const Matrix &
BeamContact2D::getTangentStiff(void)
// this function computes the tangent stiffness matrix for the element
{
mTangentStiffness.Zero();
if (inContact) {
Matrix Cmat = theMaterial->getTangent();
double Css = Cmat(1,1);
double Csn = Cmat(1,2);
for (int i = 0; i < BC2D_NUM_DOF-2; i++) {
for (int j = 0; j < BC2D_NUM_DOF-2; j++) {
mTangentStiffness(i,j) = mBs(i)*mBs(j)*Css;
}
}
for (int i = 0; i < BC2D_NUM_DOF-2; i++) {
mTangentStiffness(8,i) = -mBn(i);
mTangentStiffness(i,8) = -mBn(i) + Csn*mBs(i);
}
mTangentStiffness(9,9) = 1.0;
} else {
mTangentStiffness(8,8) = 1.0;
mTangentStiffness(9,9) = 1.0;
}
return mTangentStiffness;
}
const Vector &
BeamContact2D::getResistingForce()
// this function computes the resisting force vector for the element
{
mInternalForces.Zero();
// get contact "stress" vector
Vector stress = theMaterial->getStress();
if (inContact) {
for (int i = 0; i < BC2D_NUM_DOF - 2; i++) {
mInternalForces(i) = -mLambda*mBn(i) + stress(1)*mBs(i);
}
mInternalForces(BC2D_NUM_DOF - 2) = -mGap;
} else {
mInternalForces(BC2D_NUM_DOF - 2) = mLambda;
}
return mInternalForces;
}
const Matrix &
BeamContact2Dp::getTangentStiff(void)
// this function computes the tangent stiffness matrix for the element
{
mTangentStiffness.Zero();
if (inContact) {
Matrix Cmat = theMaterial->getTangent();
double Css = Cmat(1,1);
double Csn = Cmat(1,2);
for (int i = 0; i < BC2D_NUM_DOF; i++) {
for (int j = 0; j < BC2D_NUM_DOF; j++) {
mTangentStiffness(i,j) = mBs(i)*mBs(j)*Css - mPenalty*(Csn*mBs(i)*mBn(j) - mBn(i)*mBn(j));
}
}
}
return mTangentStiffness;
}
void
BeamContact2Dp::ComputeB(void)
// this function computes the finite element equation vectors Bn and Bs
{
double Ka1n;
double Kb1n;
double Ka1g;
double Kb1g;
Vector a1(BC2D_NUM_DIM);
Vector b1(BC2D_NUM_DIM);
// initialize Bn and Bs
mBn.Zero();
mBs.Zero();
// get tangent vectors
a1 = Geta1();
b1 = Getb1();
// compute terms for vector Bn
Ka1n = (mEyeS*a1)^mNormal;
Kb1n = (mEyeS*b1)^mNormal;
mBn(0) = -mShape(0)*mNormal(0);
mBn(1) = -mShape(0)*mNormal(1);
mBn(2) = -mShape(1)*mLength*Ka1n;
mBn(3) = -mShape(2)*mNormal(0);
mBn(4) = -mShape(2)*mNormal(1);
mBn(5) = -mShape(3)*mLength*Kb1n;
mBn(6) = mNormal(0);
mBn(7) = mNormal(1);
// compute terms for vector Bs
Ka1g = (mEyeS*a1)^mg_xi;
Kb1g = (mEyeS*b1)^mg_xi;
mBs(0) = -mg_xi(0)*(mShape(0) + mRadius*mDshape(0));
mBs(1) = -mg_xi(1)*(mShape(0) + mRadius*mDshape(0));
mBs(2) = -Ka1g*mLength*(mShape(1) + mRadius*mDshape(1));
mBs(3) = -mg_xi(0)*(mShape(2) + mRadius*mDshape(2));
mBs(4) = -mg_xi(1)*(mShape(2) + mRadius*mDshape(2));
mBs(5) = -Kb1g*mLength*(mShape(3) + mRadius*mDshape(3));
mBs(6) = mg_xi(0);
mBs(7) = mg_xi(1);
return;
}
