fei2dlinehermite.C

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/*
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 *
 *             OOFEM : Object Oriented Finite Element Code
 *
 *               Copyright (C) 1993 - 2013   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 "fei2dlinehermite.h"
#include "mathfem.h"
#include "floatmatrix.h"
#include "floatarray.h"

namespace oofem {
double FEI2dLineHermite :: giveLength(const FEICellGeometry &cellgeo) const
{
    double x2_x1, y2_y1;
    x2_x1 = cellgeo.giveVertexCoordinates(2)->at(xind) - cellgeo.giveVertexCoordinates(1)->at(xind);
    y2_y1 = cellgeo.giveVertexCoordinates(2)->at(yind) - cellgeo.giveVertexCoordinates(1)->at(yind);
    return sqrt(x2_x1 * x2_x1 + y2_y1 * y2_y1);
}

void FEI2dLineHermite :: evalN(FloatArray &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
{
    double ksi = lcoords.at(1);
    double l = this->giveLength(cellgeo);

    answer.resize(4);
    answer.zero();

    answer.at(1) = 0.25 * ( 1.0 - ksi ) * ( 1.0 - ksi ) * ( 2.0 + ksi );
    answer.at(2) =  0.125 * l * ( 1.0 - ksi ) * ( 1.0 - ksi ) * ( 1.0 + ksi );
    answer.at(3) = 0.25 * ( 1.0 + ksi ) * ( 1.0 + ksi ) * ( 2.0 - ksi );
    answer.at(4) = -0.125 * l * ( 1.0 + ksi ) * ( 1.0 + ksi ) * ( 1.0 - ksi );
}

double FEI2dLineHermite :: evaldNdx(FloatMatrix &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
{
    // This is dNds projected on the direction if the linear edge. If any other interpolation is used for geometry, this can't be used anymore.
    FloatArray dNds;
    this->edgeEvaldNds(dNds, 1, lcoords, cellgeo);
    // Tangent line to project on
    FloatArray vec(2);
    vec.at(1) = cellgeo.giveVertexCoordinates(2)->at(xind) - cellgeo.giveVertexCoordinates(1)->at(xind);
    vec.at(2) = cellgeo.giveVertexCoordinates(2)->at(yind) - cellgeo.giveVertexCoordinates(1)->at(yind);
    double detJ = vec.normalize() * 0.5;

    answer.beDyadicProductOf(dNds, vec);
    return detJ;
}

void FEI2dLineHermite :: local2global(FloatArray &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
{
    FloatArray n;
    this->evalN(n, lcoords, cellgeo);
    answer.resize( max(xind, yind) );
    answer.zero();
    answer.at(xind) = ( n.at(1) * cellgeo.giveVertexCoordinates(1)->at(xind) +
                       n.at(2) * cellgeo.giveVertexCoordinates(2)->at(xind) );
    answer.at(yind) = ( n.at(1) * cellgeo.giveVertexCoordinates(1)->at(yind) +
                       n.at(2) * cellgeo.giveVertexCoordinates(2)->at(yind) );
}

int FEI2dLineHermite :: global2local(FloatArray &answer, const FloatArray &gcoords, const FEICellGeometry &cellgeo)
{
    double xi;
    double x2_x1, y2_y1;

    x2_x1 = cellgeo.giveVertexCoordinates(2)->at(xind) - cellgeo.giveVertexCoordinates(1)->at(xind);
    y2_y1 = cellgeo.giveVertexCoordinates(2)->at(yind) - cellgeo.giveVertexCoordinates(1)->at(yind);

    // Projection of the global coordinate gives the value interpolated in [0,1].
    xi = ( x2_x1 * gcoords(0) + y2_y1 * gcoords(1) ) / ( sqrt(x2_x1 * x2_x1 + y2_y1 * y2_y1) );
    // Map to [-1,1] domain.
    xi = xi * 2.0 - 1.0;

    answer.resize(1);
    answer(0) = clamp(xi, -1., 1.);
    return false;
}

void FEI2dLineHermite :: edgeEvaldNds(FloatArray &answer, int iedge, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
{
    double l_inv = this->giveLength(cellgeo);
    double ksi = lcoords.at(1);

    answer.resize(4);
    answer.zero();

    answer.at(1) =  1.5 * ( ksi * ksi - 1.0 ) * l_inv;
    answer.at(2) =  0.25 * ( ksi - 1.0 ) * ( 3.0 * ksi + 1.0 );
    answer.at(3) = -1.5 * ( ksi * ksi - 1.0 ) * l_inv;
    answer.at(4) =  0.25 * ( ksi + 1.0 ) * ( 3.0 * ksi - 1.0 );
}

void FEI2dLineHermite :: edgeEvald2Nds2(FloatArray &answer, int iedge, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
{
    double l_inv = this->giveLength(cellgeo);
    double ksi = lcoords.at(1);

    answer.resize(4);
    answer.zero();

    answer.at(1) =  l_inv * 6.0 * ksi * l_inv;
    answer.at(2) =  l_inv * ( 3.0 * ksi - 1.0 );
    answer.at(3) = -l_inv * 6.0 * ksi * l_inv;
    answer.at(4) =  l_inv * ( 3.0 * ksi + 1.0 );
}

double FEI2dLineHermite :: edgeEvalNormal(FloatArray &normal, int iedge, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
{
    normal.resize(2);
    normal.at(1) = cellgeo.giveVertexCoordinates(2)->at(xind) - cellgeo.giveVertexCoordinates(1)->at(xind);
    normal.at(2) = -( cellgeo.giveVertexCoordinates(2)->at(yind) - cellgeo.giveVertexCoordinates(1)->at(yind) );

    return normal.normalize() * 0.5;
}

double FEI2dLineHermite :: giveTransformationJacobian(const FloatArray &lcoords, const FEICellGeometry &cellgeo)
{
    double x2_x1, y2_y1;
    x2_x1 = cellgeo.giveVertexCoordinates(2)->at(xind) - cellgeo.giveVertexCoordinates(1)->at(xind);
    y2_y1 = cellgeo.giveVertexCoordinates(2)->at(yind) - cellgeo.giveVertexCoordinates(1)->at(yind);
    return sqrt(x2_x1 * x2_x1 + y2_y1 * y2_y1) * 0.5;
}

IntegrationRule *FEI2dLineHermite :: giveIntegrationRule(int order)
{
    OOFEM_ERROR("Not supported.");
    return NULL;
}
} // end namespace oofem