void
SimpleCrossSection :: giveGeneralizedStress_Shell(FloatArray &answer, GaussPoint *gp, const FloatArray &strain, TimeStep *tStep)
{
/**Note: (by bp): This assumes that the behaviour is elastic
there exist a nuumber of nonlinear integral material models for beams/plates/shells
defined directly in terms of integral forces and moments and corresponding
deformations and curvatures. This would require to implement support at material model level.
Mikael: See earlier response to comment
*/
StructuralMaterial *mat = static_cast< StructuralMaterial * >( this->giveMaterial(gp) );
FloatArray elasticStrain, et, e0;
FloatMatrix tangent;
elasticStrain = strain;
this->giveTemperatureVector(et, gp, tStep);
if ( et.giveSize() ) {
double thick = this->give(CS_Thickness, gp);
mat->giveThermalDilatationVector(e0, gp, tStep);
elasticStrain.at(1) -= e0.at(1) * ( et.at(1) - mat->giveReferenceTemperature() );
elasticStrain.at(2) -= e0.at(2) * ( et.at(1) - mat->giveReferenceTemperature() );
if ( et.giveSize() > 1 ) {
elasticStrain.at(4) -= e0.at(1) * et.at(2) / thick; // kappa_x
elasticStrain.at(5) -= e0.at(2) * et.at(2) / thick; // kappa_y
}
}
this->give3dShellStiffMtrx(tangent, ElasticStiffness, gp, tStep);
answer.beProductOf(tangent, elasticStrain);
StructuralMaterialStatus *status = static_cast< StructuralMaterialStatus * >( mat->giveStatus(gp) );
status->letTempStrainVectorBe(strain);
status->letTempStressVectorBe(answer);
}
void SimpleVitrificationMaterial :: giveRealStressVector_3d(FloatArray &answer, GaussPoint *gp,
const FloatArray &reducedStrain, TimeStep *tStep)
{
FloatArray strainVector;
FloatMatrix d;
FloatArray deltaStrain;
StructuralMaterialStatus *status = dynamic_cast< StructuralMaterialStatus * >( this->giveStatus(gp) );
this->giveStressDependentPartOfStrainVector(strainVector, gp, reducedStrain, tStep, VM_Total);
deltaStrain.beDifferenceOf( strainVector, status->giveStrainVector() );
this->give3dMaterialStiffnessMatrix(d, TangentStiffness, gp, tStep);
FloatArray deltaStress;
deltaStress.beProductOf(d, deltaStrain);
answer = status->giveStressVector();
answer.add(deltaStress);
// update gp
status->letTempStrainVectorBe(reducedStrain);
status->letTempStressVectorBe(answer);
}
void
SimpleCrossSection :: giveGeneralizedStress_Beam2d(FloatArray &answer, GaussPoint *gp, const FloatArray &strain, TimeStep *tStep)
{
/**Note: (by bp): This assumes that the behaviour is elastic
there exist a nuumber of nonlinear integral material models for beams defined directly in terms of integral forces and moments and corresponding
deformations and curvatures. This would require to implement support at material model level.
Mikael: That would not be a continuum material model, but it would highly depend on the cross-section shape, thus, it should be a special cross-section model instead.
This cross-section assumes you can split the response into inertia moments and pure material response. This is only possible for a constant, elastic response (i.e. elastic).
Therefore, this cross-section may only be allowed to give the elastic response.
*/
StructuralMaterial *mat = static_cast< StructuralMaterial * >( this->giveMaterial(gp) );
FloatArray elasticStrain, et, e0;
FloatMatrix tangent;
elasticStrain = strain;
this->giveTemperatureVector(et, gp, tStep);
if ( et.giveSize() > 0 ) {
mat->giveThermalDilatationVector(e0, gp, tStep);
double thick = this->give(CS_Thickness, gp);
elasticStrain.at(1) -= e0.at(1) * ( et.at(1) - mat->giveReferenceTemperature() );
if ( et.giveSize() > 1 ) {
elasticStrain.at(2) -= e0.at(1) * et.at(2) / thick; // kappa_x
}
}
this->give2dBeamStiffMtrx(tangent, ElasticStiffness, gp, tStep);
answer.beProductOf(tangent, elasticStrain);
StructuralMaterialStatus *status = static_cast< StructuralMaterialStatus * >( mat->giveStatus(gp) );
status->letTempStrainVectorBe(strain);
status->letTempStressVectorBe(answer);
}
void
HyperElasticMaterial :: giveRealStressVector_3d(FloatArray &answer, GaussPoint *gp, const FloatArray &totalStrain, TimeStep *tStep)
{
double J2;
FloatMatrix C(3, 3);
FloatMatrix invC;
FloatArray strainVector;
StructuralMaterialStatus *status = static_cast< StructuralMaterialStatus * >( this->giveStatus(gp) );
this->giveStressDependentPartOfStrainVector_3d(strainVector, gp,
totalStrain,
tStep, VM_Total);
C.at(1, 1) = 1. + 2. * strainVector.at(1);
C.at(2, 2) = 1. + 2. * strainVector.at(2);
C.at(3, 3) = 1. + 2. * strainVector.at(3);
C.at(1, 2) = C.at(2, 1) = strainVector.at(6);
C.at(1, 3) = C.at(3, 1) = strainVector.at(5);
C.at(2, 3) = C.at(3, 2) = strainVector.at(4);
invC.beInverseOf(C);
J2 = C.giveDeterminant();
answer.resize(6);
double aux = ( K - 2. / 3. * G ) * ( J2 - 1. ) / 2. - G;
answer.at(1) = aux * invC.at(1, 1) + G;
answer.at(2) = aux * invC.at(2, 2) + G;
answer.at(3) = aux * invC.at(3, 3) + G;
answer.at(4) = aux * invC.at(2, 3);
answer.at(5) = aux * invC.at(1, 3);
answer.at(6) = aux * invC.at(1, 2);
// update gp
status->letTempStrainVectorBe(totalStrain);
status->letTempStressVectorBe(answer);
}
void
WinklerPasternakMaterial::giveRealStressVector_2dPlateSubSoil(FloatArray &answer, GaussPoint *gp, const FloatArray &reducedE, TimeStep *tStep)
{
FloatMatrix tangent;
this->give2dPlateSubSoilStiffMtrx(tangent, ElasticStiffness, gp, tStep);
answer.beProductOf(tangent, reducedE);
StructuralMaterialStatus *status = static_cast< StructuralMaterialStatus * >( this->giveStatus(gp) );
status->letTempStrainVectorBe(reducedE);
status->letTempStressVectorBe(answer);
}
void
FiberedCrossSection :: giveGeneralizedStress_Beam3d(FloatArray &answer, GaussPoint *gp, const FloatArray &strain, TimeStep *tStep)
{
double fiberThick, fiberWidth, fiberZCoord, fiberYCoord;
FloatArray fiberStrain, reducedFiberStress;
StructuralElement *element = static_cast< StructuralElement * >( gp->giveElement() );
FiberedCrossSectionInterface *interface;
if ( ( interface = static_cast< FiberedCrossSectionInterface * >( element->giveInterface(FiberedCrossSectionInterfaceType) ) ) == NULL ) {
OOFEM_ERROR("element with no fiber support encountered");
}
answer.resize(6);
answer.zero();
for ( int i = 1; i <= numberOfFibers; i++ ) {
GaussPoint *fiberGp = this->giveSlaveGaussPoint(gp, i - 1);
StructuralMaterial *fiberMat = static_cast< StructuralMaterial * >( domain->giveMaterial( fiberMaterials.at(i) ) );
// the question is whether this function should exist ?
// if yes the element details will be hidden.
// good idea also should be existence of element::GiveBmatrixOfLayer
// and computing strains here - but first idea looks better
// but treating of geometric non-linearities may become more complicated
// another approach - use several functions with assumed kinematic constraints
// resolve current layer z-coordinate
fiberThick = this->fiberThicks.at(i);
fiberWidth = this->fiberWidths.at(i);
fiberYCoord = fiberGp->giveNaturalCoordinate(1);
fiberZCoord = fiberGp->giveNaturalCoordinate(2);
interface->FiberedCrossSectionInterface_computeStrainVectorInFiber(fiberStrain, strain, fiberGp, tStep);
fiberMat->giveRealStressVector_Fiber(reducedFiberStress, fiberGp, fiberStrain, tStep);
// perform integration
// 1) membrane terms N, Qz, Qy
answer.at(1) += reducedFiberStress.at(1) * fiberWidth * fiberThick;
answer.at(2) += reducedFiberStress.at(2) * fiberWidth * fiberThick;
answer.at(3) += reducedFiberStress.at(3) * fiberWidth * fiberThick;
// 2) bending terms mx, my, mxy
answer.at(4) += ( reducedFiberStress.at(2) * fiberWidth * fiberThick * fiberYCoord -
reducedFiberStress.at(3) * fiberWidth * fiberThick * fiberZCoord );
answer.at(5) += reducedFiberStress.at(1) * fiberWidth * fiberThick * fiberZCoord;
answer.at(6) -= reducedFiberStress.at(1) * fiberWidth * fiberThick * fiberYCoord;
}
// now we must update master gp ///@ todo simply chosen the first fiber material as master material /JB
StructuralMaterialStatus *status = static_cast< StructuralMaterialStatus * >
( domain->giveMaterial( fiberMaterials.at(1) )->giveStatus(gp) );
status->letTempStrainVectorBe(strain);
status->letTempStressVectorBe(answer);
}
void
StructuralMaterialSettable :: giveRealStressVector_3d(FloatArray &answer,
GaussPoint *gp,
const FloatArray &totalStrain,
TimeStep *atTime)
{
StructuralMaterialStatus *status = static_cast< StructuralMaterialStatus * >( this->giveStatus(gp) );
const FloatArray& stressVector = status->giveStressVector();
status->letTempStrainVectorBe(totalStrain);
status->letTempStressVectorBe(stressVector);
answer = stressVector;
}
void
SimpleCrossSection :: giveGeneralizedStress_MembraneRot(FloatArray &answer, GaussPoint *gp, const FloatArray &strain, TimeStep *tStep)
{
FloatMatrix tangent;
this->giveMembraneRotStiffMtrx(tangent, ElasticStiffness, gp, tStep);
answer.beProductOf(tangent, strain);
StructuralMaterialStatus *status = static_cast< StructuralMaterialStatus * >( this->giveMaterial(gp)->giveStatus(gp) );
status->letTempStrainVectorBe(strain);
status->letTempStressVectorBe(answer);
///@todo We should support nonlinear behavior for the membrane part. In fact, should be even bundle the rotation part with the membrane?
/// We gain nothing from this design anyway as the rotation field is always separate. Separate manual integration by the element would be an option.
}
void
MicroplaneMaterial_Bazant :: giveRealStressVector(FloatArray &answer,
GaussPoint *gp,
const FloatArray &totalStrain,
TimeStep *tStep)
{
int i, mPlaneIndex, mPlaneIndex1;
double SvDash, SvSum = 0.;
double SD;
FloatArray mPlaneNormalStress(numberOfMicroplanes), mPlaneShear_L_Stress(numberOfMicroplanes),
mPlaneShear_M_Stress(numberOfMicroplanes);
double mPlaneIntegrationWeight;
Microplane *mPlane;
FloatArray mPlaneStressCmpns, mPlaneStrainCmpns;
FloatArray stressIncrement;
answer.resize(6);
answer.zero();
StructuralMaterialStatus *status = static_cast< StructuralMaterialStatus * >( this->giveStatus(gp) );
this->initTempStatus(gp);
for ( mPlaneIndex = 0; mPlaneIndex < numberOfMicroplanes; mPlaneIndex++ ) {
mPlane = this->giveMicroplane(mPlaneIndex, gp);
mPlaneIndex1 = mPlaneIndex + 1;
// compute strain projections on mPlaneIndex-th microplane
computeStrainVectorComponents(mPlaneStrainCmpns, mPlane, totalStrain);
// compute real stresses on this microplane
giveRealMicroplaneStressVector(mPlaneStressCmpns, mPlane, mPlaneStrainCmpns, tStep);
mPlaneNormalStress.at(mPlaneIndex1) = mPlaneStressCmpns.at(2);
mPlaneShear_L_Stress.at(mPlaneIndex1) = mPlaneStressCmpns.at(3);
mPlaneShear_M_Stress.at(mPlaneIndex1) = mPlaneStressCmpns.at(4);
mPlaneIntegrationWeight = this->giveMicroplaneIntegrationWeight(mPlane);
SvSum += mPlaneNormalStress.at(mPlaneIndex1) * mPlaneIntegrationWeight;
SD = mPlaneNormalStress.at(mPlaneIndex1) - mPlaneStressCmpns.at(1);
//SDSum += SD* mPlaneIntegrationWeight;
// perform homogenization
// mPlaneStressCmpns.at(1) je SVdash
// mPlaneStressCmpns.at(2) je SN
// mPlaneStressCmpns.at(3) je SL
// mPlaneStressCmpns.at(4) je SM
// answer (1 az 6)
for ( i = 0; i < 6; i++ ) {
answer.at(i + 1) += ( ( N [ mPlaneIndex ] [ i ] - Kronecker [ i ] / 3. ) * SD +
L [ mPlaneIndex ] [ i ] * mPlaneShear_L_Stress.at(mPlaneIndex1) +
M [ mPlaneIndex ] [ i ] * mPlaneShear_M_Stress.at(mPlaneIndex1) )
* mPlaneIntegrationWeight;
}
}
SvSum = SvSum * 6.;
//nakonec answer take *6
SvDash = mPlaneStressCmpns.at(1);
//volumetric stress is the same for all mplanes
//and does not need to be homogenized .
//Only updating accordinging to mean normal stress must be done.
//Use updateVolumetricStressTo() if necessary
// sv=min(integr(sn)/2PI,SvDash)
if ( SvDash > SvSum / 3. ) {
SvDash = SvSum / 3.;
answer.zero();
for ( mPlaneIndex = 0; mPlaneIndex < numberOfMicroplanes; mPlaneIndex++ ) {
mPlane = this->giveMicroplane(mPlaneIndex, gp);
mPlaneIndex1 = mPlaneIndex + 1;
updateVolumetricStressTo(mPlane, SvDash);
SD = mPlaneNormalStress.at(mPlaneIndex1) - SvDash;
mPlaneIntegrationWeight = this->giveMicroplaneIntegrationWeight(mPlane);
for ( i = 0; i < 6; i++ ) {
answer.at(i + 1) += ( ( N [ mPlaneIndex ] [ i ] - Kronecker [ i ] / 3. ) * SD +
L [ mPlaneIndex ] [ i ] * mPlaneShear_L_Stress.at(mPlaneIndex1) +
M [ mPlaneIndex ] [ i ] * mPlaneShear_M_Stress.at(mPlaneIndex1) )
* mPlaneIntegrationWeight;
}
}
}
answer.times(6.0);
//2nd constraint, addition of volumetric part
answer.at(1) += SvDash;
answer.at(2) += SvDash;
answer.at(3) += SvDash;
// uncomment this
//status -> letStrainIncrementVectorBe (reducedStrainIncrement);
status->letTempStrainVectorBe(totalStrain);
// uncomment this
// stressIncrement = answer;
// crossSection->giveReducedCharacteristicVector(stressIncrement, gp, answer);
// stressIncrement.subtract (status -> giveStressVector());
// status -> letStressIncrementVectorBe (stressIncrement);
status->letTempStressVectorBe(answer);
}
