bool ASMs1D::getElementNodalRotations (TensorVec& T, size_t iel) const
{
#ifdef INDEX_CHECK
if (iel >= MNPC.size())
{
std::cerr <<" *** ASMs1D::getElementNodalRotations: Element index "<< iel
<<" out of range [0,"<< MNPC.size() <<">."<< std::endl;
return false;
}
#endif
T.clear();
if (nodalT.empty())
return true;
const IntVec& mnpc = MNPC[iel];
Tensor Tgl(elmCS[iel],true);
T.reserve(mnpc.size());
for (size_t i = 0; i < mnpc.size(); i++)
T.push_back(Tgl*nodalT[mnpc[i]]);
return true;
}
// set up the transformation matrix for orientation
void YamamotoBiaxialHDR::setUp()
{
const Vector &end1Crd = theNodes[0]->getCrds();
const Vector &end2Crd = theNodes[1]->getCrds();
Vector oriXp = end2Crd - end1Crd;
double elmLen = oriXp.Norm();
if (elmLen > DBL_EPSILON) {
if (oriX.Size() == 0) {
oriX.resize(3);
oriX = oriXp;
} else {
opserr << "WARNING YamamotoBiaxialHDR::setUp() - "
<< "element: " << this->getTag() << endln
<< "ignoring nodes and using specified "
<< "local x vector to determine orientation\n";
}
}
// check that vectors for orientation are of correct size
if (oriX.Size() != 3 || oriYp.Size() != 3) {
opserr << "YamamotoBiaxialHDR::setUp() - "
<< "element: " << this->getTag() << endln
<< "incorrect dimension of orientation vectors\n";
exit(-1);
}
// establish orientation of element for the transformation matrix
// z = x cross yp
Vector oriZ(3);
oriZ(0) = oriX(1)*oriYp(2) - oriX(2)*oriYp(1);
oriZ(1) = oriX(2)*oriYp(0) - oriX(0)*oriYp(2);
oriZ(2) = oriX(0)*oriYp(1) - oriX(1)*oriYp(0);
// y = z cross x
Vector oriY(3);
oriY(0) = oriZ(1)*oriX(2) - oriZ(2)*oriX(1);
oriY(1) = oriZ(2)*oriX(0) - oriZ(0)*oriX(2);
oriY(2) = oriZ(0)*oriX(1) - oriZ(1)*oriX(0);
// compute length(norm) of vectors
double xn = oriX.Norm();
double yn = oriY.Norm();
double zn = oriZ.Norm();
// check valid x and y vectors, i.e. not parallel and of zero length
if (xn == 0 || yn == 0 || zn == 0) {
opserr << "YamamotoBiaxialHDR::setUp() - "
<< "element: " << this->getTag() << endln
<< "invalid orientation vectors\n";
exit(-1);
}
// create transformation matrix from global to local system
Tgl.Zero();
Tgl(0,0) = Tgl(3,3) = Tgl(6,6) = Tgl(9,9) = oriX(0)/xn;
Tgl(0,1) = Tgl(3,4) = Tgl(6,7) = Tgl(9,10) = oriX(1)/xn;
Tgl(0,2) = Tgl(3,5) = Tgl(6,8) = Tgl(9,11) = oriX(2)/xn;
Tgl(1,0) = Tgl(4,3) = Tgl(7,6) = Tgl(10,9) = oriY(0)/yn;
Tgl(1,1) = Tgl(4,4) = Tgl(7,7) = Tgl(10,10) = oriY(1)/yn;
Tgl(1,2) = Tgl(4,5) = Tgl(7,8) = Tgl(10,11) = oriY(2)/yn;
Tgl(2,0) = Tgl(5,3) = Tgl(8,6) = Tgl(11,9) = oriZ(0)/zn;
Tgl(2,1) = Tgl(5,4) = Tgl(8,7) = Tgl(11,10) = oriZ(1)/zn;
Tgl(2,2) = Tgl(5,5) = Tgl(8,8) = Tgl(11,11) = oriZ(2)/zn;
// create transformation matrix from local to basic system (linear)
Tlb.Zero();
Tlb(0,0) = Tlb(1,1) = Tlb(2,2) = Tlb(3,3) = Tlb(4,4) = Tlb(5,5) = -1.0;
Tlb(0,6) = Tlb(1,7) = Tlb(2,8) = Tlb(3,9) = Tlb(4,10) = Tlb(5,11) = 1.0;
Tlb(1,5) = Tlb(1,11) = -0.5*elmLen;
Tlb(2,4) = Tlb(2,10) = 0.5*elmLen;
}
// set up the transformation matrix for orientation
void ElastomericBearingBoucWen2d::setUp()
{
const Vector &end1Crd = theNodes[0]->getCrds();
const Vector &end2Crd = theNodes[1]->getCrds();
Vector xp = end2Crd - end1Crd;
L = xp.Norm();
if (L > DBL_EPSILON) {
if (x.Size() == 0) {
x.resize(3);
x(0) = xp(0); x(1) = xp(1); x(2) = 0.0;
y.resize(3);
y(0) = -x(1); y(1) = x(0); y(2) = 0.0;
} else if (onP0) {
opserr << "WARNING ElastomericBearingBoucWen2d::setUp() - "
<< "element: " << this->getTag()
<< " - ignoring nodes and using specified "
<< "local x vector to determine orientation.\n";
}
}
// check that vectors for orientation are of correct size
if (x.Size() != 3 || y.Size() != 3) {
opserr << "ElastomericBearingBoucWen2d::setUp() - "
<< "element: " << this->getTag()
<< " - incorrect dimension of orientation vectors.\n";
exit(-1);
}
// establish orientation of element for the tranformation matrix
// z = x cross y
static Vector z(3);
z(0) = x(1)*y(2) - x(2)*y(1);
z(1) = x(2)*y(0) - x(0)*y(2);
z(2) = x(0)*y(1) - x(1)*y(0);
// y = z cross x
y(0) = z(1)*x(2) - z(2)*x(1);
y(1) = z(2)*x(0) - z(0)*x(2);
y(2) = z(0)*x(1) - z(1)*x(0);
// compute length(norm) of vectors
double xn = x.Norm();
double yn = y.Norm();
double zn = z.Norm();
// check valid x and y vectors, i.e. not parallel and of zero length
if (xn == 0 || yn == 0 || zn == 0) {
opserr << "ElastomericBearingBoucWen2d::setUp() - "
<< "element: " << this->getTag()
<< " - invalid orientation vectors.\n";
exit(-1);
}
// create transformation matrix from global to local system
Tgl.Zero();
Tgl(0,0) = Tgl(3,3) = x(0)/xn;
Tgl(0,1) = Tgl(3,4) = x(1)/xn;
Tgl(1,0) = Tgl(4,3) = y(0)/yn;
Tgl(1,1) = Tgl(4,4) = y(1)/yn;
Tgl(2,2) = Tgl(5,5) = z(2)/zn;
// create transformation matrix from local to basic system (linear)
Tlb.Zero();
Tlb(0,0) = Tlb(1,1) = Tlb(2,2) = -1.0;
Tlb(0,3) = Tlb(1,4) = Tlb(2,5) = 1.0;
Tlb(1,2) = -shearDistI*L;
Tlb(1,5) = -(1.0 - shearDistI)*L;
}
void ElasticTimoshenkoBeam2d::setUp()
{
// element projection
static Vector dx(2);
const Vector &ndICoords = theNodes[0]->getCrds();
const Vector &ndJCoords = theNodes[1]->getCrds();
dx = ndJCoords - ndICoords;
//if (nodeIInitialDisp != 0) {
// dx(0) -= nodeIInitialDisp[0];
// dx(1) -= nodeIInitialDisp[1];
//}
//if (nodeJInitialDisp != 0) {
// dx(0) += nodeJInitialDisp[0];
// dx(1) += nodeJInitialDisp[1];
//}
//if (nodeJOffset != 0) {
// dx(0) += nodeJOffset[0];
// dx(1) += nodeJOffset[1];
//}
//if (nodeIOffset != 0) {
// dx(0) -= nodeIOffset[0];
// dx(1) -= nodeIOffset[1];
//}
// determine the element length
L = dx.Norm();
if (L == 0.0) {
opserr << "ElasticTimoshenkoBeam2d::setUp() - "
<< "element: " << this->getTag() << " has zero length.\n";
return;
}
// create transformation matrix from global to local system
Tgl.Zero();
Tgl(0,0) = Tgl(1,1) = Tgl(3,3) = Tgl(4,4) = dx(0)/L;
Tgl(0,1) = Tgl(3,4) = dx(1)/L;
Tgl(1,0) = Tgl(4,3) = -dx(1)/L;
Tgl(2,2) = Tgl(5,5) = 1.0;
// determine ratio of bending to shear stiffness
phi = 12.0*E*Iz/(L*L*G*Avy);
// compute initial stiffness matrix in local system
kl.Zero();
kl(0,0) = kl(3,3) = E*A/L;
kl(0,3) = kl(3,0) = -kl(0,0);
double a1z = E*Iz/(1.0 + phi);
kl(1,1) = kl(4,4) = 12.0*a1z/(L*L*L);
kl(1,4) = kl(4,1) = -kl(1,1);
kl(2,2) = kl(5,5) = (4.0 + phi)*a1z/L;
kl(2,5) = kl(5,2) = (2.0 - phi)*a1z/L;
kl(1,2) = kl(2,1) = kl(1,5) = kl(5,1) = 6.0*a1z/(L*L);
kl(2,4) = kl(4,2) = kl(4,5) = kl(5,4) = -kl(1,2);
// compute geometric stiffness matrix in local system
klgeo.Zero();
if (nlGeo == 1) {
double b1z = 1.0/(30.0*L*pow(1.0 + phi,2));
klgeo(1,1) = klgeo(4,4) = b1z*(30.0*phi*phi + 60.0*phi + 36.0);
klgeo(1,4) = klgeo(4,1) = -klgeo(1,1);
klgeo(2,2) = klgeo(5,5) = b1z*L*L*(2.5*phi*phi + 5.0*phi + 4.0);
klgeo(2,5) = klgeo(5,2) = -b1z*L*L*(2.5*phi*phi + 5.0*phi + 1.0);
klgeo(1,2) = klgeo(2,1) = klgeo(1,5) = klgeo(5,1) = 3.0*L;
klgeo(2,4) = klgeo(4,2) = klgeo(4,5) = klgeo(5,4) = -klgeo(1,2);
}
// compute initial stiffness matrix in global system
Ki.addMatrixTripleProduct(0.0, Tgl, kl, 1.0);
// compute mass matrix in global system
M.Zero();
if (rho > 0.0) {
if (cMass == 0) {
// lumped mass matrix
double m = 0.5*rho*L;
for (int i=0; i<2; i++) {
M(i,i) = m;
M(i+3,i+3) = m;
}
} else {
// consistent mass matrix
Matrix mlTrn(6,6), mlRot(6,6), ml(6,6);
mlTrn.Zero(); mlRot.Zero(); ml.Zero();
double c1x = rho*L/210.0;
mlTrn(0,0) = mlTrn(3,3) = c1x*70.0;
mlTrn(0,3) = mlTrn(3,0) = c1x*35.0;
double c1z = c1x/pow(1.0 + phi,2);
mlTrn(1,1) = mlTrn(4,4) = c1z*(70.0*phi*phi + 147.0*phi + 78.0);
mlTrn(1,4) = mlTrn(4,1) = c1z*(35.0*phi*phi + 63.0*phi + 27.0);
mlTrn(2,2) = mlTrn(5,5) = c1z*L*L/4.0*(7.0*phi*phi + 14.0*phi + 8.0);
mlTrn(2,5) = mlTrn(5,2) = -c1z*L*L/4.0*(7.0*phi*phi + 14.0*phi + 6.0);
mlTrn(1,2) = mlTrn(2,1) = c1z*L/4.0*(35.0*phi*phi + 77.0*phi + 44.0);
mlTrn(4,5) = mlTrn(5,4) = -mlTrn(1,2);
mlTrn(1,5) = mlTrn(5,1) = -c1z*L/4.0*(35.0*phi*phi + 63.0*phi + 26.0);
mlTrn(2,4) = mlTrn(4,2) = -mlTrn(1,5);
double c2z = rho/A*Iz/(30.0*L*pow(1.0 + phi,2));
mlRot(1,1) = mlRot(4,4) = c2z*36.0;
mlRot(1,4) = mlRot(4,1) = -mlRot(1,1);
mlRot(2,2) = mlRot(5,5) = c2z*L*L*(10.0*phi*phi + 5.0*phi + 4.0);
mlRot(2,5) = mlRot(5,2) = c2z*L*L*(5.0*phi*phi - 5.0*phi - 1.0);
mlRot(1,2) = mlRot(2,1) = mlRot(1,5) = mlRot(5,1) = -c2z*L*(15.0*phi - 3.0);
mlRot(2,4) = mlRot(4,2) = mlRot(4,5) = mlRot(5,4) = -mlRot(1,2);
// add translational and rotational parts
ml = mlTrn + mlRot;
// transform from local to global system
M.addMatrixTripleProduct(0.0, Tgl, ml, 1.0);
}
}
}
// set transformation matrix from global to local system
void TwoNodeLink::setTranGlobalLocal()
{
// resize transformation matrix and zero it
Tgl.resize(numDOF,numDOF);
Tgl.Zero();
// switch on dimensionality of element
switch (elemType) {
case D1N2:
Tgl(0,0) = Tgl(1,1) = trans(0,0);
break;
case D2N4:
Tgl(0,0) = Tgl(2,2) = trans(0,0);
Tgl(0,1) = Tgl(2,3) = trans(0,1);
Tgl(1,0) = Tgl(3,2) = trans(1,0);
Tgl(1,1) = Tgl(3,3) = trans(1,1);
break;
case D2N6:
Tgl(0,0) = Tgl(3,3) = trans(0,0);
Tgl(0,1) = Tgl(3,4) = trans(0,1);
Tgl(1,0) = Tgl(4,3) = trans(1,0);
Tgl(1,1) = Tgl(4,4) = trans(1,1);
Tgl(2,2) = Tgl(5,5) = trans(2,2);
break;
case D3N6:
Tgl(0,0) = Tgl(3,3) = trans(0,0);
Tgl(0,1) = Tgl(3,4) = trans(0,1);
Tgl(0,2) = Tgl(3,5) = trans(0,2);
Tgl(1,0) = Tgl(4,3) = trans(1,0);
Tgl(1,1) = Tgl(4,4) = trans(1,1);
Tgl(1,2) = Tgl(4,5) = trans(1,2);
Tgl(2,0) = Tgl(5,3) = trans(2,0);
Tgl(2,1) = Tgl(5,4) = trans(2,1);
Tgl(2,2) = Tgl(5,5) = trans(2,2);
break;
case D3N12:
Tgl(0,0) = Tgl(3,3) = Tgl(6,6) = Tgl(9,9) = trans(0,0);
Tgl(0,1) = Tgl(3,4) = Tgl(6,7) = Tgl(9,10) = trans(0,1);
Tgl(0,2) = Tgl(3,5) = Tgl(6,8) = Tgl(9,11) = trans(0,2);
Tgl(1,0) = Tgl(4,3) = Tgl(7,6) = Tgl(10,9) = trans(1,0);
Tgl(1,1) = Tgl(4,4) = Tgl(7,7) = Tgl(10,10) = trans(1,1);
Tgl(1,2) = Tgl(4,5) = Tgl(7,8) = Tgl(10,11) = trans(1,2);
Tgl(2,0) = Tgl(5,3) = Tgl(8,6) = Tgl(11,9) = trans(2,0);
Tgl(2,1) = Tgl(5,4) = Tgl(8,7) = Tgl(11,10) = trans(2,1);
Tgl(2,2) = Tgl(5,5) = Tgl(8,8) = Tgl(11,11) = trans(2,2);
break;
}
}
