int
SSPquad::update(void)
// this function updates variables for an incremental step n to n+1
{
// get trial displacement
const Vector &mDisp_1 = theNodes[0]->getTrialDisp();
const Vector &mDisp_2 = theNodes[1]->getTrialDisp();
const Vector &mDisp_3 = theNodes[2]->getTrialDisp();
const Vector &mDisp_4 = theNodes[3]->getTrialDisp();
// assemble displacement vector
Vector u(8);
u(0) = mDisp_1(0);
u(1) = mDisp_1(1);
u(2) = mDisp_2(0);
u(3) = mDisp_2(1);
u(4) = mDisp_3(0);
u(5) = mDisp_3(1);
u(6) = mDisp_4(0);
u(7) = mDisp_4(1);
Vector strain(3);
strain = Mmem*u;
theMaterial->setTrialStrain(strain);
return 0;
}
const Vector &
SSPquad::getResistingForce(void)
// this function computes the resisting force vector for the element
{
// get stress from the material
mStress = theMaterial->getStress();
// get trial displacement
const Vector &mDisp_1 = theNodes[0]->getTrialDisp();
const Vector &mDisp_2 = theNodes[1]->getTrialDisp();
const Vector &mDisp_3 = theNodes[2]->getTrialDisp();
const Vector &mDisp_4 = theNodes[3]->getTrialDisp();
Vector d(8);
d(0) = mDisp_1(0);
d(1) = mDisp_1(1);
d(2) = mDisp_2(0);
d(3) = mDisp_2(1);
d(4) = mDisp_3(0);
d(5) = mDisp_3(1);
d(6) = mDisp_4(0);
d(7) = mDisp_4(1);
// add stabilization force to internal force vector
mInternalForces = Kstab*d;
// add internal force from the stress -> fint = Kstab*d + 4*t*Jo*Mmem'*stress
mInternalForces.addMatrixTransposeVector(1.0, Mmem, mStress, 4.0*mThickness*J0);
// subtract body forces from internal force vector
double xi[4];
double eta[4];
xi[0] = -1.0;
xi[1] = 1.0;
xi[2] = 1.0;
xi[3] = -1.0;
eta[0] = -1.0;
eta[1] = -1.0;
eta[2] = 1.0;
eta[3] = 1.0;
if (applyLoad == 0) {
for (int i = 0; i < 4; i++) {
mInternalForces(2*i) -= b[0]*mThickness*(J0 + J1*xi[i] + J2*eta[i]);
mInternalForces(2*i+1) -= b[1]*mThickness*(J0 + J1*xi[i] + J2*eta[i]);
}
} else {
for (int i = 0; i < 4; i++) {
mInternalForces(2*i) -= appliedB[0]*mThickness*(J0 + J1*xi[i] + J2*eta[i]);
mInternalForces(2*i+1) -= appliedB[1]*mThickness*(J0 + J1*xi[i] + J2*eta[i]);
}
}
// inertial unbalance load
mInternalForces.addVector(1.0, Q, -1.0);
return mInternalForces;
}
const Vector &
SSPquadUP::getResistingForce(void)
// this function computes the resisting force vector for the element
{
Vector f1(8);
Vector f2(4);
Vector mStress(3);
// get stress from the material
mStress = theMaterial->getStress();
// get trial displacement
const Vector &mDisp_1 = theNodes[0]->getTrialDisp();
const Vector &mDisp_2 = theNodes[1]->getTrialDisp();
const Vector &mDisp_3 = theNodes[2]->getTrialDisp();
const Vector &mDisp_4 = theNodes[3]->getTrialDisp();
Vector d(8);
d(0) = mDisp_1(0);
d(1) = mDisp_1(1);
d(2) = mDisp_2(0);
d(3) = mDisp_2(1);
d(4) = mDisp_3(0);
d(5) = mDisp_3(1);
d(6) = mDisp_4(0);
d(7) = mDisp_4(1);
// add stabilization force to internal force vector
f1 = Kstab*d;
// add internal force from the stress
f1.addMatrixTransposeVector(1.0, Mmem, mStress, 4.0*mThickness*J0);
// get mass density from the material
double density = theMaterial->getRho();
// subtract body forces from internal force vector
double xi[4];
double eta[4];
xi[0] = -1.0; xi[1] = 1.0; xi[2] = 1.0; xi[3] = -1.0;
eta[0] = -1.0; eta[1] = -1.0; eta[2] = 1.0; eta[3] = 1.0;
if (applyLoad == 0) {
for (int i = 0; i < 4; i++) {
f1(2*i) -= density*b[0]*mThickness*(J0 + J1*xi[i] + J2*eta[i]);
f1(2*i+1) -= density*b[1]*mThickness*(J0 + J1*xi[i] + J2*eta[i]);
}
} else {
for (int i = 0; i < 4; i++) {
f1(2*i) -= density*appliedB[0]*mThickness*(J0 + J1*xi[i] + J2*eta[i]);
f1(2*i+1) -= density*appliedB[1]*mThickness*(J0 + J1*xi[i] + J2*eta[i]);
}
}
// account for fluid body forces
Matrix k(2,2);
Vector body(2);
// permeability tensor
k(0,0) = perm[0];
k(1,1) = perm[1];
// body force vector
if (applyLoad == 0) {
body(0) = b[0];
body(1) = b[1];
} else {
body(0) = appliedB[0];
body(1) = appliedB[1];
}
f2 = 4.0*J0*mThickness*fDens*dN*k*body;
// assemble full internal force vector for the element
mInternalForces(0) = f1(0);
mInternalForces(1) = f1(1);
mInternalForces(2) = f2(0);
mInternalForces(3) = f1(2);
mInternalForces(4) = f1(3);
mInternalForces(5) = f2(1);
mInternalForces(6) = f1(4);
mInternalForces(7) = f1(5);
mInternalForces(8) = f2(2);
mInternalForces(9) = f1(6);
mInternalForces(10) = f1(7);
mInternalForces(11) = f2(3);
// inertial unbalance load
mInternalForces.addVector(1.0, Q, -1.0);
return mInternalForces;
}