const Matrix&
PFEMElement2DBubble::getDamp()
{
// resize K
int ndf = this->getNumDOF();
K.resize(ndf, ndf);
K.Zero();
Vector G(6);
getG(G);
Matrix L(3,3);
getL(L);
// other matrices
for(int a=0; a<3; a++) {
for(int b=0; b<3; b++) {
K(numDOFs(2*a+1), numDOFs(2*b)) = G(2*b); // GxT
K(numDOFs(2*a+1), numDOFs(2*b)+1) = G(2*b+1); // GyT
K(numDOFs(2*a), numDOFs(2*b+1)) = -G(2*a); // -Gx
K(numDOFs(2*a)+1, numDOFs(2*b+1)) = -G(2*a+1); // -Gy
K(numDOFs(2*a+1), numDOFs(2*b+1)) = L(a,b); // bubble
}
}
//opserr<<"K = "<<K;
return K;
}
int
PFEMElement2DCompressible::recvSelf(int commitTag, Channel &theChannel, FEM_ObjectBroker &theBroker)
{
int res;
int dataTag = this->getDbTag();
// receive vector
static Vector data(12);
res = theChannel.recvVector(dataTag, commitTag, data);
if(res < 0) {
opserr<<"WARNING: PFEMElement2DCompressible::recvSelf - failed to receive vector\n";
return -1;
}
this->setTag((int)data(0));
rho = data(1);
mu = data(2);
bx = data(3);
by = data(4);
for(int i=0; i<3; i++) {
dNdx[i] = data(5+i);
dNdy[i] = data(8+i);
}
J = data(11);
for(int i=0; i<6; i++) {
ntags(i) = (int)data(12+i);
numDOFs(i) = (int)data(18+i);
}
numDOFs(6) = (int)data(24);
return 0;
}
int
PFEMElement2DCompressible::sendSelf(int commitTag, Channel &theChannel)
{
int res = 0;
int dataTag = this->getDbTag();
// send vector
static Vector data(25);
data(0) = this->getTag();
data(1) = rho;
data(2) = mu;
data(3) = bx;
data(4) = by;
for(int i=0; i<3; i++) {
data(5+i) = dNdx[i];
data(8+i) = dNdy[i];
}
data(11) = J;
for(int i=0; i<6; i++) {
data(12+i) = ntags(i);
data(18+i) = numDOFs(i);
}
data(24) = numDOFs(6);
res = theChannel.sendVector(dataTag, commitTag, data);
if(res < 0) {
opserr<<"WARNING: PFEMElement2DCompressible::sendSelf - "<<this->getTag()<<" failed to send vector\n";
return -1;
}
return 0;
}
const Matrix&
PFEMElement2DBubble::getMass()
{
// resize K
int ndf = this->getNumDOF();
K.resize(ndf, ndf);
K.Zero();
double m = getM();
double mp = getMp();
// mass
for(int a=0; a<3; a++) {
K(numDOFs(2*a), numDOFs(2*a)) = m; // Mxd
K(numDOFs(2*a)+1, numDOFs(2*a)+1) = m; // Myd
for(int b=0; b<3; b++) {
if(a == b) {
K(numDOFs(2*a+1), numDOFs(2*b+1)) = 2*mp; // Mp
} else {
K(numDOFs(2*a+1), numDOFs(2*b+1)) = mp; // Mp
}
}
}
//opserr<<"M = "<<K;
return K;
}
const Vector&
PFEMElement2DBubble::getResistingForceIncInertia()
{
// resize P
int ndf = this->getNumDOF();
P.resize(ndf);
P.Zero();
// get velocity, accleration
Vector v(ndf), vdot(ndf);
for(int i=0; i<3; i++) {
const Vector& accel = nodes[2*i]->getTrialAccel();
vdot(numDOFs(2*i)) = accel(0);
vdot(numDOFs(2*i)+1) = accel(1);
const Vector& accel2 = nodes[2*i+1]->getTrialAccel(); // pressure
vdot(numDOFs(2*i+1)) = accel2(0);
const Vector& vel = nodes[2*i]->getTrialVel();
v(numDOFs(2*i)) = vel(0);
v(numDOFs(2*i)+1) = vel(1);
const Vector& vel2 = nodes[2*i+1]->getTrialVel(); // pressure
v(numDOFs(2*i+1)) = vel2(0);
}
// bubble force
Vector fp(3);
getFp(fp);
// internal force
P.addMatrixVector(1.0, getMass(), vdot, 1.0);
P.addMatrixVector(1.0, getDamp(), v, 1.0);
// external force
Vector F(6);
getF(F);
for(int i=0; i<3; i++) {
P(numDOFs(2*i)) -= F(2*i);
P(numDOFs(2*i)+1) -= F(2*i+1);
P(numDOFs(2*i+1)) -= fp(i);
}
//opserr<<"F = "<<F;
return P;
}
const Matrix&
PFEMElement2DCompressible::getMass()
{
// resize K
int ndf = this->getNumDOF();
K.resize(ndf, ndf);
K.Zero();
double J2 = J/2.;
// mass
for(int a=0; a<3; a++) {
for(int b=0; b<3; b++) {
double m = rho*J2/12.0;
if(a == b) m *= 2.0;
K(numDOFs(2*a), numDOFs(2*b)) = m; // Mx
K(numDOFs(2*a)+1, numDOFs(2*b)+1) = m; // My
m = J2/12.0/kappa;
if(a == b) m *= 2.0;
K(numDOFs(2*a+1), numDOFs(2*a+1)) += m; // Mp
}
}
return K;
}
const Vector&
PFEMElement2DCompressible::getResistingForceIncInertia()
{
// resize P
int ndf = this->getNumDOF();
P.resize(ndf);
P.Zero();
// get velocity, accleration
Vector v(ndf), vdot(ndf);
for(int i=0; i<3; i++) {
const Vector& accel = nodes[2*i]->getTrialAccel();
vdot(numDOFs(2*i)) = accel(0);
vdot(numDOFs(2*i)+1) = accel(1);
const Vector& accel2 = nodes[2*i+1]->getTrialAccel();
vdot(numDOFs(2*i+1)) = accel2(0);
const Vector& vel = nodes[2*i]->getTrialVel();
v(numDOFs(2*i)) = vel(0);
v(numDOFs(2*i)+1) = vel(1);
const Vector& vel2 = nodes[2*i+1]->getTrialVel();
v(numDOFs(2*i+1)) = vel2(0);
}
// Ma+k1v-Gp
// Gt*v+Mp*p
P.addMatrixVector(1.0, getMass(), vdot, 1.0);
P.addMatrixVector(1.0, getDamp(), v, 1.0);
// f
double J2 = J/2.0;
for(int i=0; i<3; i++) {
P(numDOFs(2*i)) -= rho*bx/3.*J2;
P(numDOFs(2*i)+1) -= rho*by/3.*J2;
}
return P;
}
const Matrix&
PFEMElement3D::getMass()
{
// resize K
int ndf = this->getNumDOF();
K.resize(ndf, ndf);
K.Zero();
// mass
for(int a=0; a<4; a++) {
double m = rho*J/24.0;
K(numDOFs(2*a), numDOFs(2*a)) = m; // Mxd
K(numDOFs(2*a)+1, numDOFs(2*a)+1) = m; // Myd
K(numDOFs(2*a)+2, numDOFs(2*a)+2) = m; // Mzd
}
return K;
}
const Vector &
PFEMElement2DBubble::getResistingForceSensitivity(int gradnumber)
{
// resize P
int ndf = this->getNumDOF();
P.resize(ndf);
P.Zero();
Vector dF(6), dFp(3), vdot(6), v(6), p(3), du(6);
for(int i=0; i<3; i++) {
const Vector& accel = nodes[2*i]->getTrialAccel();
vdot(2*i) = accel(0);
vdot(2*i+1) = accel(1);
const Vector& vel = nodes[2*i]->getTrialVel();
v(2*i) = vel(0);
v(2*i+1) = vel(1);
const Vector& vel2 = nodes[2*i+1]->getTrialVel(); // pressure
p(i) = vel2(0);
du(2*i) = nodes[2*i]->getDispSensitivity(1,gradnumber);
du(2*i+1) = nodes[2*i]->getDispSensitivity(2,gradnumber);
}
// consditional sensitivity
getdF(dF);
double dm = getdM();
dF.addVector(-1.0, vdot, dm);
getdFp(dFp);
Matrix dl;
getdL(dl);
dFp.addMatrixVector(-1.0, dl, p, 1.0);
// geometric sensitivity
Matrix dM, dg, df;
getdM(vdot, dM);
getdG(p, dg);
getdF(df);
dF.addMatrixVector(1.0, dM, du, 1.0);
dF.addMatrixVector(1.0, dg, du, -1.0);
dF.addMatrixVector(1.0, df, du, -1.0);
Matrix dgt, dL, dfp;
getdGt(v, dgt);
getdL(p, dL);
getdFp(dfp);
dFp.addMatrixVector(1.0, dgt, du, 1.0);
dFp.addMatrixVector(1.0, dL, du, 1.0);
dFp.addMatrixVector(1.0, dfp, du, -1.0);
// copy
for(int i=0; i<3; i++) {
P(numDOFs(2*i)) += dF(2*i);
P(numDOFs(2*i)+1) += dF(2*i+1);
P(numDOFs(2*i+1)) += dFp(i);
}
return P;
}
void
PFEMElement2DBubble::setDomain(Domain *theDomain)
{
numDOFs.resize(7);
this->DomainComponent::setDomain(theDomain);
if(theDomain == 0) {
return;
}
numDOFs.Zero();
int ndf = 0;
int eletag = this->getTag();
for(int i=0; i<3; i++) {
// set ndf
numDOFs(2*i) = ndf;
// get node
nodes[2*i] = theDomain->getNode(ntags(2*i));
if(nodes[2*i] == 0) {
opserr<<"WARNING: node "<<ntags(2*i)<<" does not exist ";
opserr<<"in PFEMElement2DBubble - setDomain() "<<eletag<<"\n ";
return;
}
ndf += nodes[2*i]->getNumberDOF();
// set ndf
numDOFs(2*i+1) = ndf;
// get pc
int pndf = 1;
thePCs[i] = theDomain->getPressure_Constraint(ntags(2*i));
if(thePCs[i] != 0) {
thePCs[i]->setDomain(theDomain);
} else {
thePCs[i] = new Pressure_Constraint(ntags(2*i), pndf);
if(thePCs[i] == 0) {
opserr<<"WARNING: no enough memory for Pressure_Constraint -- ";
opserr<<"PFEMElement2DBubble::setDomain "<<eletag<<"\n";
return;
}
if(theDomain->addPressure_Constraint(thePCs[i]) == false) {
opserr<<"WARNING: failed to add Pressure_Constraint to domain -- ";
opserr<<"PFEMElement2DBubble::setDomain "<<eletag<<"\n";
delete thePCs[i];
thePCs[i] = 0;
return;
}
}
// connect
thePCs[i]->connect(eletag);
// get pressure node
// ntags(2*i+1) = thePCs[i]->getPressureNode();
// nodes[2*i+1] = theDomain->getNode(ntags(2*i+1));
nodes[2*i+1] = thePCs[i]->getPressureNode();
if(nodes[2*i+1] == 0) {
opserr<<"WARNING: pressure node does not exist ";
opserr<<"in PFEMElement2DBubble - setDomain() "<<eletag<<"\n ";
return;
}
ntags(2*i+1) = nodes[2*i+1]->getTag();
ndf += nodes[2*i+1]->getNumberDOF();
}
numDOFs(numDOFs.Size()-1) = ndf;
}
int
PFEMElement2DBubble::getNumDOF()
{
if(numDOFs.Size() == 0) return 0;
return numDOFs(numDOFs.Size()-1);
}
int
PFEMElement3D::getNumDOF()
{
return numDOFs(numDOFs.Size()-1);
}
const Vector&
PFEMElement3D::getResistingForceIncInertia()
{
// resize P
int ndf = this->getNumDOF();
P.resize(ndf);
P.Zero();
// get velocity, accleration
Vector v(ndf), vdot(ndf);
for(int i=0; i<4; i++) {
const Vector& accel = nodes[2*i]->getTrialAccel();
vdot(numDOFs(2*i)) = accel(0);
vdot(numDOFs(2*i)+1) = accel(1);
vdot(numDOFs(2*i)+2) = accel(2);
const Vector& vel = nodes[2*i]->getTrialVel();
v(numDOFs(2*i)) = vel(0);
v(numDOFs(2*i)+1) = vel(1);
v(numDOFs(2*i)+2) = vel(2);
const Vector& vel2 = nodes[2*i+1]->getTrialVel();
v(numDOFs(2*i+1)) = vel2(0);
v(numDOFs(2*i+1)+1) = vel2(1);
v(numDOFs(2*i+1)+2) = vel2(2);
v(numDOFs(2*i+1)+3) = vel2(3);
}
double d = v.Norm();
if(d!=d) opserr<<"v "<<this->getTag()<<"\n";
d = vdot.Norm();
if(d!=d) opserr<<"vdot "<<this->getTag()<<"\n";
P.addMatrixVector(1.0, getMass(), vdot, 1.0);
P.addMatrixVector(1.0, getDampWithK(), v, 1.0);
Vector ones(ndf);
for(int i=0;i<ndf;i++) ones(i) = 1.0;
Vector Q1(ndf), Q2(ndf);
Q1.addMatrixVector(1.0, getMass(), ones, 1.0);
Q2.addMatrixVector(1.0, getDampWithK(), ones, 1.0);
d = Q1.Norm();
if(d!=d) opserr<<"mass "<<this->getTag()<<"\n";
d = Q2.Norm();
if(d!=d) {
opserr<<"damp "<<this->getTag()<<"\n";
exit(1);
}
// get Jacobi
for(int i=0; i<4; i++) {
P(numDOFs(2*i)) -= rho*bx/24.*J;
P(numDOFs(2*i)+1) -= rho*by/24.*J;
P(numDOFs(2*i)+2) -= rho*bz/24.*J;
}
return P;
}
const Matrix&
PFEMElement3D::getDampWithK()
{
// resize K
int ndf = this->getNumDOF();
K.resize(ndf, ndf);
K.Zero();
double V = fabs(J/6.0);
double h = exp(log(V)/3.0); // cubic root of V
double tau = 1./(rho/ops_Dt+8*mu/(3*h*h));
for(int a=0; a<4; a++) {
for(int b=0; b<4; b++) {
// K(1,1:3)
K(numDOFs(2*a), numDOFs(2*b))
= mu*J/6.0*(2*dNdx[a]*dNdx[b]+dNdy[a]*dNdy[b]+dNdz[a]*dNdz[b]);
K(numDOFs(2*a), numDOFs(2*b)+1) = mu*J/6.0*dNdy[a]*dNdx[b];
K(numDOFs(2*a), numDOFs(2*b)+2) = mu*J/6.0*dNdz[a]*dNdx[b];
// K(2,1:3)
K(numDOFs(2*a)+1, numDOFs(2*b)) = mu*J/6.0*dNdx[a]*dNdy[b];
K(numDOFs(2*a)+1, numDOFs(2*b)+1)
= mu*J/6.0*(2*dNdy[a]*dNdy[b]+dNdx[a]*dNdx[b]+dNdz[a]*dNdz[b]);
K(numDOFs(2*a)+1, numDOFs(2*b)+2) = mu*J/6.0*dNdz[a]*dNdy[b];
// K(3,1:3)
K(numDOFs(2*a)+2, numDOFs(2*b)) = mu*J/6.0*dNdx[a]*dNdz[b];
K(numDOFs(2*a)+2, numDOFs(2*b)+1) = mu*J/6.0*dNdy[a]*dNdz[b];
K(numDOFs(2*a)+2, numDOFs(2*b)+2)
= mu*J/6.0*(2*dNdz[a]*dNdz[b]+dNdx[a]*dNdx[b]+dNdy[a]*dNdy[b]);
K(numDOFs(2*a), numDOFs(2*b+1)) = -dNdx[a]/24.*J; // -Gx
K(numDOFs(2*a)+1, numDOFs(2*b+1)) = -dNdy[a]/24.*J; // -Gy
K(numDOFs(2*a)+2, numDOFs(2*b+1)) = -dNdz[a]/24.*J; // -Gz
K(numDOFs(2*a+1), numDOFs(2*b)) = dNdx[b]/24.*J; // GxT
K(numDOFs(2*a+1), numDOFs(2*b)+1) = dNdy[b]/24.*J; // GyT
K(numDOFs(2*a+1), numDOFs(2*b)+2) = dNdz[b]/24.*J; // GzT
K(numDOFs(2*a+1), numDOFs(2*b+1))
= tau*J/6.0*(dNdx[a]*dNdx[b]+dNdy[a]*dNdy[b]+dNdz[a]*dNdz[b]); // L
K(numDOFs(2*a+1), numDOFs(2*b+1)+1) = tau*dNdx[a]/24.*J; // Qx
K(numDOFs(2*a+1), numDOFs(2*b+1)+2) = tau*dNdy[a]/24.*J; // Qy
K(numDOFs(2*a+1), numDOFs(2*b+1)+3) = tau*dNdz[a]/24.*J; // Qz
K(numDOFs(2*a+1)+1, numDOFs(2*b+1)) = tau*dNdx[b]/24.*J; // QxT
K(numDOFs(2*a+1)+2, numDOFs(2*b+1)) = tau*dNdy[b]/24.*J; // QyT
K(numDOFs(2*a+1)+3, numDOFs(2*b+1)) = tau*dNdz[b]/24.*J; // QzT
}
double m = tau*J/24.0;
K(numDOFs(2*a+1)+1, numDOFs(2*a+1)+1) = m; // Mhatxd
K(numDOFs(2*a+1)+2, numDOFs(2*a+1)+2) = m; // Mhatyd
K(numDOFs(2*a+1)+3, numDOFs(2*a+1)+3) = m; // Mhatzd
}
return K;
}
const Matrix&
PFEMElement2DCompressible::getDamp()
{
// resize K
int ndf = this->getNumDOF();
K.resize(ndf, ndf);
K.Zero();
double J2 = J/2.;
double lambda = -2*mu/3.0;
for(int a=0; a<3; a++) {
for(int b=0; b<3; b++) {
K(numDOFs(2*a), numDOFs(2*b)) += mu*J2*(2*dNdx[a]*dNdx[b] + dNdy[a]*dNdy[b]); // K1
K(numDOFs(2*a), numDOFs(2*b)+1) += mu*J2*dNdy[a]*dNdx[b]; // K1
K(numDOFs(2*a)+1, numDOFs(2*b)) += mu*J2*dNdx[a]*dNdy[b]; // K1
K(numDOFs(2*a)+1, numDOFs(2*b)+1) += mu*J2*(2*dNdy[a]*dNdy[b] + dNdx[a]*dNdx[b]); // K1
K(numDOFs(2*a), numDOFs(2*b)) += lambda*J2*dNdx[a]*dNdx[b]; // K2
K(numDOFs(2*a), numDOFs(2*b)+1) += lambda*J2*dNdx[a]*dNdy[b]; // K2
K(numDOFs(2*a)+1, numDOFs(2*b)) += lambda*J2*dNdy[a]*dNdx[b]; // K2
K(numDOFs(2*a)+1, numDOFs(2*b)+1) += lambda*J2*dNdy[a]*dNdy[b]; // K2
K(numDOFs(2*a), numDOFs(2*b+1)) += -dNdx[a]/3.*J2; // -Gx
K(numDOFs(2*a)+1, numDOFs(2*b+1)) += -dNdy[a]/3.*J2; // -Gy
K(numDOFs(2*a+1), numDOFs(2*b)) += dNdx[b]/3.*J2; // GxT
K(numDOFs(2*a+1), numDOFs(2*b)+1) += dNdy[b]/3.*J2; // GyT
// K(numDOFs(2*a+1), numDOFs(2*b+1)) += Lfact*tau*J2*(dNdx[a]*dNdx[b] + dNdy[a]*dNdy[b]); // L
// K(numDOFs(2*a+1), numDOFs(2*b+1)+1) = tau*dNdx[a]/3.*J2; // Qx
// K(numDOFs(2*a+1), numDOFs(2*b+1)+2) = tau*dNdy[a]/3.*J2; // Qy
// K(numDOFs(2*a+1)+1, numDOFs(2*b+1)) = tau*dNdx[b]/3.*J2; // QxT
// K(numDOFs(2*a+1)+2, numDOFs(2*b+1)) = tau*dNdy[b]/3.*J2; // QyT
}
// double m = tau*J2/3.0;
// K(numDOFs(2*a+1)+1, numDOFs(2*a+1)+1) = m; // Mhatxd
// K(numDOFs(2*a+1)+2, numDOFs(2*a+1)+2) = m; // Mhatyd
}
return K;
}
