boundary, Element_Geometry_Type egt) const
{
    OOFEM_ERROR("FEI3dTrQuad :: giveBoundaryIntegrationRule - Not supported");
    //return nullptr;
}
 
 
double
FEI3dTrQuad :: giveArea(const FEICellGeometry &cellgeo) const
{
    const auto &p1 = cellgeo.giveVertexCoordinates(1);
    double x1 = p1.at(1);
    double y1 = p1.at(2);
    const auto &p2 = cellgeo.giveVertexCoordinates(2);
    double x2 = p2.at(1);
    double y2 = p2.at(2);
    const auto &p3 = cellgeo.giveVertexCoordinates(3);
    double x3 = p3.at(1);
    double y3 = p3.at(2);
    const auto &p4 = cellgeo.giveVertexCoordinates(4);
    double x4 = p4.at(1);
    double y4 = p4.at(2);
    const auto &p5 = cellgeo.giveVertexCoordinates(5);
    double x5 = p5.at(1);
    double y5 = p5.at(2);
    const auto &p6 = cellgeo.giveVertexCoordinates(6);
    double x6 = p6.at(1);
    double y6 = p6.at(2);
 
    return (4*(-(x4*y1) + x6*y1 + x4*y2 - x5*y2 + x5*y3 - x6*y3) + x2*(y1 - y3 - 4*y4 + 4*y5) +
            x1*(-y2 + y3 + 4*y4 - 4*y6) + x3*(-y1 + y2 - 4*y5 + 4*y6))/6;
}
} // end namespace oofem