lattice3d.C

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/*
 *
 *                 #####    #####   ######  ######  ###   ###
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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 program is free software; you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
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 *  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 General Public License for more details.
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 *  You should have received a copy of the GNU General Public License
 *  along with this program; if not, write to the Free Software
 *  Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
 */
 
#include "domain.h"
#include "lattice3d.h"
#include "../sm/Materials/LatticeMaterials/latticematstatus.h"
#include "node.h"
#include "material.h"
#include "gausspoint.h"
#include "gaussintegrationrule.h"
#include "floatmatrix.h"
#include "floatmatrixf.h"
#include "intarray.h"
#include "floatarray.h"
#include "floatarrayf.h"
#include "mathfem.h"
#include "latticestructuralelement.h"
#include "contextioerr.h"
#include "datastream.h"
#include "classfactory.h"
#include "sm/CrossSections/latticecrosssection.h"
#include "parametermanager.h"
#include "paramkey.h"
 
#ifdef __OOFEG
 #include "oofeggraphiccontext.h"
 #include "../sm/Materials/structuralmaterial.h"
#endif
 
namespace oofem {
REGISTER_Element(Lattice3d);
 
ParamKey Lattice3d::IPK_Lattice3d_mlength("mlength");
ParamKey Lattice3d::IPK_Lattice3d_polycoords("polycoords");
ParamKey Lattice3d::IPK_Lattice3d_couplingflag("couplingflag");
ParamKey Lattice3d::IPK_Lattice3d_couplingnumber("couplingnumber");
ParamKey Lattice3d::IPK_Lattice3d_pressures("pressures");
 
Lattice3d :: Lattice3d(int n, Domain *aDomain) : LatticeStructuralElement(n, aDomain)
{
    numberOfDofMans = 2;
    geometryFlag = 0;
    this->eccS = 0.;
    this->eccT = 0.;
    minLength = 1.e-20;
    couplingFlag = 0;
 
}
 
Lattice3d :: ~Lattice3d()
{}
 
 
void
Lattice3d :: computeBmatrixAt(GaussPoint *aGaussPoint, FloatMatrix &answer, int li, int ui)
// Returns the strain matrix of the receiver.
{
    if ( geometryFlag == 0 ) {
        computeGeometryProperties();
    }
 
    //Assemble Bmatrix (used to compute strains and rotations}
    answer.resize(6, 12);
    answer.zero();
 
    //Normal displacement jump in x-direction
    //First node
    answer.at(1, 1) = -1.;
    answer.at(1, 2) = 0.;
    answer.at(1, 3) = 0.;
    answer.at(1, 4) = 0.;
    answer.at(1, 5) = -this->eccT;
    answer.at(1, 6) = this->eccS;
    //Second node
    answer.at(1, 7) = 1.;
    answer.at(1, 8) = 0.;
    answer.at(1, 9) = 0.;
    answer.at(1, 10) = 0.;
    answer.at(1, 11) = this->eccT;
    answer.at(1, 12) = -this->eccS;
 
    //Shear displacement jump in y-plane
    //first node
    answer.at(2, 1) = 0.;
    answer.at(2, 2) = -1.;
    answer.at(2, 3) =  0.;
    answer.at(2, 4) = this->eccT;
    answer.at(2, 5) = 0;
    answer.at(2, 6) = -this->length / 2.;
    //Second node
    answer.at(2, 7) = 0.;
    answer.at(2, 8) = 1.;
    answer.at(2, 9) =  0.;
    answer.at(2, 10) = -this->eccT;
    answer.at(2, 11) = 0;
    answer.at(2, 12) = -this->length / 2.;
 
    //Shear displacement jump in z-plane
    //first node
    answer.at(3, 1) = 0.;
    answer.at(3, 2) = 0.;
    answer.at(3, 3) = -1.;
    answer.at(3, 4) = -this->eccS;
    answer.at(3, 5) = this->length / 2.;
    answer.at(3, 6) = 0.;
    //Second node
    answer.at(3, 7) = 0.;
    answer.at(3, 8) = 0.;
    answer.at(3, 9) =  1.;
    answer.at(3, 10) = this->eccS;
    answer.at(3, 11) = this->length / 2.;
    answer.at(3, 12) = 0.;
 
    //Rotation around x-axis
    //First node
    answer.at(4, 1) = 0.;
    answer.at(4, 2) = 0;
    answer.at(4, 3) = 0.;
    answer.at(4, 4) = -sqrt(Ip / this->area);
    answer.at(4, 5) = 0.;
    answer.at(4, 6) = 0.;
    //Second node
    answer.at(4, 7) = 0.;
    answer.at(4, 8) = 0.;
    answer.at(4, 9) = 0.;
    answer.at(4, 10) = sqrt(Ip / this->area);
    answer.at(4, 11) = 0.;
    answer.at(4, 12) = 0.;
 
    //Rotation around y-axis
    //First node
    answer.at(5, 1) = 0.;
    answer.at(5, 2) = 0.;
    answer.at(5, 3) = 0.;
    answer.at(5, 4) = 0.;
    answer.at(5, 5) = -sqrt(I1 / this->area);
    answer.at(5, 6) = 0.;
    //Second node
    answer.at(5, 7) = 0.;
    answer.at(5, 8) = 0.;
    answer.at(5, 9) =  0.;
    answer.at(5, 10) = 0.;
    answer.at(5, 11) = sqrt(I1 / this->area);
    answer.at(5, 12) = 0.;
 
    //Rotation around z-axis
    //First node
    answer.at(6, 1) = 0.;
    answer.at(6, 2) = 0.;
    answer.at(6, 3) = 0.;
    answer.at(6, 4) = 0.;
    answer.at(6, 5) = 0.;
    answer.at(6, 6) = -sqrt(I2 / this->area);
    //Second node
    answer.at(6, 7) = 0.;
    answer.at(6, 8) = 0.;
    answer.at(6, 9) =  0.;
    answer.at(6, 10) = 0.;
    answer.at(6, 11) = 0.;
    answer.at(6, 12) = sqrt(I2 / this->area);
 
    answer.times(1. / this->length);
 
    return;
}
 
void
Lattice3d :: giveGPCoordinates(FloatArray &coords)
{
    if ( geometryFlag == 0 ) {
        computeGeometryProperties();
    }
    coords.resize(3);
    coords = this->globalCentroid;
    return;
}
 
double
Lattice3d :: giveLength()
{
    if ( geometryFlag == 0 ) {
        computeGeometryProperties();
    }
 
    return this->length;
}
 
 
int
Lattice3d :: giveCrackFlag()
{
    GaussPoint *gp = this->giveDefaultIntegrationRulePtr()->getIntegrationPoint(0);
    LatticeMaterialStatus *status = static_cast< LatticeMaterialStatus * >( gp->giveMaterialStatus() );
    int crackFlag = 0;
    crackFlag = status->giveCrackFlag();
 
    return crackFlag;
}
 
 
double
Lattice3d :: giveCrackWidth()
{
    GaussPoint *gp = this->giveDefaultIntegrationRulePtr()->getIntegrationPoint(0);
    LatticeMaterialStatus *status = static_cast< LatticeMaterialStatus * >( gp->giveMaterialStatus() );
    double crackWidth = 0;
    crackWidth = status->giveCrackWidth();
 
    return crackWidth;
}
 
void
Lattice3d :: givePlasticStrain(FloatArray &plasticStrain)
{
    GaussPoint *gp = this->giveDefaultIntegrationRulePtr()->getIntegrationPoint(0);
    LatticeMaterialStatus *status = static_cast< LatticeMaterialStatus * >( this->giveMaterial()->giveStatus(gp) );
    plasticStrain = status->givePlasticLatticeStrain();
    return;
}
 
void
Lattice3d :: giveOldPlasticStrain(FloatArray &plasticStrain)
{
    GaussPoint *gp = this->giveDefaultIntegrationRulePtr()->getIntegrationPoint(0);
    LatticeMaterialStatus *status = static_cast< LatticeMaterialStatus * >( this->giveMaterial()->giveStatus(gp) );
    plasticStrain = status->giveOldPlasticLatticeStrain();
    return;
}
 
void
Lattice3d :: computeConstitutiveMatrixAt(FloatMatrix &answer, MatResponseMode rMode, GaussPoint *gp, TimeStep *tStep)
{
    answer = static_cast< LatticeCrossSection * >( this->giveCrossSection() )->give3dStiffnessMatrix(rMode, gp, tStep);
}
 
void
Lattice3d :: computeStressVector(FloatArray &answer, const FloatArray &strain, GaussPoint *gp, TimeStep *tStep)
{
    answer = static_cast< LatticeCrossSection * >( this->giveCrossSection() )->giveLatticeStress3d(strain, gp, tStep);
}
 
void
Lattice3d :: computeStiffnessMatrix(FloatMatrix &answer, MatResponseMode rMode,
                                    TimeStep *tStep)
// Computes numerically the stiffness matrix of the receiver.
{
    FloatMatrix d, bi, bj, bjt, dbj, dij;
 
    answer.resize(12, 12);
    answer.zero();
    this->computeBmatrixAt(integrationRulesArray [ 0 ]->getIntegrationPoint(0), bj);
    this->computeConstitutiveMatrixAt(d, rMode, integrationRulesArray [ 0 ]->getIntegrationPoint(0), tStep);
 
    double volume = this->computeVolumeAround(integrationRulesArray [ 0 ]->getIntegrationPoint(0) );
 
    for ( int i = 1; i <= 6; i++ ) {
        d.at(i, i) *= volume;
    }
 
    dbj.beProductOf(d, bj);
    bjt.beTranspositionOf(bj);
    answer.beProductOf(bjt, dbj);
 
    return;
}
 
void Lattice3d :: computeGaussPoints()
// Sets up the array of Gauss Points of the receiver.
{
    integrationRulesArray.resize(1);
    integrationRulesArray [ 0 ].reset(new GaussIntegrationRule(1, this, 1, 3) );
    integrationRulesArray [ 0 ]->SetUpPointsOnLine(1, _3dLattice);
}
 
 
 
double Lattice3d :: giveArea() {
    if ( geometryFlag == 0 ) {
        computeGeometryProperties();
    }
 
    return this->area;
}
 
 
bool
Lattice3d :: computeGtoLRotationMatrix(FloatMatrix &answer)
{
    FloatMatrix lcs;
    int i, j;
 
    answer.resize(12, 12);
    answer.zero();
 
    this->giveLocalCoordinateSystem(lcs);
    for ( i = 1; i <= 3; i++ ) {
        for ( j = 1; j <= 3; j++ ) {
            answer.at(i, j) = lcs.at(i, j);
            answer.at(i + 3, j + 3) = lcs.at(i, j);
            answer.at(i + 6, j + 6) = lcs.at(i, j);
            answer.at(i + 9, j + 9) = lcs.at(i, j);
        }
    }
 
    return 1;
}
 
 
double
Lattice3d :: giveNormalStress()
{
    GaussPoint *gp = this->giveDefaultIntegrationRulePtr()->getIntegrationPoint(0);
    LatticeMaterialStatus *status = static_cast< LatticeMaterialStatus * >( gp->giveMaterialStatus() );
    double normalStress = 0;
    normalStress = status->giveNormalLatticeStress();
 
    return normalStress;
}
 
 
int
Lattice3d :: giveLocalCoordinateSystem(FloatMatrix &answer)
{
    if ( geometryFlag == 0 ) {
        computeGeometryProperties();
    }
 
    answer = this->localCoordinateSystem;
 
    return 1;
}
 
 
double
Lattice3d :: computeVolumeAround(GaussPoint *aGaussPoint)
{
    if ( geometryFlag == 0 ) {
        computeGeometryProperties();
    }
 
    return this->area * this->length;
}
 
void
Lattice3d :: giveDofManDofIDMask(int inode, IntArray &answer) const
{
    answer = {
        D_u, D_v, D_w, R_u, R_v, R_w
    };
}
 
void
Lattice3d :: initializeFrom(InputRecord &ir, int priority)
{
    ParameterManager &ppm = this->giveDomain()->elementPPM;
    LatticeStructuralElement :: initializeFrom(ir, priority);
 
    PM_UPDATE_PARAMETER(minLength, ppm, ir, this->number, IPK_Lattice3d_mlength, priority);
    PM_UPDATE_PARAMETER(polygonCoords, ppm, ir, this->number, IPK_Lattice3d_polycoords, priority);
    PM_UPDATE_PARAMETER(couplingFlag, ppm, ir, this->number, IPK_Lattice3d_couplingflag, priority);
    PM_UPDATE_PARAMETER(couplingNumbers, ppm, ir, this->number, IPK_Lattice3d_couplingnumber, priority);
    PM_UPDATE_PARAMETER(pressures, ppm, ir, this->number, IPK_Lattice3d_pressures, priority);
}
 
void
Lattice3d :: postInitialize()
{
    this->LatticeStructuralElement :: postInitialize();
    numberOfPolygonVertices = (int) (polygonCoords.giveSize() / 3.);
}
 
int
Lattice3d :: computeGlobalCoordinates(FloatArray &answer, const FloatArray &lcoords)
{
    if ( geometryFlag == 0 ) {
        computeGeometryProperties();
    }
 
    answer.resize(3);
    answer = this->globalCentroid;
 
    return 1;
}
 
 
void
Lattice3d :: computeGeometryProperties()
{
    //coordinates of the two nodes
    Node *nodeA, *nodeB;
    FloatArray coordsA(3), coordsB(3);
 
    nodeA  = this->giveNode(1);
    nodeB  = this->giveNode(2);
 
    for ( int i = 0; i < 3; i++ ) {
        coordsA.at(i + 1) =  nodeA->giveCoordinate(i + 1);
        coordsB.at(i + 1) =  nodeB->giveCoordinate(i + 1);
    }
 
    //Construct an initial temporary local coordinate system
    FloatArray s(3), t(3);
 
    //Calculate normal vector
    this->normal.resize(3);
    for ( int i = 0; i < 3; i++ ) {
        this->normal.at(i + 1) = coordsB.at(i + 1) - coordsA.at(i + 1);
    }
 
    this->length  = sqrt(pow(normal.at(1), 2.) + pow(normal.at(2), 2.) + pow(normal.at(3), 2.) );
 
    // Compute midpoint
    this->midPoint.resize(3);
    for ( int i = 0; i < 3; i++ ) {
        this->midPoint.at(i + 1) = 0.5 * ( coordsB.at(i + 1) + coordsA.at(i + 1) );
    }
 
    for ( int i = 0; i < 3; i++ ) {
        this->normal.at(i + 1) /= length;
    }
 
    computeCrossSectionProperties();
 
    this->geometryFlag = 1;
 
    return;
}
 
 
void
Lattice3d :: computeLumpedMassMatrix(FloatMatrix &answer, TimeStep *tStep)
// Returns the lumped mass matrix of the receiver. This expression is
// valid in both local and global axes.
{
    GaussPoint *gp = integrationRulesArray [ 0 ]->getIntegrationPoint(0);
    double density = static_cast< LatticeCrossSection * >( this->giveCrossSection() )->give('d', gp);
    double halfMass = density * computeVolumeAround(gp) / 2.;
    answer.resize(12, 12);
    answer.zero();
    answer.at(1, 1) = answer.at(2, 2) = answer.at(3, 3) = halfMass;
    answer.at(7, 7) = answer.at(8, 8) = answer.at(9, 9) = halfMass;
}
 
 
  
void
Lattice3d :: computeCrossSectionProperties() {
    if ( this->numberOfPolygonVertices < 3 ) {
        printf("Too small number of polygon vertices\n");
        return;
    }
 
    //Construct two perpendicular axis so that n is normal to the plane which they create
    //Check, if one of the components of the normal-direction is zero
    FloatArray s(3), t(3);
    if ( this->normal.at(1) == 0 ) {
        s.at(1) = 0.;
        s.at(2) = this->normal.at(3);
        s.at(3) = -this->normal.at(2);
    } else if ( this->normal.at(2) == 0 ) {
        s.at(1) = this->normal.at(3);
        s.at(2) = 0.;
        s.at(3) = -this->normal.at(1);
    } else {
        s.at(1) = this->normal.at(2);
        s.at(2) = -this->normal.at(1);
        s.at(3) = 0.;
    }
 
    s.normalize();
 
    t.beVectorProductOf(this->normal, s);
    t.normalize();
 
    //Set up rotation matrix
    FloatMatrix lcs(3, 3);
 
    for ( int i = 1; i <= 3; i++ ) {
        lcs.at(1, i) = this->normal.at(i);
        lcs.at(2, i) = s.at(i);
        lcs.at(3, i) = t.at(i);
    }
 
 
    //Calculate the local coordinates of the polygon vertices
    FloatArray help(3), test(3);
    FloatArray lpc(3 * numberOfPolygonVertices);
    for ( int k = 0; k < numberOfPolygonVertices; k++ ) {
        for ( int n = 0; n < 3; n++ ) {
            help(n) = polygonCoords(3 * k + n);
        }
 
        test.beProductOf(lcs, help);
        for ( int n = 0; n < 3; n++ ) {
            lpc(3 * k + n) = test(n);
        }
    }
 
    this->area = 0.;
 
    for ( int k = 0; k < numberOfPolygonVertices; k++ ) {
        if ( k < numberOfPolygonVertices - 1 ) {
            this->area += lpc(3 * k + 1) * lpc(3 * ( k + 1 ) + 2) - lpc(3 * ( k + 1 ) + 1) * lpc(3 * k + 2);
        } else {   //Back to zero for n+1
            this->area += lpc(3 * k + 1) * lpc(2) - lpc(1) * lpc(3 * k + 2);
        }
    }
 
    this->area *= 0.5;
 
    FloatArray tempCoords(3 * numberOfPolygonVertices);
    if ( this->area < 0 ) { //Set area to a positive value and rearrange the coordinate entries
        this->area *= -1.;
 
        for ( int k = 0; k < numberOfPolygonVertices; k++ ) {
            for ( int m = 0; m < 3; m++ ) {
                tempCoords.at(3 * k + m + 1) = polygonCoords.at(3 * ( numberOfPolygonVertices - k - 1 ) + m + 1);
            }
        }
 
        polygonCoords = tempCoords;
 
        // Calculate again local co-ordinate system for different order
        for ( int k = 0; k < numberOfPolygonVertices; k++ ) {
            for ( int n = 0; n < 3; n++ ) {
                help(n) = polygonCoords(3 * k + n);
            }
 
            test.beProductOf(lcs, help);
            for ( int n = 0; n < 3; n++ ) {
                lpc(3 * k + n) = test(n);
            }
        }
    }
 
    if ( this->area < pow(minLength, 2.) ) {
        this->area = pow(minLength, 2.);
    }
 
    //Calculate centroids
    centroid.resize(3);
    for ( int k = 0; k < numberOfPolygonVertices; k++ ) {
        if ( k < numberOfPolygonVertices - 1 ) {
            centroid.at(2) += ( lpc(3 * k + 1) + lpc(3 * ( k + 1 ) + 1) ) * ( lpc(3 * k + 1) * lpc(3 * ( k + 1 ) + 2) - lpc(3 * ( k + 1 ) + 1) * lpc(3 * k + 2) );
            centroid.at(3) += ( lpc(3 * k + 2) + lpc(3 * ( k + 1 ) + 2) ) * ( lpc(3 * k + 1) * lpc(3 * ( k + 1 ) + 2) - lpc(3 * ( k + 1 ) + 1) * lpc(3 * k + 2) );
        } else { //Back to zero for n+1
            centroid.at(2) += ( lpc(3 * k + 1) + lpc(1) ) * ( lpc(3 * k + 1) * lpc(2) - lpc(1) * lpc(3 * k + 2) );
            centroid.at(3) += ( lpc(3 * k + 2) + lpc(2) ) * ( lpc(3 * k + 1) * lpc(2) - lpc(1) * lpc(3 * k + 2) );
        }
    }
 
    centroid.times(1. / ( 6. * this->area ) );
 
    centroid.at(1) = lpc.at(1); //The first component of all lpcs should be the same
 
    //Shift coordinates to centroid
    for ( int k = 0; k < numberOfPolygonVertices; k++ ) {
        for ( int l = 0; l < 3; l++ ) {
            lpc(3 * k + l) -= centroid(l);
        }
    }
 
    //Compute second moments of area.
    //This is for the temporary coordinate system
    double Ixx = 0.;
    double Iyy = 0.;
    double Ixy = 0.;
    double a;
 
    for ( int k = 0; k < numberOfPolygonVertices; k++ ) {
        if ( k < numberOfPolygonVertices - 1 ) {
            a = lpc(3 * k + 1) * lpc(3 * ( k + 1 ) + 2) - lpc(3 * ( k + 1 ) + 1) * lpc(3 * k + 2);
 
            Ixx += ( ( pow(lpc(3 * k + 2), 2.) + lpc(3 * k + 2) * lpc(3 * ( k + 1 ) + 2) + pow(lpc(3 * ( k + 1 ) + 2), 2.) ) * a ) / 12.;
 
            Iyy += ( ( pow(lpc(3 * k + 1), 2.) + lpc(3 * k + 1) * lpc(3 * ( k + 1 ) + 1) + pow(lpc(3 * ( k + 1 ) + 1), 2.) ) * a ) / 12.;
 
            Ixy += ( ( lpc(3 * k + 1) * lpc(3 * ( k + 1 ) + 2) + 2. * lpc(3 * k + 1) * lpc(3 * k + 2) +
                       2 * lpc(3 * ( k + 1 ) + 1) * lpc(3 * ( k + 1 ) + 2) + lpc(3 * ( k + 1 ) + 1) * lpc(3 * k + 2) ) * a ) / 24.;
        } else {   //Back to zero for n+1
            a = lpc(3 * k + 1) * lpc(2) - lpc(1) * lpc(3 * k + 2);
 
            Ixx += ( ( pow(lpc(3 * k + 2), 2.) + lpc(3 * k + 2) * lpc(2) + pow(lpc(2), 2.) ) * a ) / 12.;
 
            Iyy += ( ( pow(lpc(3 * k + 1), 2.) + lpc(3 * k + 1) * lpc(1) + pow(lpc(1), 2.) ) * a ) / 12.;
 
            Ixy += ( ( lpc(3 * k + 1) * lpc(2) + 2. * lpc(3 * k + 1) * lpc(3 * k + 2) +
                       2 * lpc(1) * lpc(2) + lpc(1) * lpc(3 * k + 2) ) * a ) / 24.;
        }
    }
 
    //Compute main axis of the cross-section
    double angleChange = 0.;
    double sum = fabs(Ixx + Iyy);
    double pi = 3.14159265;
    if ( ( fabs(Ixx - Iyy) / sum > 1.e-6 ) && fabs(Ixy) / sum > 1.e-6 ) {
        angleChange = 0.5 * atan(-2 * Ixy / ( Ixx - Iyy ) );
    } else if ( ( fabs(Ixx - Iyy) / sum < 1.e-6 ) && fabs(Ixy) / sum > 1.e-6 ) {
        angleChange = pi / 4.;
    }
 
    if ( Iyy > Ixx ) {
        angleChange = angleChange + pi / 2.;
    }
 
    //Moment of inertias saved in the element
 
    this->I1 = ( Ixx + Iyy ) / 2. + sqrt(pow( ( Ixx - Iyy ) / 2., 2. ) + pow(Ixy, 2.) );
    this->I2 = ( Ixx + Iyy ) / 2. - sqrt(pow( ( Ixx - Iyy ) / 2., 2. ) + pow(Ixy, 2.) );
 
    this->Ip = I1 + I2;
 
    //Rotation around normal axis by angleChange
 
    FloatMatrix rotationChange(3, 3);
    rotationChange.zero();
 
    rotationChange.at(1, 1) = 1.;
    rotationChange.at(2, 2) = cos(angleChange);
    rotationChange.at(2, 3) = -sin(angleChange);
 
    rotationChange.at(3, 2) = sin(angleChange);
    rotationChange.at(3, 3) = cos(angleChange);
 
    this->localCoordinateSystem.beProductOf(rotationChange, lcs);
 
    //Calculate the polygon vertices in the new coordinate system
    for ( int k = 0; k < numberOfPolygonVertices; k++ ) {
        for ( int n = 0; n < 3; n++ ) {
            help(n) = polygonCoords(3 * k + n);
        }
 
        test.beProductOf(this->localCoordinateSystem, help);
        for ( int n = 0; n < 3; n++ ) {
            lpc(3 * k + n) = test(n);
        }
    }
 
    //Calculate centroid again in local coordinate system
    centroid.zero();
    for ( int k = 0; k < numberOfPolygonVertices; k++ ) {
        if ( k < numberOfPolygonVertices - 1 ) {
            centroid.at(2) += ( lpc(3 * k + 1) + lpc(3 * ( k + 1 ) + 1) ) * ( lpc(3 * k + 1) * lpc(3 * ( k + 1 ) + 2) - lpc(3 * ( k + 1 ) + 1) * lpc(3 * k + 2) );
            centroid.at(3) += ( lpc(3 * k + 2) + lpc(3 * ( k + 1 ) + 2) ) * ( lpc(3 * k + 1) * lpc(3 * ( k + 1 ) + 2) - lpc(3 * ( k + 1 ) + 1) * lpc(3 * k + 2) );
        } else {   //Back to zero for n+1
            centroid.at(2) += ( lpc(3 * k + 1) + lpc(1) ) * ( lpc(3 * k + 1) * lpc(2) - lpc(1) * lpc(3 * k + 2) );
            centroid.at(3) += ( lpc(3 * k + 2) + lpc(2) ) * ( lpc(3 * k + 1) * lpc(2) - lpc(1) * lpc(3 * k + 2) );
        }
    }
 
    centroid.times(1. / ( 6. * this->area ) );
 
    centroid.at(1) = lpc.at(1); //The first component of all lpcs should be the same
 
    FloatArray midPointLocal(3);
    midPointLocal.beProductOf(this->localCoordinateSystem, midPoint);
 
    //eccentricities stored in the element
    this->eccS = centroid.at(2) - midPointLocal.at(2);
    this->eccT = centroid.at(3) - midPointLocal.at(3);
 
    FloatMatrix transposeLCS;
    transposeLCS.beTranspositionOf(this->localCoordinateSystem);
 
    this->globalCentroid.beProductOf(transposeLCS, centroid);
 
    return;
}
 
 
void
Lattice3d :: saveContext(DataStream &stream, ContextMode mode)
{
    LatticeStructuralElement :: saveContext(stream, mode);
 
    contextIOResultType iores;
 
    if ( ( mode & CM_Definition ) ) {
        if ( ( iores = polygonCoords.storeYourself(stream) ) != CIO_OK ) {
            THROW_CIOERR(iores);
        }
 
        if ( !stream.write(couplingFlag) ) {
            THROW_CIOERR(CIO_IOERR);
        }
 
        if ( ( iores = couplingNumbers.storeYourself(stream) ) != CIO_OK ) {
            THROW_CIOERR(iores);
        }
    }
}
 
 
void
Lattice3d :: restoreContext(DataStream &stream, ContextMode mode)
{
    LatticeStructuralElement :: restoreContext(stream, mode);
 
    contextIOResultType iores;
 
    if ( mode & CM_Definition ) {
        if ( ( iores = this->polygonCoords.restoreYourself(stream) ) != CIO_OK ) {
            THROW_CIOERR(iores);
        }
 
        if ( !stream.read(this->couplingFlag) ) {
            THROW_CIOERR(CIO_IOERR);
        }
 
        if ( ( iores = this->couplingNumbers.restoreYourself(stream) ) != CIO_OK ) {
            THROW_CIOERR(iores);
        }
    }
}
 
#ifdef __OOFEG
 
void
Lattice3d :: drawYourself(oofegGraphicContext &gc, TimeStep *tStep)
{
    OGC_PlotModeType mode = gc.giveIntVarPlotMode();
 
    if ( mode == OGC_rawGeometry ) {
        this->drawRawGeometry(gc, tStep);
        this->drawRawCrossSections(gc, tStep);
    } else if ( mode == OGC_deformedGeometry ) {
        this->drawDeformedGeometry(gc, tStep, DisplacementVector);
    } else if ( mode == OGC_eigenVectorGeometry ) {
        this->drawDeformedGeometry(gc, tStep, EigenVector);
    } else if ( mode == OGC_scalarPlot ) {
        this->drawScalar(gc, tStep);
    } else if ( mode == OGC_elemSpecial ) {
        this->drawSpecial(gc, tStep);
    } else {
        OOFEM_ERROR("unsupported mode");
    }
}
 
 
 
 
void Lattice3d :: drawRawGeometry(oofegGraphicContext &gc, TimeStep *tStep)
{
    GraphicObj *go;
 
    WCRec p [ 2 ]; /* points */
    if ( !gc.testElementGraphicActivity(this) ) {
        return;
    }
 
    EASValsSetLineWidth(OOFEG_RAW_GEOMETRY_WIDTH);
    EASValsSetColor(gc.getElementColor() );
    EASValsSetLayer(OOFEG_RAW_GEOMETRY_LAYER);
 
    p [ 0 ].x = ( FPNum ) this->giveNode(1)->giveCoordinate(1);
    p [ 0 ].y = ( FPNum ) this->giveNode(1)->giveCoordinate(2);
    p [ 0 ].z = ( FPNum ) this->giveNode(1)->giveCoordinate(3);
    p [ 1 ].x = ( FPNum ) this->giveNode(2)->giveCoordinate(1);
    p [ 1 ].y = ( FPNum ) this->giveNode(2)->giveCoordinate(2);
    p [ 1 ].z = ( FPNum ) this->giveNode(2)->giveCoordinate(3);
 
    go = CreateLine3D(p);
    EGWithMaskChangeAttributes(WIDTH_MASK | COLOR_MASK | LAYER_MASK, go);
    EGAttachObject(go, ( EObjectP ) this);
    EMAddGraphicsToModel(ESIModel(), go);
}
 
 
void
Lattice3d :: drawRawCrossSections(oofegGraphicContext &gc, TimeStep *tStep)
{
    GraphicObj *go;
 
    //Create as many points as we have polygon vertices
    numberOfPolygonVertices = this->polygonCoords.giveSize() / 3.;
    WCRec p [ numberOfPolygonVertices ]; /* poin */
 
    if ( !gc.testElementGraphicActivity(this) ) {
        return;
    }
 
    EASValsSetLineWidth(OOFEG_RAW_GEOMETRY_WIDTH);
 
    EASValsSetLayer(OOFEG_RAW_CROSSSECTION_LAYER);
 
    for ( int i = 0; i < numberOfPolygonVertices; i++ ) {
        p [ i ].x = ( FPNum ) polygonCoords(3 * i);
        p [ i ].y = ( FPNum ) polygonCoords(3 * i + 1);
        p [ i ].z = ( FPNum ) polygonCoords(3 * i + 2);
    }
 
 
    WCRec pTemp [ 2 ]; /* points */
    for ( int i = 0; i < numberOfPolygonVertices; i++ ) {
        if ( i < numberOfPolygonVertices - 1 ) {
            pTemp [ 0 ] = p [ i ];
            pTemp [ 1 ] = p [ i + 1 ];
        } else {
            pTemp [ 0 ] = p [ i ];
            pTemp [ 1 ] = p [ 0 ];
        }
 
        go = CreateLine3D(pTemp);
        EGWithMaskChangeAttributes(WIDTH_MASK | COLOR_MASK | LAYER_MASK, go);
        EGAttachObject(go, ( EObjectP ) this);
        EMAddGraphicsToModel(ESIModel(), go);
    }
}
 
 
 
void Lattice3d :: drawDeformedGeometry(oofegGraphicContext &gc, TimeStep *tStep, UnknownType type)
{
    GraphicObj *go;
 
    if ( !gc.testElementGraphicActivity(this) ) {
        return;
    }
 
    double defScale = gc.getDefScale();
 
    WCRec p [ 2 ]; /* points */
 
    EASValsSetLineWidth(OOFEG_DEFORMED_GEOMETRY_WIDTH);
    EASValsSetColor(gc.getDeformedElementColor() );
    EASValsSetLayer(OOFEG_DEFORMED_GEOMETRY_LAYER);
 
    p [ 0 ].x = ( FPNum ) this->giveNode(1)->giveUpdatedCoordinate(1, tStep, defScale);
    p [ 0 ].y = ( FPNum ) this->giveNode(1)->giveUpdatedCoordinate(2, tStep, defScale);
    p [ 0 ].z = ( FPNum ) this->giveNode(1)->giveUpdatedCoordinate(3, tStep, defScale);
 
    p [ 1 ].x = ( FPNum ) this->giveNode(2)->giveUpdatedCoordinate(1, tStep, defScale);
    p [ 1 ].y = ( FPNum ) this->giveNode(2)->giveUpdatedCoordinate(2, tStep, defScale);
    p [ 1 ].z = ( FPNum ) this->giveNode(2)->giveUpdatedCoordinate(3, tStep, defScale);
 
    go = CreateLine3D(p);
    EGWithMaskChangeAttributes(WIDTH_MASK | COLOR_MASK | LAYER_MASK, go);
    EMAddGraphicsToModel(ESIModel(), go);
}
 
#endif
} // end namespace oofem