libeam3dnl2.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 "sm/Elements/Beams/libeam3dnl2.h"
#include "sm/CrossSections/structuralcrosssection.h"
#include "sm/Materials/structuralms.h"
#include "node.h"
#include "material.h"
#include "gausspoint.h"
#include "gaussintegrationrule.h"
#include "floatmatrix.h"
#include "intarray.h"
#include "floatarray.h"
#include "mathfem.h"
#include "timestep.h"
#include "contextioerr.h"
#include "classfactory.h"
#include "parametermanager.h"
#include "paramkey.h"
 
#ifdef __OOFEG
 #include "oofeggraphiccontext.h"
#endif
 
namespace oofem {
REGISTER_Element(LIBeam3dNL2);
ParamKey LIBeam3dNL2::IPK_LIBeam3dNL2_refnode("refnode");
 
LIBeam3dNL2::LIBeam3dNL2(int n, Domain *aDomain) : NLStructuralElement(n, aDomain), q(4), tempQ(4)   //, kappa (3)
{
    numberOfDofMans    = 2;
    l0                 = 0.;
    tempQCounter       = 0;
    referenceNode      = 0;
    // init kappa vector at centre
    // kappa.zero();
}
 
 
void
LIBeam3dNL2::computeSMtrx(FloatMatrix &answer, FloatArray &vec)
{
    if ( vec.giveSize() != 3 ) {
        OOFEM_ERROR("vec param size mismatch");
    }
 
    answer.resize(3, 3);
 
    answer.at(1, 1) = answer.at(2, 2) = answer.at(3, 3) = 0.;
    answer.at(1, 2) = -vec.at(3);
    answer.at(1, 3) =  vec.at(2);
    answer.at(2, 1) =  vec.at(3);
    answer.at(2, 3) = -vec.at(1);
    answer.at(3, 1) = -vec.at(2);
    answer.at(3, 2) =  vec.at(1);
}
 
 
void
LIBeam3dNL2::computeRotMtrx(FloatMatrix &answer, FloatArray &psi)
{
    FloatMatrix S(3, 3), SS(3, 3);
    double psiSize;
 
    if ( psi.giveSize() != 3 ) {
        OOFEM_ERROR("psi param size mismatch");
    }
 
    answer.resize(3, 3);
    answer.zero();
 
    psiSize = psi.computeNorm();
    answer.at(1, 1) = answer.at(2, 2) = answer.at(3, 3) = 1.;
 
    if ( psiSize <= 1.e-40 ) {
        return;
    }
 
    this->computeSMtrx(S, psi);
    SS.beProductOf(S, S);
    S.times(sin(psiSize) / psiSize);
    SS.times( ( 1. - cos(psiSize) ) / ( psiSize * psiSize ) );
 
    answer.add(S);
    answer.add(SS);
}
 
 
void
LIBeam3dNL2::updateTempQuaternion(TimeStep *tStep)
{
    // test if not previously updated temporary quaternion
    if ( tStep->giveSolutionStateCounter() != tempQCounter ) {
        // update temporary quaternion
        FloatArray u, centreSpin(3), q2(4);
        double centreSpinSize;
 
        // ask element's displacement increments
        this->computeVectorOf(VM_Incremental, tStep, u);
 
        // interpolate spin at the centre
        centreSpin.at(1) = 0.5 * ( u.at(4) + u.at(10) );
        centreSpin.at(2) = 0.5 * ( u.at(5) + u.at(11) );
        centreSpin.at(3) = 0.5 * ( u.at(6) + u.at(12) );
 
        centreSpinSize = centreSpin.computeNorm();
        if ( centreSpinSize > 1.e-30 ) {
            centreSpin.normalize();
            q2.at(1) = sin(centreSpinSize / 2.) * centreSpin.at(1);
            q2.at(2) = sin(centreSpinSize / 2.) * centreSpin.at(2);
            q2.at(3) = sin(centreSpinSize / 2.) * centreSpin.at(3);
            q2.at(4) = cos(centreSpinSize / 2.);
 
            // update temporary quaternion at the center
            tempQ.at(1) = q.at(4) * q2.at(1) + q2.at(4) * q.at(1) - ( q.at(2) * q2.at(3) - q.at(3) * q2.at(2) );
            tempQ.at(2) = q.at(4) * q2.at(2) + q2.at(4) * q.at(2) - ( q.at(3) * q2.at(1) - q.at(1) * q2.at(3) );
            tempQ.at(3) = q.at(4) * q2.at(3) + q2.at(4) * q.at(3) - ( q.at(1) * q2.at(2) - q.at(2) * q2.at(1) );
            tempQ.at(4) = q.at(4) * q2.at(4) - ( q.at(1) * q2.at(1) + q.at(2) * q2.at(2) + q.at(3) * q2.at(3) );
        } else {
            tempQ = q;
        }
 
        // remember timestamp
        tempQCounter = tStep->giveSolutionStateCounter();
    }
}
 
 
void
LIBeam3dNL2::computeRotMtrxFromQuaternion(FloatMatrix &answer, FloatArray &q)
{
    answer.resize(3, 3);
 
    answer.at(1, 1) = q.at(4) * q.at(4) + q.at(1) * q.at(1) - 0.5;
    answer.at(1, 2) = q.at(1) * q.at(2) - q.at(3) * q.at(4);
    answer.at(1, 3) = q.at(1) * q.at(3) + q.at(2) * q.at(4);
 
    answer.at(2, 1) = q.at(2) * q.at(1) + q.at(3) * q.at(4);
    answer.at(2, 2) = q.at(4) * q.at(4) + q.at(2) * q.at(2) - 0.5;
    answer.at(2, 3) = q.at(2) * q.at(3) - q.at(1) * q.at(4);
 
    answer.at(3, 1) = q.at(3) * q.at(1) - q.at(2) * q.at(4);
    answer.at(3, 2) = q.at(3) * q.at(2) + q.at(1) * q.at(4);
    answer.at(3, 3) = q.at(4) * q.at(4) + q.at(3) * q.at(3) - 0.5;
 
    answer.times(2.);
}
 
 
void
LIBeam3dNL2::computeQuaternionFromRotMtrx(FloatArray &answer, FloatMatrix &R)
{
    // Spurrier's algorithm
 
    int i, ii;
    double a, trR;
 
    answer.resize(4);
 
    trR = R.at(1, 1) + R.at(2, 2) + R.at(3, 3);
    a = trR;
    ii = 0;
    for ( i = 1; i <= 3; i++ ) {
        if ( R.at(i, i) > a ) {
            a = R.at(i, i);
            ii = i;
        }
    }
 
    if ( a == trR ) {
        //printf (".");
        answer.at(4) = 0.5 * sqrt(1. + a);
        answer.at(1) = ( R.at(3, 2) - R.at(2, 3) ) / ( 4. * answer.at(4) );
        answer.at(2) = ( R.at(1, 3) - R.at(3, 1) ) / ( 4. * answer.at(4) );
        answer.at(3) = ( R.at(2, 1) - R.at(1, 2) ) / ( 4. * answer.at(4) );
    } else {
        //printf (":");
        int jj, kk;
        if ( ii == 1 ) {
            jj = 2;
            kk = 3;
        } else if ( ii == 2 ) {
            jj = 3;
            kk = 1;
        } else {
            jj = 1;
            kk = 2;
        }
 
        answer.at(ii) = sqrt(0.5 * a + 0.25 * ( 1. - trR ) );
        answer.at(4) = 0.25 * ( R.at(kk, jj) - R.at(jj, kk) ) / answer.at(ii);
        answer.at(jj) = 0.25 * ( R.at(jj, ii) + R.at(ii, jj) ) / answer.at(ii);
        answer.at(kk) = 0.25 * ( R.at(kk, ii) + R.at(ii, kk) ) / answer.at(ii);
    }
}
 
 
void
LIBeam3dNL2::computeStrainVector(FloatArray &answer, GaussPoint *gp, TimeStep *tStep)
{
    FloatArray xd(3), eps(3), curv(3);
    FloatMatrix tempTc;
 
    // update temp triad
    this->updateTempQuaternion(tStep);
    this->computeRotMtrxFromQuaternion(tempTc, this->tempQ);
 
    this->computeXdVector(xd, tStep);
 
    // compute eps_xl, gamma_l2, gamma_l3
    eps.beTProductOf(tempTc, xd);
    eps.times(1. / this->l0);
    eps.at(1) -= 1.0;
 
    // update curvature at midpoint
    this->computeTempCurv(curv, tStep);
 
    answer.resize(6);
    answer.at(1) = eps.at(1); // eps_xl
    answer.at(2) = eps.at(2); // gamma_l2
    answer.at(3) = eps.at(3); // gamma_l3
    answer.at(4) = curv.at(1); // kappa_1
    answer.at(5) = curv.at(2); // kappa_2
    answer.at(6) = curv.at(3); // kappa_3
}
 
 
void
LIBeam3dNL2::computeXMtrx(FloatMatrix &answer, TimeStep *tStep)
{
    FloatArray xd(3);
    FloatMatrix s(3, 3);
 
    this->computeXdVector(xd, tStep);
    this->computeSMtrx(s, xd);
 
    answer.resize(12, 6);
    answer.zero();
 
    for ( int i = 1; i < 4; i++ ) {
        answer.at(i, i)      = -1.0;
        answer.at(i + 6, i)   =  1.0;
        answer.at(i + 3, i + 3) = -1.0;
        answer.at(i + 9, i + 3) =  1.0;
 
        for ( int j = 1; j < 4; j++ ) {
            answer.at(i + 3, j) = answer.at(i + 9, j) = 0.5 * s.at(j, i);
        }
    }
}
 
 
void
LIBeam3dNL2::giveInternalForcesVector(FloatArray &answer, TimeStep *tStep, int useUpdatedGpRecord)
{
    GaussPoint *gp = this->giveDefaultIntegrationRulePtr()->getIntegrationPoint(0);
    FloatArray nm(6), stress, strain;
    FloatMatrix x, tempTc;
    double s1, s2;
 
    // update temp triad
    this->updateTempQuaternion(tStep);
    this->computeRotMtrxFromQuaternion(tempTc, this->tempQ);
 
    if ( useUpdatedGpRecord == 1 ) {
        stress = static_cast< StructuralMaterialStatus * >( gp->giveMaterialStatus() )->giveStressVector();
    } else {
        this->computeStrainVector(strain, gp, tStep);
        this->computeStressVector(stress, strain, gp, tStep);
    }
 
    for ( int i = 1; i <= 3; i++ ) {
        s1 = s2 = 0.0;
        for ( int j = 1; j <= 3; j++ ) {
            s1 += tempTc.at(i, j) * stress.at(j);
            s2 += tempTc.at(i, j) * stress.at(j + 3);
        }
 
        nm.at(i)   = s1;
        nm.at(i + 3) = s2;
    }
 
    this->computeXMtrx(x, tStep);
    answer.beProductOf(x, nm);
}
 
 
void
LIBeam3dNL2::computeXdVector(FloatArray &answer, TimeStep *tStep)
{
    FloatArray u(3);
 
    answer.resize(3);
    // ask element's displacements
    this->computeVectorOf(VM_Total, tStep, u);
 
    answer.at(1) = ( this->giveNode(2)->giveCoordinate(1) + u.at(7) ) -
                   ( this->giveNode(1)->giveCoordinate(1) + u.at(1) );
    answer.at(2) = ( this->giveNode(2)->giveCoordinate(2) + u.at(8) ) -
                   ( this->giveNode(1)->giveCoordinate(2) + u.at(2) );
    answer.at(3) = ( this->giveNode(2)->giveCoordinate(3) + u.at(9) ) -
                   ( this->giveNode(1)->giveCoordinate(3) + u.at(3) );
}
 
 
void
LIBeam3dNL2::computeStiffnessMatrix(FloatMatrix &answer, MatResponseMode rMode, TimeStep *tStep)
{
    double s1, s2;
    FloatMatrix d, x, xt(12, 6), dxt, sn, sm, sxd, y, tempTc;
    FloatArray n(3), m(3), xd(3), stress, strain;
    GaussPoint *gp = this->giveDefaultIntegrationRulePtr()->getIntegrationPoint(0);
 
    answer.clear();
 
    // linear part
 
    this->updateTempQuaternion(tStep);
    this->computeRotMtrxFromQuaternion(tempTc, this->tempQ);
    this->computeXMtrx(x, tStep);
    xt.zero();
    for ( int i = 1; i <= 12; i++ ) {
        for ( int j = 1; j <= 3; j++ ) {
            for ( int k = 1; k <= 3; k++ ) {
                // compute x*Tbar, taking into account sparsity of Tbar
                xt.at(i, j)   += x.at(i, k) * tempTc.at(k, j);
                xt.at(i, j + 3) += x.at(i, k + 3) * tempTc.at(k, j);
            }
        }
    }
 
    this->computeConstitutiveMatrixAt(d, rMode, gp, tStep);
    dxt.beProductTOf(d, xt);
    answer.beProductOf(xt, dxt);
    answer.times(1. / this->l0);
 
    // geometric stiffness ks = ks1+ks2
    // ks1
    this->computeStrainVector(strain, gp, tStep);
    this->computeStressVector(stress, strain, gp, tStep);
 
    for ( int i = 1; i <= 3; i++ ) {
        s1 = s2 = 0.0;
        for ( int j = 1; j <= 3; j++ ) {
            s1 += tempTc.at(i, j) * stress.at(j);
            s2 += tempTc.at(i, j) * stress.at(j + 3);
        }
 
        n.at(i)   = s1;
        m.at(i)   = s2;
    }
 
    this->computeSMtrx(sn, n);
    this->computeSMtrx(sm, m);
 
    for ( int i = 1; i <= 3; i++ ) {
        for ( int j = 1; j <= 3; j++ ) {
            answer.at(i, j + 3)   += sn.at(i, j);
            answer.at(i, j + 9)   += sn.at(i, j);
            answer.at(i + 3, j + 3) += sm.at(i, j);
            answer.at(i + 3, j + 9) += sm.at(i, j);
 
            answer.at(i + 6, j + 3) -= sn.at(i, j);
            answer.at(i + 6, j + 9) -= sn.at(i, j);
            answer.at(i + 9, j + 3) -= sm.at(i, j);
            answer.at(i + 9, j + 9) -= sm.at(i, j);
        }
    }
 
    // ks2
    this->computeXdVector(xd, tStep);
    this->computeSMtrx(sxd, xd);
 
    y.beProductOf(sxd, sn);
    y.times(0.5);
 
    for ( int i = 1; i <= 3; i++ ) {
        for ( int j = 1; j <= 3; j++ ) {
            answer.at(i + 3, j)     -= sn.at(i, j);
            answer.at(i + 3, j + 3)   += y.at(i, j);
            answer.at(i + 3, j + 6)   += sn.at(i, j);
            answer.at(i + 3, j + 9)   += y.at(i, j);
 
            answer.at(i + 9, j)     -= sn.at(i, j);
            answer.at(i + 9, j + 3)   += y.at(i, j);
            answer.at(i + 9, j + 6)   += sn.at(i, j);
            answer.at(i + 9, j + 9)   += y.at(i, j);
        }
    }
}
 
 
void
LIBeam3dNL2::computeGaussPoints()
// Sets up the array of Gauss Points of the receiver.
{
    if ( integrationRulesArray.size() == 0 ) {
        integrationRulesArray.resize(1);
        integrationRulesArray [ 0 ] = std::make_unique< GaussIntegrationRule >(1, this, 1, 2);
        this->giveCrossSection()->setupIntegrationPoints(* integrationRulesArray [ 0 ], 1, this);
    }
}
 
 
void
LIBeam3dNL2::computeConstitutiveMatrixAt(FloatMatrix &answer, MatResponseMode rMode, GaussPoint *gp, TimeStep *tStep)
{
    answer = this->giveStructuralCrossSection()->give3dBeamStiffMtrx(rMode, gp, tStep);
}
 
void
LIBeam3dNL2::computeConstitutiveMatrix_dPdF_At(FloatMatrix &answer, MatResponseMode rMode, GaussPoint *gp, TimeStep *tStep)
{
    OOFEM_ERROR("computeConstitutiveMatrix_dPdF_At Not implemented");
}
 
 
void
LIBeam3dNL2::computeStressVector(FloatArray &answer, const FloatArray &strain, GaussPoint *gp, TimeStep *tStep)
{
    answer = this->giveStructuralCrossSection()->giveGeneralizedStress_Beam3d(strain, gp, tStep);
}
 
 
void
LIBeam3dNL2::initializeFrom(InputRecord &ir, int priority)
{
    // first call parent
    NLStructuralElement::initializeFrom(ir, priority);
    ParameterManager &ppm = domain->elementPPM;
    PM_UPDATE_PARAMETER(referenceNode, ppm, ir, this->number, IPK_LIBeam3dNL2_refnode, priority);
}
 
void
LIBeam3dNL2::postInitialize()
{
    NLStructuralElement::postInitialize();
    ParameterManager &ppm = domain->elementPPM;
    PM_ELEMENT_ERROR_IFNOTSET(ppm, this->number, IPK_LIBeam3dNL2_refnode);
    if ( referenceNode == 0 ) {
        OOFEM_ERROR("wrong reference node specified");
    }
    // compute initial triad at centre - requires nodal coordinates
    FloatMatrix lcs, tc;
    this->giveLocalCoordinateSystem(lcs);
    tc.beTranspositionOf(lcs);
 
    this->computeQuaternionFromRotMtrx(q, tc);
    this->nlGeometry = 0; // element always nonlinear, this is to force ouput in strains and stresses in GP (see structuralms.C)
}
 
double
LIBeam3dNL2::computeLength()
// Returns the original length (l0) of the receiver.
{
    double dx, dy, dz;
    Node *nodeA, *nodeB;
 
    if ( l0 == 0. ) {
        nodeA   = this->giveNode(1);
        nodeB   = this->giveNode(2);
        dx      = nodeB->giveCoordinate(1) - nodeA->giveCoordinate(1);
        dy      = nodeB->giveCoordinate(2) - nodeA->giveCoordinate(2);
        dz      = nodeB->giveCoordinate(3) - nodeA->giveCoordinate(3);
        l0      = sqrt(dx * dx + dy * dy + dz * dz);
    }
 
    return l0;
}
 
 
void
LIBeam3dNL2::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 = this->giveStructuralCrossSection()->give('d', gp);
    double halfMass   = density * this->giveCrossSection()->give(CS_Area, gp) * this->computeLength() / 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
LIBeam3dNL2::computeNmatrixAt(const FloatArray &iLocCoord, FloatMatrix &answer)
// Returns the displacement interpolation matrix {N} of the receiver, eva-
// luated at gp.
{
    double ksi, n1, n2;
 
    ksi = iLocCoord.at(1);
    n1  = ( 1. - ksi ) * 0.5;
    n2  = ( 1. + ksi ) * 0.5;
 
    answer.resize(6, 12);
    answer.zero();
 
    // u
    answer.at(1, 1) = n1;
    answer.at(1, 7) = n2;
    // v
    answer.at(2, 2) = n1;
    answer.at(2, 8) = n2;
    // w
    answer.at(3, 3) = n1;
    answer.at(3, 9) = n2;
    // fi_x
    answer.at(4, 4)  = n1;
    answer.at(4, 10) = n2;
    // fi_y
    answer.at(5, 5)  = n1;
    answer.at(5, 11) = n2;
    // fi_z
    answer.at(6, 6)  = n1;
    answer.at(6, 12) = n2;
}
 
 
double
LIBeam3dNL2::computeVolumeAround(GaussPoint *gp)
// Returns the length of the receiver. This method is valid only if 1
// Gauss point is used.
{
    double weight  = gp->giveWeight();
    return weight * 0.5 * this->computeLength();
}
 
 
void
LIBeam3dNL2::giveDofManDofIDMask(int inode, IntArray &answer) const
{
    answer = { D_u, D_v, D_w, R_u, R_v, R_w };
}
 
int
LIBeam3dNL2::computeGlobalCoordinates(FloatArray &answer, const FloatArray &lcoords)
{
    double ksi, n1, n2;
 
    ksi = lcoords.at(1);
    n1  = ( 1. - ksi ) * 0.5;
    n2  = ( 1. + ksi ) * 0.5;
 
    answer.resize(3);
    answer.at(1) = n1 * this->giveNode(1)->giveCoordinate(1) + n2 * this->giveNode(2)->giveCoordinate(1);
    answer.at(2) = n1 * this->giveNode(1)->giveCoordinate(2) + n2 * this->giveNode(2)->giveCoordinate(2);
    answer.at(3) = n1 * this->giveNode(1)->giveCoordinate(3) + n2 * this->giveNode(2)->giveCoordinate(3);
 
    return 1;
}
 
 
void
LIBeam3dNL2::giveEdgeDofMapping(IntArray &answer, int iEdge) const
{
    /*
     * provides dof mapping of local edge dofs (only nonzero are taken into account)
     * to global element dofs
     */
    if ( iEdge != 1 ) {
        OOFEM_ERROR("wrong edge number");
    }
 
    answer.resize(12);
    for ( int i = 1; i <= 12; i++ ) {
        answer.at(i) = i;
    }
}
 
 
double
LIBeam3dNL2::computeEdgeVolumeAround(GaussPoint *gp, int iEdge)
{
    if ( iEdge != 1 ) { // edge between nodes 1 2
        OOFEM_ERROR("wrong egde number");
    }
 
    double weight  = gp->giveWeight();
    return 0.5 * this->computeLength() * weight;
}
 
 
int
LIBeam3dNL2::giveLocalCoordinateSystem(FloatMatrix &answer)
//
// returns a unit vectors of local coordinate system at element
// stored rowwise (mainly used by some materials with ortho and anisotrophy)
//
{
    FloatArray lx(3), ly(3), lz(3), help(3);
    double length = this->computeLength();
    Node *nodeA, *nodeB, *refNode;
 
    answer.resize(3, 3);
    answer.zero();
    nodeA  = this->giveNode(1);
    nodeB  = this->giveNode(2);
    refNode = this->giveDomain()->giveNode(this->referenceNode);
 
    for ( int i = 1; i <= 3; i++ ) {
        lx.at(i) = ( nodeB->giveCoordinate(i) - nodeA->giveCoordinate(i) ) / length;
        help.at(i) = ( refNode->giveCoordinate(i) - nodeA->giveCoordinate(i) );
    }
 
    lz.beVectorProductOf(lx, help);
    lz.normalize();
    ly.beVectorProductOf(lz, lx);
    ly.normalize();
 
    for ( int i = 1; i <= 3; i++ ) {
        answer.at(1, i) = lx.at(i);
        answer.at(2, i) = ly.at(i);
        answer.at(3, i) = lz.at(i);
    }
 
    return 1;
}
 
 
int
LIBeam3dNL2::computeLoadGToLRotationMtrx(FloatMatrix &answer)
{
    /*
     * Returns transformation matrix from global coordinate system to local
     * element coordinate system for element load vector components.
     * If no transformation is necessary, answer is empty matrix (default);
     *
     * Does not support follower load
     */
 
    FloatMatrix lcs;
 
    answer.resize(6, 6);
    answer.zero();
 
    this->giveLocalCoordinateSystem(lcs);
 
    for ( int i = 1; i <= 3; i++ ) {
        for ( int j = 1; j <= 3; j++ ) {
            answer.at(i, j) = lcs.at(i, j);
            answer.at(3 + i, 3 + j) = lcs.at(i, j);
        }
    }
 
    return 1;
}
 
 
int
LIBeam3dNL2::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)
    //
    answer.clear();
    return 0;
}
 
 
void
LIBeam3dNL2::computeBodyLoadVectorAt(FloatArray &answer, Load *load, TimeStep *tStep, ValueModeType mode)
{
    FloatArray lc(1);
    NLStructuralElement::computeBodyLoadVectorAt(answer, load, tStep, mode);
    answer.times(this->giveCrossSection()->give(CS_Area, lc, this) );
}
 
 
void
LIBeam3dNL2::updateYourself(TimeStep *tStep)
// Updates the receiver at end of step.
{
    NLStructuralElement::updateYourself(tStep);
 
    // update quaternion
    this->updateTempQuaternion(tStep);
    q = tempQ;
 
    // update curvature
    //FloatArray curv;
    //this->computeTempCurv (curv, tStep);
    //kappa = curv;
}
 
void
LIBeam3dNL2::initForNewStep()
// initializes receiver to new time step or can be used
// if current time step must be restarted
{
    NLStructuralElement::initForNewStep();
    tempQ = q;
}
 
 
void
LIBeam3dNL2::computeTempCurv(FloatArray &answer, TimeStep *tStep)
{
    GaussPoint *gp = this->giveDefaultIntegrationRulePtr()->getIntegrationPoint(0);
    FloatArray ui(3), ac(3), PrevEpsilon;
 
    answer.resize(3);
 
    /*
     * // update curvature at midpoint
     * // first, compute Tmid
     * // ask increments
     * this -> computeVectorOf(UnknownMode_Incremental,tStep, ui) ;
     * ac.at(1) = 0.5*(ui.at(10) - ui.at(4));
     * ac.at(2) = 0.5*(ui.at(11) - ui.at(5));
     * ac.at(3) = 0.5*(ui.at(12) - ui.at(6));
     * this->computeSMtrx (sc, ac);
     * sc.times (1./2.);
     * // compute I+sc
     * sc.at(1,1) += 1.0;
     * sc.at(2,2) += 1.0;
     * sc.at(3,3) += 1.0;
     *
     * this->computeRotMtrxFromQuaternion(tc, this->q);
     * tmid.beProductOf (sc, tc);
     *
     * // update curvature at centre
     * ac.at(1) = (ui.at(10) - ui.at(4));
     * ac.at(2) = (ui.at(11) - ui.at(5));
     * ac.at(3) = (ui.at(12) - ui.at(6));
     *
     * answer.beTProductOf (tmid, ac);
     * answer.times (1/this->l0);
     * // ask for previous kappa
     * PrevEpsilon = ((StructuralMaterialStatus*) mat->giveStatus(gp)) -> giveStrainVector ();
     * if (PrevEpsilon.giveSize()) {
     * answer.at(1) += PrevEpsilon.at(4);
     * answer.at(2) += PrevEpsilon.at(5);
     * answer.at(3) += PrevEpsilon.at(6);
     * }
     */
    // update curvature
    // exact procedure due to Simo & Vu Quoc
    FloatMatrix dR, Rn, Ro;
    FloatArray om, omp, acp(3), kapgn1(3);
    double acSize, coeff;
 
    this->computeVectorOf(VM_Incremental, tStep, ui);
 
    ac.at(1) = 0.5 * ( ui.at(10) - ui.at(4) );
    ac.at(2) = 0.5 * ( ui.at(11) - ui.at(5) );
    ac.at(3) = 0.5 * ( ui.at(12) - ui.at(6) );
 
    this->computeRotMtrx(dR, ac);
    this->computeRotMtrxFromQuaternion(Ro, this->q);
    Rn.beProductOf(dR, Ro);
 
    acSize = ac.computeSquaredNorm();
 
    if ( acSize > 1.e-30 ) {
        FloatMatrix h(3, 3);
        ac.normalize();
        om = ac;
        om.times(2. * tan(acSize / 2.) );
 
        coeff = ( 1. - ( acSize / sin(acSize) ) );
        for ( int i = 1; i <= 3; i++ ) {
            for ( int j = 1; j <= 3; j++ ) {
                h.at(i, j) = coeff * ac.at(i) * ac.at(j);
            }
        }
 
        for ( int i = 1; i <= 3; i++ ) {
            h.at(i, i) = 1. - h.at(i, i);
        }
 
        // compute dPsi/ds
        acp.at(1) = ( ui.at(10) - ui.at(4) ) / this->l0;
        acp.at(2) = ( ui.at(11) - ui.at(5) ) / this->l0;
        acp.at(3) = ( ui.at(12) - ui.at(6) ) / this->l0;
 
        omp.beProductOf(h, acp);
        omp.times(2. * tan(acSize / 2.) / acSize);
 
        kapgn1.beVectorProductOf(om, omp);
        kapgn1.times(1. / 2.);
        kapgn1.add(omp);
 
        coeff = 1. / ( 1. + 0.25 * om.computeSquaredNorm() );
        kapgn1.times(coeff);
 
        answer.beTProductOf(Rn, kapgn1);
    }
 
    // ask for previous kappa
    StructuralMaterialStatus *matStat = static_cast< StructuralMaterialStatus * >( gp->giveMaterialStatus() );
    if ( matStat ) {
        PrevEpsilon = matStat->giveStrainVector();
    }
    if ( PrevEpsilon.giveSize() ) {
        answer.at(1) += PrevEpsilon.at(4);
        answer.at(2) += PrevEpsilon.at(5);
        answer.at(3) += PrevEpsilon.at(6);
    }
}
 
 
void
LIBeam3dNL2::saveContext(DataStream &stream, ContextMode mode)
{
    contextIOResultType iores;
    NLStructuralElement::saveContext(stream, mode);
 
    if ( ( iores = q.storeYourself(stream) ) != CIO_OK ) {
        THROW_CIOERR(iores);
    }
}
 
 
void
LIBeam3dNL2::restoreContext(DataStream &stream, ContextMode mode)
{
    contextIOResultType iores;
    NLStructuralElement::restoreContext(stream, mode);
 
    if ( ( iores = q.restoreYourself(stream) ) != CIO_OK ) {
        THROW_CIOERR(iores);
    }
}
 
 
#ifdef __OOFEG
void LIBeam3dNL2::drawRawGeometry(oofegGraphicContext &gc, TimeStep *tStep)
{
    GraphicObj *go;
 
    if ( !gc.testElementGraphicActivity(this) ) {
        return;
    }
 
    //  if (!go) { // create new one
    WCRec p[ 2 ];    /* poin */
    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 LIBeam3dNL2::drawDeformedGeometry(oofegGraphicContext &gc, TimeStep *tStep, UnknownType type)
{
    GraphicObj *go;
 
    if ( !gc.testElementGraphicActivity(this) ) {
        return;
    }
 
    double defScale = gc.getDefScale();
    //  if (!go) { // create new one
    WCRec p[ 2 ];  /* poin */
    const char *colors[] = {
        "red", "green", "blue"
    };
 
    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);
 
    // draw centre triad
    FloatMatrix tc;
    int i, succ;
    double coeff = this->l0 / 3.;
    this->computeRotMtrxFromQuaternion(tc, this->q);
 
    p [ 0 ].x = 0.5 * ( ( FPNum ) this->giveNode(1)->giveUpdatedCoordinate(1, tStep, defScale) + ( FPNum ) this->giveNode(2)->giveUpdatedCoordinate(1, tStep, defScale) );
    p [ 0 ].y = 0.5 * ( ( FPNum ) this->giveNode(1)->giveUpdatedCoordinate(2, tStep, defScale) + ( FPNum ) this->giveNode(2)->giveUpdatedCoordinate(2, tStep, defScale) );
    p [ 0 ].z = 0.5 * ( ( FPNum ) this->giveNode(1)->giveUpdatedCoordinate(3, tStep, defScale) + ( FPNum ) this->giveNode(2)->giveUpdatedCoordinate(3, tStep, defScale) );
 
    // draw t1
    for ( i = 1; i <= 3; i++ ) {
        p [ 1 ].x = p [ 0 ].x + coeff * tc.at(1, i);
        p [ 1 ].y = p [ 0 ].y + coeff * tc.at(2, i);
        p [ 1 ].z = p [ 0 ].z + coeff * tc.at(3, i);
 
        EASValsSetColor(ColorGetPixelFromString(const_cast< char * >( colors [ i - 1 ] ), & succ) );
 
        go = CreateLine3D(p);
        EGWithMaskChangeAttributes(WIDTH_MASK | COLOR_MASK | LAYER_MASK, go);
        EMAddGraphicsToModel(ESIModel(), go);
    }
}
#endif
} // end namespace oofem