const Matrix &
SSPquad::getMass(void)
{
mMass.Zero();
// get mass density from the material
double density = theMaterial->getRho();
// return zero matrix if density is zero
if (density == 0.0) {
return mMass;
}
// local coordinates of nodes
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;
double massTerm;
for (int i = 0; i < 4; i++) {
massTerm = density*mThickness*(J0 + J1*xi[i] + J2*eta[i]);
mMass(2*i,2*i) += massTerm;
mMass(2*i+1,2*i+1) += massTerm;
}
return mMass;
}
const Matrix &
SSPquadUP::getMass(void)
{
mMass.Zero();
// compute compressibility matrix term
double oneOverQ = -0.25*J0*mThickness*mPorosity/fBulk;
// get mass density from the material
double density = theMaterial->getRho();
// transpose the shape function derivative array
Matrix dNp(2,4);
dNp(0,0) = dN(0,0); dNp(0,1) = dN(1,0); dNp(0,2) = dN(2,0); dNp(0,3) = dN(3,0);
dNp(1,0) = dN(0,1); dNp(1,1) = dN(1,1); dNp(1,2) = dN(2,1); dNp(1,3) = dN(3,1);
// compute stabilization matrix for incompressible problems
Matrix Kp(4,4);
Kp = -4.0*mAlpha*J0*mThickness*dN*dNp;
// return zero matrix if density is zero
if (density == 0.0) {
return mMass;
}
// full mass matrix for the element [ M 0 ]
// includes M and S submatrices [ 0 -S ]
for (int i = 0; i < 4; i++) {
int I = 2*i;
int Ip1 = 2*i+1;
int II = 3*i;
int IIp1 = 3*i+1;
int IIp2 = 3*i+2;
for (int j = 0; j < 4; j++) {
int J = 2*j;
int Jp1 = 2*j+1;
int JJ = 3*j;
int JJp1 = 3*j+1;
int JJp2 = 3*j+2;
mMass(II,JJ) = mSolidM(I,J);
mMass(IIp1,JJ) = mSolidM(Ip1,J);
mMass(IIp1,JJp1) = mSolidM(Ip1,Jp1);
mMass(II,JJp1) = mSolidM(I,Jp1);
// contribution of compressibility matrix
mMass(IIp2,JJp2) = Kp(i,j) + oneOverQ;
}
}
return mMass;
}
const Vector &
SSPquad::getResistingForceIncInertia()
{
// get mass density from the material
double density = theMaterial->getRho();
// if density is zero only add damping terms
if (density == 0.0) {
this->getResistingForce();
// add the damping forces if rayleigh damping
if (betaK != 0.0 || betaK0 != 0.0 || betaKc != 0.0) {
mInternalForces += this->getRayleighDampingForces();
}
return mInternalForces;
}
const Vector &accel1 = theNodes[0]->getTrialAccel();
const Vector &accel2 = theNodes[1]->getTrialAccel();
const Vector &accel3 = theNodes[2]->getTrialAccel();
const Vector &accel4 = theNodes[3]->getTrialAccel();
static double a[8];
a[0] = accel1(0);
a[1] = accel1(1);
a[2] = accel2(0);
a[3] = accel2(1);
a[4] = accel3(0);
a[5] = accel3(1);
a[6] = accel4(0);
a[7] = accel4(1);
// compute current resisting force
this->getResistingForce();
// compute mass matrix
this->getMass();
for (int i = 0; i < 8; i++) {
mInternalForces(i) += mMass(i,i)*a[i];
}
// add the damping forces if rayleigh damping
if (alphaM != 0 || betaK != 0.0 || betaK0 != 0.0 || betaKc != 0.0) {
mInternalForces += this->getRayleighDampingForces();
}
return mInternalForces;
}
int
SSPquadUP::addInertiaLoadToUnbalance(const Vector &accel)
{
// get mass density from the material
double density = theMaterial->getRho();
// do nothing if density is zero
if (density == 0.0) {
return 0;
}
// Get R * accel from the nodes
const Vector &Raccel1 = theNodes[0]->getRV(accel);
const Vector &Raccel2 = theNodes[1]->getRV(accel);
const Vector &Raccel3 = theNodes[2]->getRV(accel);
const Vector &Raccel4 = theNodes[3]->getRV(accel);
if (3 != Raccel1.Size() || 3 != Raccel2.Size() || 3 != Raccel3.Size() || 3 != Raccel4.Size()) {
opserr << "SSPquadUP::addInertiaLoadToUnbalance matrix and vector sizes are incompatable\n";
return -1;
}
static double ra[12];
ra[0] = Raccel1(0);
ra[1] = Raccel1(1);
ra[2] = 0.0;
ra[3] = Raccel2(0);
ra[4] = Raccel2(1);
ra[5] = 0.0;
ra[6] = Raccel3(0);
ra[7] = Raccel3(1);
ra[8] = 0.0;
ra[9] = Raccel4(0);
ra[10] = Raccel4(1);
ra[11] = 0.0;
// compute mass matrix
this->getMass();
for (int i = 0; i < 8; i++) {
Q(i) += -mMass(i,i)*ra[i];
}
return 0;
}
