void MixedGradientPressureWeakPeriodic :: computeStress(FloatArray &sigmaDev, FloatArray &tractions, double rve_size)
{
FloatMatrix mMatrix;
FloatArray normal, coords, t;
int nsd = domain->giveNumberOfSpatialDimensions();
Set *set = this->giveDomain()->giveSet(this->set);
const IntArray &boundaries = set->giveBoundaryList();
// Reminder: sigma = int t * n dA, where t = sum( C_i * n t_i ).
// This loop will construct sigma in matrix form.
FloatMatrix sigma;
for ( int pos = 1; pos <= boundaries.giveSize() / 2; ++pos ) {
Element *el = this->giveDomain()->giveElement( boundaries.at(pos * 2 - 1) );
int boundary = boundaries.at(pos * 2);
FEInterpolation *interp = el->giveInterpolation(); // Geometry interpolation. The displacements or velocities must have the same interpolation scheme (on the boundary at least).
int maxorder = this->order + interp->giveInterpolationOrder() * 3;
std :: unique_ptr< IntegrationRule >ir( interp->giveBoundaryIntegrationRule(maxorder, boundary) );
for ( GaussPoint *gp: *ir ) {
const FloatArray &lcoords = gp->giveNaturalCoordinates();
FEIElementGeometryWrapper cellgeo(el);
double detJ = interp->boundaryEvalNormal(normal, boundary, lcoords, cellgeo);
// Compute v_m = d_dev . x
interp->boundaryLocal2Global(coords, boundary, lcoords, cellgeo);
this->constructMMatrix(mMatrix, coords, normal);
t.beProductOf(mMatrix, tractions);
sigma.plusDyadUnsym(t, coords, detJ * gp->giveWeight());
}
}
sigma.times(1. / rve_size);
double pressure = 0.;
for ( int i = 1; i <= nsd; i++ ) {
pressure += sigma.at(i, i);
}
pressure /= 3; // Not 100% sure about this for 2D cases.
if ( nsd == 3 ) {
sigmaDev.resize(6);
sigmaDev.at(1) = sigma.at(1, 1) - pressure;
sigmaDev.at(2) = sigma.at(2, 2) - pressure;
sigmaDev.at(3) = sigma.at(3, 3) - pressure;
sigmaDev.at(4) = 0.5 * ( sigma.at(2, 3) + sigma.at(3, 2) );
sigmaDev.at(5) = 0.5 * ( sigma.at(1, 3) + sigma.at(3, 1) );
sigmaDev.at(6) = 0.5 * ( sigma.at(1, 2) + sigma.at(2, 1) );
} else if ( nsd == 2 ) {
sigmaDev.resize(3);
sigmaDev.at(1) = sigma.at(1, 1) - pressure;
sigmaDev.at(2) = sigma.at(2, 2) - pressure;
sigmaDev.at(3) = 0.5 * ( sigma.at(1, 2) + sigma.at(2, 1) );
} else {
sigmaDev.resize(1);
sigmaDev.at(1) = sigma.at(1, 1) - pressure;
}
}
void MixedGradientPressureWeakPeriodic :: integrateTractionXTangent(FloatMatrix &answer, Element *el, int boundary)
{
// Computes the integral: int dt . dx_m dA
FloatMatrix mMatrix;
FloatArray normal, coords, vM_vol;
FEInterpolation *interp = el->giveInterpolation(); // Geometry interpolation. The displacements or velocities must have the same interpolation scheme (on the boundary at least).
int maxorder = this->order + interp->giveInterpolationOrder() * 3;
std :: unique_ptr< IntegrationRule >ir( interp->giveBoundaryIntegrationRule(maxorder, boundary) );
FloatArray tmpAnswer;
for ( GaussPoint *gp: *ir ) {
const FloatArray &lcoords = gp->giveNaturalCoordinates();
FEIElementGeometryWrapper cellgeo(el);
double detJ = interp->boundaryEvalNormal(normal, boundary, lcoords, cellgeo);
interp->boundaryLocal2Global(coords, boundary, lcoords, cellgeo);
vM_vol.beScaled(1.0/3.0, coords);
this->constructMMatrix(mMatrix, coords, normal);
tmpAnswer.plusProduct(mMatrix, vM_vol, detJ * gp->giveWeight());
}
answer.resize(tmpAnswer.giveSize(), 1);
answer.setColumn(tmpAnswer, 1);
}
void MixedGradientPressureWeakPeriodic :: integrateTractionDev(FloatArray &answer, Element *el, int boundary, const FloatMatrix &ddev)
{
// Computes the integral: int dt . dx dA
FloatMatrix mMatrix;
FloatArray normal, coords, vM_dev;
FEInterpolation *interp = el->giveInterpolation(); // Geometry interpolation. The displacements or velocities must have the same interpolation scheme (on the boundary at least).
int maxorder = this->order + interp->giveInterpolationOrder() * 3;
std :: unique_ptr< IntegrationRule >ir( interp->giveBoundaryIntegrationRule(maxorder, boundary) );
answer.clear();
for ( GaussPoint *gp: *ir ) {
const FloatArray &lcoords = gp->giveNaturalCoordinates();
FEIElementGeometryWrapper cellgeo(el);
double detJ = interp->boundaryEvalNormal(normal, boundary, lcoords, cellgeo);
// Compute v_m = d_dev . x
interp->boundaryLocal2Global(coords, boundary, lcoords, cellgeo);
vM_dev.beProductOf(ddev, coords);
this->constructMMatrix(mMatrix, coords, normal);
answer.plusProduct(mMatrix, vM_dev, detJ * gp->giveWeight());
}
}
int
DofManValueField :: evaluateAt(FloatArray &answer, const FloatArray &coords, ValueModeType mode, TimeStep *tStep)
{
int result = 0; // assume ok
FloatArray lc, n;
// request element containing target point
Element *elem = this->domain->giveSpatialLocalizer()->giveElementContainingPoint(coords);
if ( elem ) { // ok element containing target point found
FEInterpolation *interp = elem->giveInterpolation();
if ( interp ) {
// map target point to element local coordinates
if ( interp->global2local( lc, coords, FEIElementGeometryWrapper(elem) ) ) {
// evaluate interpolation functions at target point
interp->evalN( n, lc, FEIElementGeometryWrapper(elem) );
// loop over element nodes
for ( int i = 1; i <= n.giveSize(); i++ ) {
// multiply nodal value by value of corresponding shape function and add this to answer
answer.add( n.at(i), this->dmanvallist[elem->giveDofManagerNumber(i)-1] );
}
} else { // mapping from global to local coordinates failed
result = 1; // failed
}
} else { // element without interpolation
result = 1; // failed
}
} else { // no element containing given point found
result = 1; // failed
}
return result;
}
void
AxisymElement :: computeBmatrixAt(GaussPoint *gp, FloatMatrix &answer, int li, int ui)
//
// Returns the [ 6 x (nno*2) ] strain-displacement matrix {B} of the receiver,
// evaluated at gp.
// (epsilon_x,epsilon_y,...,Gamma_xy) = B . r
// r = ( u1,v1,u2,v2,u3,v3,u4,v4)
{
FEInterpolation *interp = this->giveInterpolation();
FloatArray N;
interp->evalN( N, gp->giveNaturalCoordinates(), *this->giveCellGeometryWrapper() );
double r = 0.0;
for ( int i = 1; i <= this->giveNumberOfDofManagers(); i++ ) {
double x = this->giveNode(i)->giveCoordinate(1);
r += x * N.at(i);
}
FloatMatrix dNdx;
interp->evaldNdx( dNdx, gp->giveNaturalCoordinates(), *this->giveCellGeometryWrapper() );
answer.resize(6, dNdx.giveNumberOfRows() * 2);
answer.zero();
for ( int i = 1; i <= dNdx.giveNumberOfRows(); i++ ) {
answer.at(1, i * 2 - 1) = dNdx.at(i, 1);
answer.at(2, i * 2 - 0) = dNdx.at(i, 2);
answer.at(3, i * 2 - 1) = N.at(i) / r;
answer.at(6, 2 * i - 1) = dNdx.at(i, 2);
answer.at(6, 2 * i - 0) = dNdx.at(i, 1);
}
}
void Space3dStructuralElementEvaluator :: computeBMatrixAt(FloatMatrix &answer, GaussPoint *gp)
{
FloatMatrix d;
Element *element = this->giveElement();
FEInterpolation *interp = element->giveInterpolation();
// this uses FEInterpolation::nodes2coords - quite inefficient in this case (large num of dofmans)
interp->evaldNdx( d, gp->giveNaturalCoordinates(), FEIIGAElementGeometryWrapper( element, gp->giveIntegrationRule()->giveKnotSpan() ) );
answer.resize(6, d.giveNumberOfRows() * 3);
answer.zero();
for ( int i = 1; i <= d.giveNumberOfRows(); i++ ) {
answer.at(1, i * 3 - 2) = d.at(i, 1);
answer.at(2, i * 3 - 1) = d.at(i, 2);
answer.at(3, i * 3 - 0) = d.at(i, 3);
answer.at(4, 3 * i - 1) = d.at(i, 3);
answer.at(4, 3 * i - 0) = d.at(i, 2);
answer.at(5, 3 * i - 2) = d.at(i, 3);
answer.at(5, 3 * i - 0) = d.at(i, 1);
answer.at(6, 3 * i - 2) = d.at(i, 2);
answer.at(6, 3 * i - 1) = d.at(i, 1);
}
}
bool EnrichmentItem :: tipIsTouchingEI(const TipInfo &iTipInfo)
{
double tol = 1.0e-9;
SpatialLocalizer *localizer = giveDomain()->giveSpatialLocalizer();
Element *tipEl = localizer->giveElementContainingPoint(iTipInfo.mGlobalCoord);
if ( tipEl != NULL ) {
// Check if the candidate tip is located on the current crack
FloatArray N;
FloatArray locCoord;
tipEl->computeLocalCoordinates(locCoord, iTipInfo.mGlobalCoord);
FEInterpolation *interp = tipEl->giveInterpolation();
interp->evalN( N, locCoord, FEIElementGeometryWrapper(tipEl) );
double normalSignDist;
evalLevelSetNormal( normalSignDist, iTipInfo.mGlobalCoord, N, tipEl->giveDofManArray() );
double tangSignDist;
evalLevelSetTangential( tangSignDist, iTipInfo.mGlobalCoord, N, tipEl->giveDofManArray() );
if ( fabs(normalSignDist) < tol && tangSignDist > tol ) {
return true;
}
}
return false;
}
void PlaneStressStructuralElementEvaluator :: computeNMatrixAt(FloatMatrix &answer, GaussPoint *gp)
{
FloatArray N;
FEInterpolation *interp = gp->giveElement()->giveInterpolation();
interp->evalN( N, gp->giveNaturalCoordinates(), FEIIGAElementGeometryWrapper( gp->giveElement(), gp->giveIntegrationRule()->giveKnotSpan() ) );
answer.beNMatrixOf(N, 2);
}
void
Structural3DElement :: computeBHmatrixAt(GaussPoint *gp, FloatMatrix &answer)
// Returns the [ 9 x (nno * 3) ] displacement gradient matrix {BH} of the receiver,
// evaluated at gp.
// BH matrix - 9 rows : du/dx, dv/dy, dw/dz, dv/dz, du/dz, du/dy, dw/dy, dw/dx, dv/dx
{
FEInterpolation *interp = this->giveInterpolation();
FloatMatrix dNdx;
interp->evaldNdx( dNdx, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(this) );
answer.resize(9, dNdx.giveNumberOfRows() * 3);
answer.zero();
for ( int i = 1; i <= dNdx.giveNumberOfRows(); i++ ) {
answer.at(1, 3 * i - 2) = dNdx.at(i, 1); // du/dx
answer.at(2, 3 * i - 1) = dNdx.at(i, 2); // dv/dy
answer.at(3, 3 * i - 0) = dNdx.at(i, 3); // dw/dz
answer.at(4, 3 * i - 1) = dNdx.at(i, 3); // dv/dz
answer.at(7, 3 * i - 0) = dNdx.at(i, 2); // dw/dy
answer.at(5, 3 * i - 2) = dNdx.at(i, 3); // du/dz
answer.at(8, 3 * i - 0) = dNdx.at(i, 1); // dw/dx
answer.at(6, 3 * i - 2) = dNdx.at(i, 2); // du/dy
answer.at(9, 3 * i - 1) = dNdx.at(i, 1); // dv/dx
}
}
void
MatlabExportModule :: doOutputHomogenizeDofIDs(TimeStep *tStep, FILE *FID)
{
std :: vector <FloatArray*> HomQuantities;
double Vol = 0.0;
// Initialize vector of arrays constaining homogenized quantities
HomQuantities.resize(internalVarsToExport.giveSize());
for (int j=0; j<internalVarsToExport.giveSize(); j++) {
HomQuantities.at(j) = new FloatArray;
}
int nelem = this->elList.giveSize();
for (int i = 1; i<=nelem; i++) {
Element *e = this->emodel->giveDomain(1)->giveElement(elList.at(i));
FEInterpolation *Interpolation = e->giveInterpolation();
Vol = Vol + e->computeVolumeAreaOrLength();
for ( GaussPoint *gp: *e->giveDefaultIntegrationRulePtr() ) {
for (int j=0; j<internalVarsToExport.giveSize(); j++) {
FloatArray elementValues;
e->giveIPValue(elementValues, gp, (InternalStateType) internalVarsToExport(j), tStep);
double detJ=fabs(Interpolation->giveTransformationJacobian( gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(e)));
elementValues.times(gp->giveWeight()*detJ);
if (HomQuantities.at(j)->giveSize() == 0) {
HomQuantities.at(j)->resize(elementValues.giveSize());
HomQuantities.at(j)->zero();
};
HomQuantities.at(j)->add(elementValues);
}
}
}
if (noscaling) Vol=1.0;
for ( std :: size_t i = 0; i < HomQuantities.size(); i ++) {
FloatArray *thisIS;
thisIS = HomQuantities.at(i);
thisIS->times(1.0/Vol);
fprintf(FID, "\tspecials.%s = [", __InternalStateTypeToString ( InternalStateType (internalVarsToExport(i)) ) );
for (int j = 0; j<thisIS->giveSize(); j++) {
fprintf(FID, "%e", thisIS->at(j+1));
if (j!=(thisIS->giveSize()-1) ) {
fprintf(FID, ", ");
}
}
fprintf(FID, "];\n");
delete HomQuantities.at(i);
}
}
/* 3D Space Elements */
void Space3dStructuralElementEvaluator :: computeNMatrixAt(FloatMatrix &answer, GaussPoint *gp)
{
FloatArray N;
Element *element = this->giveElement();
FEInterpolation *interp = element->giveInterpolation();
interp->evalN( N, gp->giveNaturalCoordinates(), FEIIGAElementGeometryWrapper( element, gp->giveIntegrationRule()->giveKnotSpan() ) );
answer.beNMatrixOf(N, 3);
}
void
PrescribedMean :: computeDomainSize()
{
if (domainSize > 0.0) return;
if (elementEdges) {
IntArray setList = ((GeneralBoundaryCondition *)this)->giveDomain()->giveSet(set)->giveBoundaryList();
elements.resize(setList.giveSize() / 2);
sides.resize(setList.giveSize() / 2);
for (int i=1; i<=setList.giveSize(); i=i+2) {
elements.at(i/2+1) = setList.at(i);
sides.at(i/2+1) = setList.at(i+1);
}
} else {
IntArray setList = ((GeneralBoundaryCondition *)this)->giveDomain()->giveSet(set)->giveElementList();
elements = setList;
}
domainSize = 0.0;
for ( int i=1; i<=elements.giveSize(); i++ ) {
int elementID = elements.at(i);
Element *thisElement = this->giveDomain()->giveElement(elementID);
FEInterpolation *interpolator = thisElement->giveInterpolation(DofIDItem(dofid));
IntegrationRule *iRule;
if (elementEdges) {
iRule = interpolator->giveBoundaryIntegrationRule(3, sides.at(i));
} else {
iRule = interpolator->giveIntegrationRule(3);
}
for ( GaussPoint * gp: * iRule ) {
FloatArray lcoords = gp->giveNaturalCoordinates();
double detJ;
if (elementEdges) {
detJ = fabs ( interpolator->boundaryGiveTransformationJacobian(sides.at(i), lcoords, FEIElementGeometryWrapper(thisElement)) );
} else {
detJ = fabs ( interpolator->giveTransformationJacobian(lcoords, FEIElementGeometryWrapper(thisElement)) );
}
domainSize = domainSize + detJ*gp->giveWeight();
}
delete iRule;
}
printf("%f\n", domainSize);
}
double MixedGradientPressureBC :: domainSize()
{
int nsd = this->domain->giveNumberOfSpatialDimensions();
double domain_size = 0.0;
// This requires the boundary to be consistent and ordered correctly.
Set *set = this->giveDomain()->giveSet(this->set);
const IntArray &boundaries = set->giveBoundaryList();
for ( int pos = 1; pos <= boundaries.giveSize() / 2; ++pos ) {
Element *e = this->giveDomain()->giveElement( boundaries.at(pos * 2 - 1) );
int boundary = boundaries.at(pos * 2);
FEInterpolation *fei = e->giveInterpolation();
domain_size += fei->evalNXIntegral( boundary, FEIElementGeometryWrapper(e) );
}
return domain_size / nsd;
}
void
IntElLine1PhF :: computeCovarBaseVectorAt(IntegrationPoint *ip, FloatArray &G)
{
FloatMatrix dNdxi;
FEInterpolation *interp = this->giveInterpolation();
interp->evaldNdxi( dNdxi, ip->giveNaturalCoordinates(), FEIElementGeometryWrapper(this) );
G.resize(2);
G.zero();
int numNodes = this->giveNumberOfNodes();
for ( int i = 1; i <= dNdxi.giveNumberOfRows(); i++ ) {
double X1_i = 0.5 * ( this->giveNode(i)->giveCoordinate(1) + this->giveNode(i + numNodes / 2)->giveCoordinate(1) ); // (mean) point on the fictious mid surface
double X2_i = 0.5 * ( this->giveNode(i)->giveCoordinate(2) + this->giveNode(i + numNodes / 2)->giveCoordinate(2) );
G.at(1) += dNdxi.at(i, 1) * X1_i;
G.at(2) += dNdxi.at(i, 1) * X2_i;
}
}
double TransportGradientPeriodic :: domainSize(Domain *d, int setNum)
{
int nsd = d->giveNumberOfSpatialDimensions();
double domain_size = 0.0;
// This requires the boundary to be consistent and ordered correctly.
Set *set = d->giveSet(setNum);
const IntArray &boundaries = set->giveBoundaryList();
for ( int pos = 1; pos <= boundaries.giveSize() / 2; ++pos ) {
Element *e = d->giveElement( boundaries.at(pos * 2 - 1) );
int boundary = boundaries.at(pos * 2);
FEInterpolation *fei = e->giveInterpolation();
domain_size += fei->evalNXIntegral( boundary, FEIElementGeometryWrapper(e) );
}
return fabs(domain_size / nsd);
}
void
IntElLine1PhF :: computeNmatrixAt(GaussPoint *ip, FloatMatrix &answer)
{
// Returns the modified N-matrix which multiplied with u give the spatial jump.
FloatArray N;
FEInterpolation *interp = this->giveInterpolation();
interp->evalN( N, ip->giveNaturalCoordinates(), FEIElementGeometryWrapper(this) );
answer.resize(2, 8);
answer.zero();
answer.at(1, 1) = answer.at(2, 2) = -N.at(1);
answer.at(1, 3) = answer.at(2, 4) = -N.at(2);
answer.at(1, 5) = answer.at(2, 6) = N.at(1);
answer.at(1, 7) = answer.at(2, 8) = N.at(2);
}
void
PlaneStressElement :: computeBmatrixAt(GaussPoint *gp, FloatMatrix &answer, int lowerIndx, int upperIndx)
{
FEInterpolation *interp = this->giveInterpolation();
FloatMatrix dNdx;
interp->evaldNdx( dNdx, gp->giveNaturalCoordinates(), * this->giveCellGeometryWrapper() );
answer.resize(3, dNdx.giveNumberOfRows() * 2);
answer.zero();
for ( int i = 1; i <= dNdx.giveNumberOfRows(); i++ ) {
answer.at(1, i * 2 - 1) = dNdx.at(i, 1);
answer.at(2, i * 2 - 0) = dNdx.at(i, 2);
answer.at(3, 2 * i - 1) = dNdx.at(i, 2);
answer.at(3, 2 * i - 0) = dNdx.at(i, 1);
}
}
void
L4Axisymm :: computeBmatrixAt(GaussPoint *gp, FloatMatrix &answer, int li, int ui)
{
// Returns the [ 6 x (nno*2) ] strain-displacement matrix {B} of the receiver,
// evaluated at gp. Uses reduced integration.
// (epsilon_x,epsilon_y,...,Gamma_xy) = B . r
// r = ( u1,v1,u2,v2,u3,v3,u4,v4)
FloatArray N, NRed, redCoord;
if ( numberOfFiAndShGaussPoints == 1 ) { // Reduced integration
redCoord = {0.0, 0.0}; // eval in centroid
} else {
redCoord = gp->giveNaturalCoordinates();
}
FEInterpolation *interp = this->giveInterpolation();
interp->evalN( N, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(this) );
interp->evalN( NRed, redCoord, FEIElementGeometryWrapper(this) );
// Evaluate radius at center
double r = 0.0;
for ( int i = 1; i <= this->giveNumberOfDofManagers(); i++ ) {
double x = this->giveNode(i)->giveCoordinate(1);
r += x * NRed.at(i);
}
FloatMatrix dNdx, dNdxRed;
interp->evaldNdx( dNdx, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(this) );
interp->evaldNdx( dNdxRed, redCoord, FEIElementGeometryWrapper(this) );
answer.resize(6, dNdx.giveNumberOfRows() * 2);
answer.zero();
for ( int i = 1; i <= dNdx.giveNumberOfRows(); i++ ) {
answer.at(1, i * 2 - 1) = dNdx.at(i, 1);
answer.at(2, i * 2 - 0) = dNdx.at(i, 2);
answer.at(3, i * 2 - 1) = NRed.at(i) / r;
answer.at(6, 2 * i - 1) = dNdxRed.at(i, 2);
answer.at(6, 2 * i - 0) = dNdxRed.at(i, 1);
}
}
const IntArray &Set :: giveNodeList()
{
// Lazy evaluation, we compute the unique set of nodes if needed (and store it).
if ( this->totalNodes.giveSize() == 0 ) {
IntArray afflictedNodes( this->domain->giveNumberOfDofManagers() );
afflictedNodes.zero();
for ( int ielem = 1; ielem <= this->elements.giveSize(); ++ielem ) {
Element *e = this->domain->giveElement( this->elements.at(ielem) );
for ( int inode = 1; inode <= e->giveNumberOfNodes(); ++inode ) {
afflictedNodes.at( e->giveNode(inode)->giveNumber() ) = 1;
}
}
IntArray bNodes;
for ( int ibnd = 1; ibnd <= this->elementBoundaries.giveSize() / 2; ++ibnd ) {
Element *e = this->domain->giveElement( this->elementBoundaries.at(ibnd * 2 - 1) );
int boundary = this->elementBoundaries.at(ibnd * 2);
FEInterpolation *fei = e->giveInterpolation();
fei->boundaryGiveNodes(bNodes, boundary);
for ( int inode = 1; inode <= bNodes.giveSize(); ++inode ) {
afflictedNodes.at( e->giveNode( bNodes.at(inode) )->giveNumber() ) = 1;
}
}
IntArray eNodes;
for ( int iedge = 1; iedge <= this->elementEdges.giveSize() / 2; ++iedge ) {
Element *e = this->domain->giveElement( this->elementEdges.at(iedge * 2 - 1) );
int edge = this->elementEdges.at(iedge * 2);
FEInterpolation3d *fei = static_cast< FEInterpolation3d * >( e->giveInterpolation() );
fei->computeLocalEdgeMapping(eNodes, edge);
for ( int inode = 1; inode <= eNodes.giveSize(); ++inode ) {
afflictedNodes.at( e->giveNode( eNodes.at(inode) )->giveNumber() ) = 1;
}
}
for ( int inode = 1; inode <= this->nodes.giveSize(); ++inode ) {
afflictedNodes.at( this->nodes.at(inode) ) = 1;
}
totalNodes.findNonzeros(afflictedNodes);
}
return this->totalNodes;
}
bool Inclusion :: isMaterialModified(GaussPoint &iGP, Element &iEl, CrossSection * &opCS) const
{
// Check if the point is located inside the inclusion
FloatArray N;
FEInterpolation *interp = iEl.giveInterpolation();
interp->evalN( N, * iGP.giveNaturalCoordinates(), FEIElementGeometryWrapper(& iEl) );
const IntArray &elNodes = iEl.giveDofManArray();
double levelSetGP = 0.0;
interpLevelSet(levelSetGP, N, elNodes);
if ( levelSetGP < 0.0 ) {
opCS = mpCrossSection;
return true;
}
return false;
}
void
PlaneStrainElement :: computeBmatrixAt(GaussPoint *gp, FloatMatrix &answer, int lowerIndx, int upperIndx)
// Returns the [ 4 x (nno*2) ] strain-displacement matrix {B} of the receiver,
// evaluated at gp.
{
FEInterpolation *interp = this->giveInterpolation();
FloatMatrix dNdx;
interp->evaldNdx( dNdx, gp->giveNaturalCoordinates(), *this->giveCellGeometryWrapper() );
answer.resize(4, dNdx.giveNumberOfRows() * 2);
answer.zero();
for ( int i = 1; i <= dNdx.giveNumberOfRows(); i++ ) {
answer.at(1, i * 2 - 1) = dNdx.at(i, 1);
answer.at(2, i * 2 - 0) = dNdx.at(i, 2);
answer.at(4, 2 * i - 1) = dNdx.at(i, 2);
answer.at(4, 2 * i - 0) = dNdx.at(i, 1);
}
}
double
NLStructuralElement :: computeCurrentVolume(TimeStep *tStep)
{
double vol=0.0;
for ( auto &gp: *this->giveDefaultIntegrationRulePtr() ) {
FloatArray F;
FloatMatrix Fm;
computeDeformationGradientVector(F, gp, tStep);
Fm.beMatrixForm(F);
double J = Fm.giveDeterminant();
FEInterpolation *interpolation = this->giveInterpolation();
double detJ = fabs( ( interpolation->giveTransformationJacobian( gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(this) ) ) );
vol += gp->giveWeight() * detJ * J;
}
return vol;
}
void MixedGradientPressureWeakPeriodic :: integrateTractionVelocityTangent(FloatMatrix &answer, Element *el, int boundary)
{
// Computes the integral: int dt . dv dA
FloatArray normal, n, coords;
FloatMatrix nMatrix, mMatrix;
FEInterpolation *interp = el->giveInterpolation(); // Geometry interpolation. The displacements or velocities must have the same interpolation scheme (on the boundary at least).
int maxorder = this->order + interp->giveInterpolationOrder() * 3;
std :: unique_ptr< IntegrationRule >ir( interp->giveBoundaryIntegrationRule(maxorder, boundary) );
int nsd = this->giveDomain()->giveNumberOfSpatialDimensions();
answer.clear();
for ( GaussPoint *gp: *ir ) {
const FloatArray &lcoords = gp->giveNaturalCoordinates();
FEIElementGeometryWrapper cellgeo(el);
double detJ = interp->boundaryEvalNormal(normal, boundary, lcoords, cellgeo);
interp->boundaryEvalN(n, boundary, lcoords, cellgeo);
interp->boundaryLocal2Global(coords, boundary, lcoords, cellgeo);
// Construct the basis functions for the tractions:
this->constructMMatrix(mMatrix, coords, normal);
nMatrix.beNMatrixOf(n, nsd);
answer.plusProductUnsym( mMatrix, nMatrix, detJ * gp->giveWeight() );
}
}
int
SmoothedNodalInternalVariableField :: evaluateAt(FloatArray &answer, FloatArray &coords, ValueModeType mode, TimeStep *tStep)
{
int result = 0; // assume ok
FloatArray lc, n;
const FloatArray *nodalValue;
// use whole domain recovery
// create a new set containing all elements
Set elemSet(0, this->domain);
elemSet.addAllElements();
this->smoother->recoverValues(elemSet, istType, tStep);
// request element containing target point
Element *elem = this->domain->giveSpatialLocalizer()->giveElementContainingPoint(coords);
if ( elem ) { // ok element containing target point found
FEInterpolation *interp = elem->giveInterpolation();
if ( interp ) {
// map target point to element local coordinates
if ( interp->global2local( lc, coords, FEIElementGeometryWrapper(elem) ) ) {
// evaluate interpolation functions at target point
interp->evalN( n, lc, FEIElementGeometryWrapper(elem) );
// loop over element nodes
for ( int i = 1; i <= n.giveSize(); i++ ) {
// request nodal value
this->smoother->giveNodalVector( nodalValue, elem->giveDofManagerNumber(i) );
// multiply nodal value by value of corresponding shape function and add this to answer
answer.add(n.at(i), * nodalValue);
}
} else { // mapping from global to local coordinates failed
result = 1; // failed
}
} else { // element without interpolation
result = 1; // failed
}
} else { // no element containing given point found
result = 1; // failed
}
return result;
}
void
Structural3DElement :: computeBmatrixAt(GaussPoint *gp, FloatMatrix &answer, int li, int ui)
// Returns the [ 6 x (nno*3) ] strain-displacement matrix {B} of the receiver, eva-
// luated at gp.
// B matrix - 6 rows : epsilon-X, epsilon-Y, epsilon-Z, gamma-YZ, gamma-ZX, gamma-XY :
{
FEInterpolation *interp = this->giveInterpolation();
FloatMatrix dNdx;
interp->evaldNdx( dNdx, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(this) );
answer.resize(6, dNdx.giveNumberOfRows() * 3);
answer.zero();
for ( int i = 1; i <= dNdx.giveNumberOfRows(); i++ ) {
answer.at(1, 3 * i - 2) = dNdx.at(i, 1);
answer.at(2, 3 * i - 1) = dNdx.at(i, 2);
answer.at(3, 3 * i - 0) = dNdx.at(i, 3);
answer.at(5, 3 * i - 2) = answer.at(4, 3 * i - 1) = dNdx.at(i, 3);
answer.at(6, 3 * i - 2) = answer.at(4, 3 * i - 0) = dNdx.at(i, 2);
answer.at(6, 3 * i - 1) = answer.at(5, 3 * i - 0) = dNdx.at(i, 1);
}
}
void
IntElLine2IntPen :: computeCovarBaseVectorAt(IntegrationPoint *ip, FloatArray &G)
{
// printf("Entering IntElLine2IntPen :: computeCovarBaseVectorAt\n");
// Since we are averaging over the whole element, always evaluate the base vectors at xi = 0.
FloatArray xi_0 = {0.0};
FloatMatrix dNdxi;
FEInterpolation *interp = this->giveInterpolation();
// interp->evaldNdxi( dNdxi, ip->giveNaturalCoordinates(), FEIElementGeometryWrapper(this) );
interp->evaldNdxi( dNdxi, xi_0, FEIElementGeometryWrapper(this) );
G.resize(2);
G.zero();
int numNodes = this->giveNumberOfNodes();
for ( int i = 1; i <= dNdxi.giveNumberOfRows(); i++ ) {
double X1_i = 0.5 * ( this->giveNode(i)->giveCoordinate(1) + this->giveNode(i + numNodes / 2)->giveCoordinate(1) ); // (mean) point on the fictious mid surface
double X2_i = 0.5 * ( this->giveNode(i)->giveCoordinate(2) + this->giveNode(i + numNodes / 2)->giveCoordinate(2) );
G.at(1) += dNdxi.at(i, 1) * X1_i;
G.at(2) += dNdxi.at(i, 1) * X2_i;
}
}
const IntArray &Set :: giveNodeList()
{
// Lazy evaluation, we compute the unique set of nodes if needed (and store it).
if ( this->totalNodes.giveSize() == 0 ) {
IntArray afflictedNodes( this->domain->giveNumberOfDofManagers() );
afflictedNodes.zero();
for ( int ielem = 1; ielem <= this->elements.giveSize(); ++ielem ) {
Element *e = this->domain->giveElement( this->elements.at(ielem) );
for ( int inode = 1; inode <= e->giveNumberOfNodes(); ++inode ) {
afflictedNodes.at( e->giveNode(inode)->giveNumber() ) = 1;
}
}
/* boundary entities are obsolete, use edges and/or surfaces instead */
IntArray bNodes;
for ( int ibnd = 1; ibnd <= this->elementBoundaries.giveSize() / 2; ++ibnd ) {
Element *e = this->domain->giveElement( this->elementBoundaries.at(ibnd * 2 - 1) );
int boundary = this->elementBoundaries.at(ibnd * 2);
FEInterpolation *fei = e->giveInterpolation();
fei->boundaryGiveNodes(bNodes, boundary);
for ( int inode = 1; inode <= bNodes.giveSize(); ++inode ) {
afflictedNodes.at( e->giveNode( bNodes.at(inode) )->giveNumber() ) = 1;
}
}
IntArray eNodes;
for ( int iedge = 1; iedge <= this->elementEdges.giveSize() / 2; ++iedge ) {
Element *e = this->domain->giveElement( this->elementEdges.at(iedge * 2 - 1) );
int edge = this->elementEdges.at(iedge * 2);
FEInterpolation *fei = e->giveInterpolation();
fei->boundaryEdgeGiveNodes(eNodes, edge);
for ( int inode = 1; inode <= eNodes.giveSize(); ++inode ) {
afflictedNodes.at( e->giveNode( eNodes.at(inode) )->giveNumber() ) = 1;
}
}
for ( int isurf = 1; isurf <= this->elementSurfaces.giveSize() / 2; ++isurf ) {
Element *e = this->domain->giveElement( this->elementSurfaces.at(isurf * 2 - 1) );
int surf = this->elementSurfaces.at(isurf * 2);
FEInterpolation *fei = e->giveInterpolation();
fei->boundarySurfaceGiveNodes(eNodes, surf);
for ( int inode = 1; inode <= eNodes.giveSize(); ++inode ) {
afflictedNodes.at( e->giveNode( eNodes.at(inode) )->giveNumber() ) = 1;
}
}
for ( int inode = 1; inode <= this->nodes.giveSize(); ++inode ) {
afflictedNodes.at( this->nodes.at(inode) ) = 1;
}
totalNodes.findNonzeros(afflictedNodes);
}
return this->totalNodes;
}
void SurfaceTensionBoundaryCondition :: computeLoadVectorFromElement(FloatArray &answer, Element *e, int side, TimeStep *tStep)
{
FEInterpolation *fei = e->giveInterpolation();
if ( !fei ) {
OOFEM_ERROR("No interpolation or default integration available for element.");
}
std :: unique_ptr< IntegrationRule > iRule( fei->giveBoundaryIntegrationRule(fei->giveInterpolationOrder()-1, side) );
int nsd = e->giveDomain()->giveNumberOfSpatialDimensions();
if ( side == -1 ) {
side = 1;
}
answer.clear();
if ( nsd == 2 ) {
FEInterpolation2d *fei2d = static_cast< FEInterpolation2d * >(fei);
///@todo More of this grunt work should be moved to the interpolation classes
IntArray bnodes;
fei2d->boundaryGiveNodes(bnodes, side);
int nodes = bnodes.giveSize();
FloatMatrix xy(2, nodes);
for ( int i = 1; i <= nodes; i++ ) {
Node *node = e->giveNode(bnodes.at(i));
///@todo This should rely on the xindex and yindex in the interpolator..
xy.at(1, i) = node->giveCoordinate(1);
xy.at(2, i) = node->giveCoordinate(2);
}
FloatArray tmp; // Integrand
FloatArray es; // Tangent vector to curve
FloatArray dNds;
if ( e->giveDomain()->isAxisymmetric() ) {
FloatArray N;
FloatArray gcoords;
for ( GaussPoint *gp: *iRule ) {
fei2d->edgeEvaldNds( dNds, side, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(e) );
fei->boundaryEvalN( N, side, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(e) );
double J = fei->boundaryGiveTransformationJacobian( side, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(e) );
fei->boundaryLocal2Global( gcoords, side, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(e) );
double r = gcoords(0); // First coordinate is the radial coord.
es.beProductOf(xy, dNds);
tmp.resize( 2 * nodes);
for ( int i = 0; i < nodes; i++ ) {
tmp(2 * i) = dNds(i) * es(0) * r + N(i);
tmp(2 * i + 1) = dNds(i) * es(1) * r;
}
answer.add(- 2 * M_PI * gamma * J * gp->giveWeight(), tmp);
}
} else {
for ( GaussPoint *gp: *iRule ) {
double t = e->giveCrossSection()->give(CS_Thickness, gp);
fei2d->edgeEvaldNds( dNds, side, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(e) );
double J = fei->boundaryGiveTransformationJacobian( side, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(e) );
es.beProductOf(xy, dNds);
tmp.resize( 2 * nodes);
for ( int i = 0; i < nodes; i++ ) {
tmp(2 * i) = dNds(i) * es(0);
tmp(2 * i + 1) = dNds(i) * es(1);
//B.at(1, 1+i*2) = B.at(2, 2+i*2) = dNds(i);
}
//tmp.beTProductOf(B, es);
answer.add(- t * gamma * J * gp->giveWeight(), tmp);
}
}
} else if ( nsd == 3 ) {
FEInterpolation3d *fei3d = static_cast< FEInterpolation3d * >(fei);
FloatArray n, surfProj;
FloatMatrix dNdx, B;
for ( GaussPoint *gp: *iRule ) {
fei3d->surfaceEvaldNdx( dNdx, side, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(e) );
double J = fei->boundaryEvalNormal( n, side, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(e) );
// [I - n(x)n] in voigt form:
surfProj = {1. - n(0)*n(0), 1. - n(1)*n(1), 1. - n(2)*n(2),
- n(1)*n(2), - n(0)*n(2), - n(0)*n(1),
};
// Construct B matrix of the surface nodes
B.resize(6, 3 * dNdx.giveNumberOfRows());
for ( int i = 1; i <= dNdx.giveNumberOfRows(); i++ ) {
B.at(1, 3 * i - 2) = dNdx.at(i, 1);
B.at(2, 3 * i - 1) = dNdx.at(i, 2);
B.at(3, 3 * i - 0) = dNdx.at(i, 3);
B.at(5, 3 * i - 2) = B.at(4, 3 * i - 1) = dNdx.at(i, 3);
B.at(6, 3 * i - 2) = B.at(4, 3 * i - 0) = dNdx.at(i, 2);
B.at(6, 3 * i - 1) = B.at(5, 3 * i - 0) = dNdx.at(i, 1);
}
answer.plusProduct(B, surfProj, -gamma * J * gp->giveWeight() );
}
}
}
void SurfaceTensionBoundaryCondition :: computeTangentFromElement(FloatMatrix &answer, Element *e, int side, TimeStep *tStep)
{
FEInterpolation *fei = e->giveInterpolation();
if ( !fei ) {
OOFEM_ERROR("No interpolation available for element.");
}
std :: unique_ptr< IntegrationRule > iRule( fei->giveBoundaryIntegrationRule(fei->giveInterpolationOrder()-1, side) );
int nsd = e->giveDomain()->giveNumberOfSpatialDimensions();
int nodes = e->giveNumberOfNodes();
if ( side == -1 ) {
side = 1;
}
answer.clear();
if ( nsd == 2 ) {
FEInterpolation2d *fei2d = static_cast< FEInterpolation2d * >(fei);
///@todo More of this grunt work should be moved to the interpolation classes
FloatMatrix xy(2, nodes);
Node *node;
for ( int i = 1; i <= nodes; i++ ) {
node = e->giveNode(i);
xy.at(1, i) = node->giveCoordinate(1);
xy.at(2, i) = node->giveCoordinate(2);
}
FloatArray tmpA(2 *nodes);
FloatArray es; // Tangent vector to curve
FloatArray dNds;
FloatMatrix B(2, 2 *nodes);
B.zero();
if ( e->giveDomain()->isAxisymmetric() ) {
FloatArray N;
FloatArray gcoords;
FloatArray tmpB(2 *nodes);
for ( GaussPoint *gp: *iRule ) {
fei2d->edgeEvaldNds( dNds, side, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(e) );
fei->boundaryEvalN( N, side, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(e) );
double J = fei->boundaryGiveTransformationJacobian( side, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(e) );
fei->boundaryLocal2Global( gcoords, side, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(e) );
double r = gcoords(0); // First coordinate is the radial coord.
es.beProductOf(xy, dNds);
// Construct the different matrices in the integrand;
for ( int i = 0; i < nodes; i++ ) {
tmpA(i * 2 + 0) = dNds(i) * es(0);
tmpA(i * 2 + 1) = dNds(i) * es(1);
tmpB(i * 2 + 0) = N(i);
tmpB(i * 2 + 1) = 0;
B(i * 2, 0) = B(i * 2 + 1, 1) = dNds(i);
}
double dV = 2 *M_PI *gamma *J *gp->giveWeight();
answer.plusDyadUnsym(tmpA, tmpB, dV);
answer.plusDyadUnsym(tmpB, tmpA, dV);
answer.plusProductSymmUpper(B, B, r * dV);
answer.plusDyadUnsym(tmpA, tmpA, -r * dV);
}
} else {
for ( GaussPoint *gp: *iRule ) {
double t = e->giveCrossSection()->give(CS_Thickness, gp); ///@todo The thickness is not often relevant or used in FM.
fei2d->edgeEvaldNds( dNds, side, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(e) );
double J = fei->boundaryGiveTransformationJacobian( side, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(e) );
es.beProductOf(xy, dNds);
// Construct the different matrices in the integrand;
for ( int i = 0; i < nodes; i++ ) {
tmpA(i * 2 + 0) = dNds(i) * es(0);
tmpA(i * 2 + 1) = dNds(i) * es(1);
B(i * 2, 0) = B(i * 2 + 1, 1) = dNds(i);
}
double dV = t * gamma * J * gp->giveWeight();
answer.plusProductSymmUpper(B, B, dV);
answer.plusDyadSymmUpper(tmpA, -dV);
}
}
answer.symmetrized();
} else if ( nsd == 3 ) {
FEInterpolation3d *fei3d = static_cast< FEInterpolation3d * >(fei);
OOFEM_ERROR("3D tangents not implemented yet.");
//FloatMatrix tmp(3 *nodes, 3 *nodes);
FloatMatrix dNdx;
FloatArray n;
for ( GaussPoint *gp: *iRule ) {
fei3d->surfaceEvaldNdx( dNdx, side, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(e) );
/*double J = */ fei->boundaryEvalNormal( n, side, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(e) );
//double dV = gamma * J * gp->giveWeight();
for ( int i = 0; i < nodes; i++ ) {
//tmp(3*i+0) = dNdx(i,0) - (dNdx(i,0)*n(0)* + dNdx(i,1)*n(1) + dNdx(i,2)*n(2))*n(0);
//tmp(3*i+1) = dNdx(i,1) - (dNdx(i,0)*n(0)* + dNdx(i,1)*n(1) + dNdx(i,2)*n(2))*n(1);
//tmp(3*i+2) = dNdx(i,2) - (dNdx(i,0)*n(0)* + dNdx(i,1)*n(1) + dNdx(i,2)*n(2))*n(2);
}
//answer.plusProductSymmUpper(A,B, dV);
///@todo Derive expressions for this.
}
} else {
OOFEM_WARNING("Only 2D or 3D is possible!");
}
}
void
ZZErrorEstimatorInterface :: ZZErrorEstimatorI_computeElementContributions(double &eNorm, double &sNorm,
ZZErrorEstimator :: NormType norm,
InternalStateType type,
TimeStep *tStep)
{
int nDofMans;
FEInterpolation *interpol = element->giveInterpolation();
const FloatArray *recoveredStress;
FloatArray sig, lsig, diff, ldiff, n;
FloatMatrix nodalRecoveredStreses;
nDofMans = element->giveNumberOfDofManagers();
// assemble nodal recovered stresses
for ( int i = 1; i <= element->giveNumberOfNodes(); i++ ) {
element->giveDomain()->giveSmoother()->giveNodalVector( recoveredStress,
element->giveDofManager(i)->giveNumber() );
if ( i == 1 ) {
nodalRecoveredStreses.resize( nDofMans, recoveredStress->giveSize() );
}
for ( int j = 1; j <= recoveredStress->giveSize(); j++ ) {
nodalRecoveredStreses.at(i, j) = recoveredStress->at(j);
}
}
/* Note: The recovered stresses should be in global coordinate system. This is important for shells, for example, to make
* sure that forces and moments in the same directions are averaged. For elements where local and global coordina systems
* are the same this does not matter.
*/
eNorm = sNorm = 0.0;
// compute the e-norm and s-norm
if ( norm == ZZErrorEstimator :: L2Norm ) {
for ( GaussPoint *gp: *this->ZZErrorEstimatorI_giveIntegrationRule() ) {
double dV = element->computeVolumeAround(gp);
interpol->evalN( n, * gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(element) );
diff.beTProductOf(nodalRecoveredStreses, n);
element->giveIPValue(sig, gp, type, tStep);
/* the internal stress difference is in global coordinate system */
diff.subtract(sig);
eNorm += diff.computeSquaredNorm() * dV;
sNorm += sig.computeSquaredNorm() * dV;
}
} else if ( norm == ZZErrorEstimator :: EnergyNorm ) {
FloatArray help, ldiff_reduced, lsig_reduced;
FloatMatrix D, DInv;
StructuralElement *selem = static_cast< StructuralElement * >(element);
for ( GaussPoint *gp: *this->ZZErrorEstimatorI_giveIntegrationRule() ) {
double dV = element->computeVolumeAround(gp);
interpol->evalN( n, * gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(element) );
selem->computeConstitutiveMatrixAt(D, TangentStiffness, gp, tStep);
DInv.beInverseOf(D);
diff.beTProductOf(nodalRecoveredStreses, n);
element->giveIPValue(sig, gp, type, tStep); // returns full value now
diff.subtract(sig);
/* the internal stress difference is in global coordinate system */
/* needs to be transformed into local system to compute associated energy */
this->ZZErrorEstimatorI_computeLocalStress(ldiff, diff);
StructuralMaterial :: giveReducedSymVectorForm( ldiff_reduced, ldiff, gp->giveMaterialMode() );
help.beProductOf(DInv, ldiff_reduced);
eNorm += ldiff_reduced.dotProduct(help) * dV;
this->ZZErrorEstimatorI_computeLocalStress(lsig, sig);
StructuralMaterial :: giveReducedSymVectorForm( lsig_reduced, lsig, gp->giveMaterialMode() );
help.beProductOf(DInv, lsig_reduced);
sNorm += lsig_reduced.dotProduct(help) * dV;
}
} else {
OOFEM_ERROR("unsupported norm type");
}
eNorm = sqrt(eNorm);
sNorm = sqrt(sNorm);
}