dkt3d.C

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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 "sm/Elements/Plates/dkt3d.h"
#include "sm/Materials/structuralms.h"
#include "fei2dtrlin.h"
#include "node.h"
#include "load.h"
#include "mathfem.h"
#include "gaussintegrationrule.h"
#include "gausspoint.h"
#include "classfactory.h"
 
#include <cstdlib>
 
namespace oofem {
REGISTER_Element(DKTPlate3d);
 
DKTPlate3d::DKTPlate3d(int n, Domain *aDomain) : DKTPlate(n, aDomain)
{}
 
 
void
DKTPlate3d::giveLocalCoordinates(FloatArray &answer, const FloatArray &global)
{
    if ( global.giveSize() != 3 ) {
        OOFEM_ERROR("cannot transform coordinates - size mismatch");
    }
 
    // first ensure that receiver's GtoLRotationMatrix[3,3] is defined
    this->computeGtoLRotationMatrix();
 
    FloatArray offset;
    offset.beDifferenceOf( global, this->giveNode(1)->giveCoordinates() );
    answer.beProductOf(GtoLRotationMatrix, offset);
}
 
 
void
DKTPlate3d::giveNodeCoordinates(double &x1, double &x2, double &x3,
                                double &y1, double &y2, double &y3,
                                double &z1, double &z2, double &z3)
{
    FloatArray nc1(3), nc2(3), nc3(3);
 
    this->giveLocalCoordinates(nc1, this->giveNode(1)->giveCoordinates() );
    this->giveLocalCoordinates(nc2, this->giveNode(2)->giveCoordinates() );
    this->giveLocalCoordinates(nc3, this->giveNode(3)->giveCoordinates() );
 
    x1 = nc1.at(1);
    x2 = nc2.at(1);
    x3 = nc3.at(1);
 
    y1 = nc1.at(2);
    y2 = nc2.at(2);
    y3 = nc3.at(2);
 
    z1 = nc1.at(3);
    z2 = nc2.at(3);
    z3 = nc3.at(3);
}
 
 
void
DKTPlate3d::giveDofManDofIDMask(int inode, IntArray &answer) const
{
    answer = { D_u, D_v, D_w, R_u, R_v, R_w };
}
 
 
const FloatMatrix *
DKTPlate3d::computeGtoLRotationMatrix()
// Returns the rotation matrix of the receiver of the size [3,3]
// coords(local) = T * coords(global)
//
// local coordinate (described by vector triplet e1',e2',e3') is defined as follows:
//
// e1'    : [N2-N1]    Ni - means i - th node
// help   : [N3-N1]
// e3'    : e1' x help
// e2'    : e3' x e1'
{
    if ( !GtoLRotationMatrix.isNotEmpty() ) {
        FloatArray e1, e2, e3, help;
 
        // compute e1' = [N2-N1]  and  help = [N3-N1]
        e1.beDifferenceOf( this->giveNode(2)->giveCoordinates(), this->giveNode(1)->giveCoordinates() );
        help.beDifferenceOf( this->giveNode(3)->giveCoordinates(), this->giveNode(1)->giveCoordinates() );
 
        // let us normalize e1'
        e1.normalize();
 
        // compute e3' : vector product of e1' x help
        e3.beVectorProductOf(e1, help);
        // let us normalize
        e3.normalize();
 
        // now from e3' x e1' compute e2'
        e2.beVectorProductOf(e3, e1);
 
        //
        GtoLRotationMatrix.resize(3, 3);
 
        for ( int i = 1; i <= 3; i++ ) {
            GtoLRotationMatrix.at(1, i) = e1.at(i);
            GtoLRotationMatrix.at(2, i) = e2.at(i);
            GtoLRotationMatrix.at(3, i) = e3.at(i);
        }
    }
 
    return & GtoLRotationMatrix;
}
 
 
bool
DKTPlate3d::computeGtoLRotationMatrix(FloatMatrix &answer)
// Returns the rotation matrix of the receiver of the size [9,18]
// r(local) = T * r(global)
// for one node (r written transposed): {w,r1,r2} = T * {u,v,w,r1,r2,r3}
{
    this->computeGtoLRotationMatrix();
 
    answer.resize(9, 18);
    answer.zero();
 
    for ( int i = 1; i <= 3; i++ ) {
        answer.at(1, i) = answer.at(1 + 3, i  + 6) = answer.at(1 + 6, i  + 12) = GtoLRotationMatrix.at(3, i);
        answer.at(2, i + 3) = answer.at(2 + 3, i + 3 + 6) = answer.at(2 + 6, i + 3 + 12) = GtoLRotationMatrix.at(1, i);
        answer.at(3, i + 3) = answer.at(3 + 3, i + 3 + 6) = answer.at(3 + 6, i + 3 + 12) = GtoLRotationMatrix.at(2, i);
    }
 
    return 1;
}
 
void
DKTPlate3d::giveCharacteristicTensor(FloatMatrix &answer, CharTensor type, GaussPoint *gp, TimeStep *tStep)
// returns characteristic tensor of the receiver at given gp and tStep
// strain vector = (Kappa_x, Kappa_y, Kappa_xy, Gamma_zx, Gamma_zy)
{
    FloatArray charVect;
    StructuralMaterialStatus *ms = static_cast< StructuralMaterialStatus * >( gp->giveMaterialStatus() );
 
    answer.resize(3, 3);
    answer.zero();
 
    if ( ( type == LocalForceTensor ) || ( type == GlobalForceTensor ) ) {
        //this->computeStressVector(charVect, gp, tStep);
        charVect = ms->giveStressVector();
 
        answer.at(1, 3) = charVect.at(4);
        answer.at(3, 1) = charVect.at(4);
        answer.at(2, 3) = charVect.at(5);
        answer.at(3, 2) = charVect.at(5);
    } else if ( ( type == LocalMomentTensor ) || ( type == GlobalMomentTensor ) ) {
        //this->computeStressVector(charVect, gp, tStep);
        charVect = ms->giveStressVector();
 
        answer.at(1, 1) = charVect.at(1);
        answer.at(2, 2) = charVect.at(2);
        answer.at(1, 2) = charVect.at(3);
        answer.at(2, 1) = charVect.at(3);
    } else if ( ( type == LocalStrainTensor ) || ( type == GlobalStrainTensor ) ) {
        //this->computeStrainVector(charVect, gp, tStep);
        charVect = ms->giveStrainVector();
 
        answer.at(1, 3) = charVect.at(4) / 2.;
        answer.at(3, 1) = charVect.at(4) / 2.;
        answer.at(2, 3) = charVect.at(5) / 2.;
        answer.at(3, 2) = charVect.at(5) / 2.;
    } else if ( ( type == LocalCurvatureTensor ) || ( type == GlobalCurvatureTensor ) ) {
        //this->computeStrainVector(charVect, gp, tStep);
        charVect = ms->giveStrainVector();
 
        answer.at(1, 1) = charVect.at(1);
        answer.at(2, 2) = charVect.at(2);
        answer.at(1, 2) = charVect.at(3) / 2.;
        answer.at(2, 1) = charVect.at(3) / 2.;
    } else {
        OOFEM_ERROR("unsupported tensor mode");
    }
 
    if ( ( type == GlobalForceTensor  ) || ( type == GlobalMomentTensor  ) ||
         ( type == GlobalStrainTensor ) || ( type == GlobalCurvatureTensor ) ) {
        this->computeGtoLRotationMatrix();
        answer.rotatedWith(GtoLRotationMatrix);
    }
}
 
 
int
DKTPlate3d::giveIPValue(FloatArray &answer, GaussPoint *gp, InternalStateType type, TimeStep *tStep)
{
    FloatMatrix globTensor;
    CharTensor cht;
 
    answer.resize(6);
 
    if (  type == IST_CurvatureTensor || type == IST_ShellStrainTensor ) {
        if ( type == IST_CurvatureTensor ) {
            cht = GlobalCurvatureTensor;
        } else {
            cht = GlobalStrainTensor;
        }
 
        this->giveCharacteristicTensor(globTensor, cht, gp, tStep);
 
        answer.at(1) = globTensor.at(1, 1); //xx
        answer.at(2) = globTensor.at(2, 2); //yy
        answer.at(3) = globTensor.at(3, 3); //zz
        answer.at(4) = 2 * globTensor.at(2, 3); //yz
        answer.at(5) = 2 * globTensor.at(1, 3); //xz
        answer.at(6) = 2 * globTensor.at(1, 2); //xy
 
        return 1;
    } else if ( type == IST_ShellMomentTensor || type == IST_ShellForceTensor ) {
        if ( type == IST_ShellMomentTensor ) {
            cht = GlobalMomentTensor;
        } else {
            cht = GlobalForceTensor;
        }
 
        this->giveCharacteristicTensor(globTensor, cht, gp, tStep);
 
        answer.at(1) = globTensor.at(1, 1); //xx
        answer.at(2) = globTensor.at(2, 2); //yy
        answer.at(3) = globTensor.at(3, 3); //zz
        answer.at(4) = globTensor.at(2, 3); //yz
        answer.at(5) = globTensor.at(1, 3); //xz
        answer.at(6) = globTensor.at(1, 2); //xy
 
        return 1;
    } else {
        return StructuralElement::giveIPValue(answer, gp, type, tStep);
    }
}
 
int
DKTPlate3d::computeLoadGToLRotationMtrx(FloatMatrix &answer)
// Returns the rotation matrix of the receiver of the size [6,6]
// f(local) = T * f(global)
{
    this->computeGtoLRotationMatrix();
 
    answer.resize(6, 6);
    answer.zero();
 
    for ( int i = 1; i <= 3; i++ ) {
        answer.at(1, i) = answer.at(4, i + 3) = GtoLRotationMatrix.at(1, i);
        answer.at(2, i) = answer.at(5, i + 3) = GtoLRotationMatrix.at(2, i);
        answer.at(3, i) = answer.at(6, i + 3) = GtoLRotationMatrix.at(3, i);
    }
 
    return 1;
}
 
void
DKTPlate3d::computeSurfaceNMatrixAt(FloatMatrix &answer, int iSurf, GaussPoint *sgp)
{
    FloatMatrix ne;
    this->computeNmatrixAt(sgp->giveNaturalCoordinates(), ne);
 
    answer.resize(6, 18);
    answer.zero();
    int ri[] = {
        2, 3, 4
    };
    int ci[] = {
        2, 3, 4, 8, 9, 10, 14, 15, 16
    };
 
    for ( int i = 0; i < 3; i++ ) {
        for ( int j = 0; j < 9; j++ ) {
            answer(ri [ i ], ci [ j ]) = ne(i, j);
        }
    }
}
 
void
DKTPlate3d::giveSurfaceDofMapping(IntArray &answer, int iSurf) const
{
    answer.resize(18);
    answer.zero();
    if ( iSurf == 1 ) {
        answer.at(3) = 1; // node 1
        answer.at(4) = 2;
        answer.at(5) = 3;
 
        answer.at(9)  = 4; // node 2
        answer.at(10) = 5;
        answer.at(11) = 6;
 
        answer.at(15) = 7; // node 3
        answer.at(16) = 8;
        answer.at(17) = 9;
    } else {
        OOFEM_ERROR("wrong surface number");
    }
}
 
 
double
DKTPlate3d::computeSurfaceVolumeAround(GaussPoint *gp, int iSurf)
{
    return this->computeVolumeAround(gp);
}
 
 
int
DKTPlate3d::computeLoadLSToLRotationMatrix(FloatMatrix &answer, int isurf, GaussPoint *gp)
{
    return 0;
}
 
void
DKTPlate3d::printOutputAt(FILE *file, TimeStep *tStep)
// Performs end-of-step operations.
{
    FloatArray v;
 
    fprintf(file, "element %d (%8d) :\n", this->giveLabel(), this->giveNumber() );
 
    for ( int i = 0; i < ( int ) integrationRulesArray.size(); i++ ) {
        for ( GaussPoint *gp: * integrationRulesArray [ i ] ) {
            fprintf(file, "  GP %2d.%-2d :", i + 1, gp->giveNumber() );
 
            this->giveIPValue(v, gp, IST_ShellStrainTensor, tStep);
            fprintf(file, "  strains    ");
            // eps_x, eps_y, eps_z, eps_yz, eps_xz, eps_xy (global)
            for ( auto &val : v ) {
                fprintf(file, " %.4e", val);
            }
 
            this->giveIPValue(v, gp, IST_CurvatureTensor, tStep);
            fprintf(file, "\n              curvatures ");
            for ( auto &val : v ) {
                fprintf(file, " %.4e", val);
            }
 
            // Forces - Moments
            this->giveIPValue(v, gp, IST_ShellForceTensor, tStep);
            fprintf(file, "\n              stresses   ");
            for ( auto &val : v ) {
                fprintf(file, " %.4e", val);
            }
 
            this->giveIPValue(v, gp, IST_ShellMomentTensor, tStep);
            fprintf(file, "\n              moments    ");
            for ( auto &val : v ) {
                fprintf(file, " %.4e", val);
            }
 
            fprintf(file, "\n");
        }
    }
}
 
 
void
DKTPlate3d::giveEdgeDofMapping(IntArray &answer, int iEdge) const
{
    /*
     * provides dof mapping of local edge dofs (only nonzero are taken into account)
     * to global element dofs
     */
 
    answer.resize(12);
    answer.zero();
    if ( iEdge == 1 ) { // edge between nodes 1,2
        answer.at(3) = 3;
        answer.at(4) = 4;
        answer.at(5) = 5;
        answer.at(9) = 9;
        answer.at(10) = 10;
        answer.at(11) = 11;
    } else if ( iEdge == 2 ) { // edge between nodes 2 3
        answer.at(3) = 9;
        answer.at(4) = 10;
        answer.at(5) = 11;
        answer.at(9) = 15;
        answer.at(10) = 16;
        answer.at(11) = 17;
    } else if ( iEdge == 3 ) { // edge between nodes 3 1
        answer.at(3) = 15;
        answer.at(4) = 16;
        answer.at(5) = 17;
        answer.at(9) = 4;
        answer.at(10) = 5;
        answer.at(11) = 6;
    } else {
        OOFEM_ERROR("wrong edge number");
    }
}
 
double
DKTPlate3d::computeEdgeVolumeAround(GaussPoint *gp, int iEdge)
{
    double detJ = this->interp_lin.edgeGiveTransformationJacobian(iEdge, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(this) );
    return detJ * gp->giveWeight();
}
 
 
int
DKTPlate3d::computeLoadLEToLRotationMatrix(FloatMatrix &answer, int iEdge, GaussPoint *gp)
{
    // returns transformation matrix from
    // edge local coordinate system
    // to element local c.s
    // (same as global c.s in this case)
    //
    // i.e. f(element local) = T * f(edge local)
    //
 
    const auto &edgeNodes = this->interp_lin.computeLocalEdgeMapping(iEdge);
 
    auto nodeA = this->giveNode(edgeNodes.at(1) );
    auto nodeB = this->giveNode(edgeNodes.at(2) );
 
    FloatArray cb(3), ca(3);
    this->giveLocalCoordinates( ca, nodeA->giveCoordinates() );
    this->giveLocalCoordinates( cb, nodeB->giveCoordinates() );
 
    double dx = cb.at(1) - ca.at(1);
    double dy = cb.at(2) - ca.at(2);
    double length = sqrt(dx * dx + dy * dy);
 
    answer.resize(3, 3);
    answer.zero();
    answer.at(1, 1) = 1.0;
    answer.at(2, 2) = dx / length;
    answer.at(2, 3) = -dy / length;
    answer.at(3, 2) = dy / length;
    answer.at(3, 3) = dx / length;
 
    return 1;
}
 
bool
DKTPlate3d::computeLocalCoordinates(FloatArray &answer, const FloatArray &coords)
//converts global coordinates to local planar area coordinates,
//does not return a coordinate in the thickness direction, but
//does check that the point is in the element thickness
{
    // rotate the input point Coordinate System into the element CS
    FloatArray inputCoords_ElCS;
    std::vector< FloatArray >lc(3);
    FloatArray llc;
    this->giveLocalCoordinates(inputCoords_ElCS, coords);
    for ( int _i = 0; _i < 3; _i++ ) {
        this->giveLocalCoordinates(lc [ _i ], this->giveNode(_i + 1)->giveCoordinates() );
    }
    FEI2dTrLin _interp(1, 2);
    bool inplane = _interp.global2local( llc, inputCoords_ElCS, FEIVertexListGeometryWrapper(lc, this->giveGeometryType()) ) > 0;
    answer.resize(2);
    answer.at(1) = inputCoords_ElCS.at(1);
    answer.at(2) = inputCoords_ElCS.at(2);
    GaussPoint _gp(NULL, 1, answer, 2.0, _2dPlate);
    // now check if the third local coordinate is within the thickness of element
    bool outofplane = ( fabs(inputCoords_ElCS.at(3) ) <= this->giveCrossSection()->give(CS_Thickness, & _gp) / 2. );
 
    return inplane && outofplane;
}
 
 
int
DKTPlate3d::computeGlobalCoordinates(FloatArray &answer, const FloatArray &lcoords)
{
    double l1 = lcoords.at(1);
    double l2 = lcoords.at(2);
    double l3 = 1. - l2 - l1;
 
    answer.resize(3);
    for ( int _i = 1; _i <= 3; _i++ ) {
        answer.at(_i) = l1 * this->giveNode(1)->giveCoordinate(_i) + l2 * this->giveNode(2)->giveCoordinate(_i) + l3 * this->giveNode(3)->giveCoordinate(_i);
    }
    return true;
}
 
void
DKTPlate3d::computeBodyLoadVectorAt(FloatArray &answer, Load *forLoad, TimeStep *tStep, ValueModeType mode)
// Computes numerically the load vector of the receiver due to the body loads, at tStep.
// load is assumed to be in global cs.
// load vector is then transformed to coordinate system in each node.
// (should be global coordinate system, but there may be defined
//  different coordinate system in each node)
{
    double dens, dV, load;
    FloatArray force;
    FloatMatrix T;
 
    if ( ( forLoad->giveBCGeoType() != BodyLoadBGT ) || ( forLoad->giveBCValType() != ForceLoadBVT ) ) {
        OOFEM_ERROR("unknown load type");
    }
 
    GaussIntegrationRule irule(1, this, 1, 5);
    irule.SetUpPointsOnTriangle(1, _2dPlate);
 
    // note: force is assumed to be in global coordinate system.
    forLoad->computeComponentArrayAt(force, tStep, mode);
 
    if ( force.giveSize() ) {
        GaussPoint *gp = irule.getIntegrationPoint(0);
 
        dens = this->giveStructuralCrossSection()->give('d', gp); // constant density assumed
        dV   = this->computeVolumeAround(gp) * this->giveCrossSection()->give(CS_Thickness, gp); // constant thickness assumed
 
        answer.resize(18);
        answer.zero();
 
        load = force.at(1) * dens * dV / 3.0;
        answer.at(1) = load;
        answer.at(7) = load;
        answer.at(13) = load;
 
        load = force.at(2) * dens * dV / 3.0;
        answer.at(2) = load;
        answer.at(8) = load;
        answer.at(14) = load;
 
        load = force.at(3) * dens * dV / 3.0;
        answer.at(3) = load;
        answer.at(9) = load;
        answer.at(15) = load;
 
        // transform result from global cs to local element cs.
        if ( this->computeGtoLRotationMatrix(T) ) {
            answer.rotatedWith(T, 'n');
        }
    } else {
        answer.clear();          // nil resultant
    }
}
} // end namespace oofem