fei1dhermite.C

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/*
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 *
 *
 *             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 "fei1dhermite.h"
#include "mathfem.h"
#include "floatmatrix.h"
#include "floatarray.h"
#include "floatmatrixf.h"
#include "floatarrayf.h"
 
namespace oofem {
 
void
FEI1dHermite :: evalN(FloatArray &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    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 );
}
 
std::pair<double, FloatMatrixF<1,4>>
FEI1dHermite :: evaldNdx(double ksi, const FEICellGeometry &cellgeo) const
{
    double l = this->giveLength(cellgeo);
    double l_inv = 1.0 / l;
    FloatMatrixF<1,4> ans = {
        1.5 * ( -1.0 + ksi * ksi ) * l_inv,
        0.25 * ( ksi - 1.0 ) * ( 1.0 + 3.0 * ksi ),
        -1.5 * ( -1.0 + ksi * ksi ) * l_inv,
        0.25 * ( ksi - 1.0 ) * ( 1.0 + 3.0 * ksi )
    };
    return {0.5 * l, ans};
}
 
double
FEI1dHermite :: evaldNdx(FloatMatrix &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    double l = this->giveLength(cellgeo);
    double l_inv = 1.0 / l;
    double ksi = lcoords.at(1);
 
    answer.resize(1, 4);
    answer.zero();
 
    answer.at(1, 1) =  1.5 * ( -1.0 + ksi * ksi ) * l_inv;
    answer.at(1, 2) =  0.25 * ( ksi - 1.0 ) * ( 1.0 + 3.0 * ksi );
    answer.at(1, 3) = -1.5 * ( -1.0 + ksi * ksi ) * l_inv;
    answer.at(1, 4) =  0.25 * ( ksi - 1.0 ) * ( 1.0 + 3.0 * ksi );
 
    return 0.5 * l;
}
 
FloatMatrixF<1,4>
FEI1dHermite :: evald2Ndx2(double ksi, const FEICellGeometry &cellgeo) const
{
    double l_inv = 1.0 / this->giveLength(cellgeo);
 
    return {
        l_inv * 6.0 * ksi * l_inv,
        l_inv * ( 3.0 * ksi - 1.0 ),
        -l_inv * 6.0 * ksi * l_inv,
        l_inv * ( 3.0 * ksi + 1.0 )
    };
}
 
void
FEI1dHermite :: evald2Ndx2(FloatMatrix &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    //answer = evald2Ndx2(lcoords[0]);
    double l_inv = 1.0 / this->giveLength(cellgeo);
    double ksi = lcoords.at(1);
    answer.resize(1, 4);
    answer.zero();
 
    answer.at(1, 1) =  l_inv * 6.0 * ksi * l_inv;
    answer.at(1, 2) =  l_inv * ( 3.0 * ksi - 1.0 );
    answer.at(1, 3) = -l_inv * 6.0 * ksi * l_inv;
    answer.at(1, 4) =  l_inv * ( 3.0 * ksi + 1.0 );
}
 
void
FEI1dHermite :: local2global(FloatArray &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    FloatArray n;
    this->evalN(n, lcoords, cellgeo);
 
    answer.resize(1);
    answer.at(1) = n.at(1) * cellgeo.giveVertexCoordinates(1).at(cindx) +
                   n.at(2) * cellgeo.giveVertexCoordinates(2).at(cindx) +
                   n.at(3) * cellgeo.giveVertexCoordinates(3).at(cindx);
}
 
int
FEI1dHermite :: global2local(FloatArray &answer, const FloatArray &coords, const FEICellGeometry &cellgeo) const
{
    double x1 = cellgeo.giveVertexCoordinates(1).at(cindx);
    double x2 = cellgeo.giveVertexCoordinates(2).at(cindx);
 
    double ksi = ( 2.0 * coords.at(1) - ( x1 + x2 ) ) / ( x2 - x1 );
    answer.resize(1);
    answer.at(1) = clamp(ksi, -1., 1.);
    return fabs(ksi) <= 1.0;
}
 
double
FEI1dHermite :: giveTransformationJacobian(const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    // This isn't really relevant, interpolation of geometry will be just linear
    double l = this->giveLength(cellgeo);
    return 0.5 * l;
}
 
double
FEI1dHermite :: giveLength(const FEICellGeometry &cellgeo) const
{
    return fabs( cellgeo.giveVertexCoordinates(2).at(cindx) - cellgeo.giveVertexCoordinates(1).at(cindx) );
}
} // end namespace oofem