void
MAST::StructuralElement2D::
initialize_von_karman_strain_operator_sensitivity(const unsigned int qp,
RealMatrixX &vk_dwdxi_mat_sens) {
const std::vector<std::vector<libMesh::RealVectorValue> >& dphi = _fe->get_dphi();
const unsigned int n_phi = (unsigned int)dphi.size();
libmesh_assert_equal_to(vk_dwdxi_mat_sens.rows(), 3);
libmesh_assert_equal_to(vk_dwdxi_mat_sens.cols(), 2);
Real dw=0.;
vk_dwdxi_mat_sens.setConstant(0.);
RealVectorX phi_vec = RealVectorX::Zero(n_phi);
dw = 0.;
for ( unsigned int i_nd=0; i_nd<n_phi; i_nd++ ) {
phi_vec(i_nd) = dphi[i_nd][qp](0); // dphi/dx
dw += phi_vec(i_nd)*_local_sol_sens(2*n_phi+i_nd); // dw/dx
}
vk_dwdxi_mat_sens(0, 0) = dw; // epsilon-xx : dw/dx
vk_dwdxi_mat_sens(2, 1) = dw; // gamma-xy : dw/dx
dw = 0.;
for ( unsigned int i_nd=0; i_nd<n_phi; i_nd++ ) {
phi_vec(i_nd) = dphi[i_nd][qp](1); // dphi/dy
dw += phi_vec(i_nd)*_local_sol_sens(2*n_phi+i_nd); // dw/dy
}
vk_dwdxi_mat_sens(1, 1) = dw; // epsilon-yy : dw/dy
vk_dwdxi_mat_sens(2, 0) = dw; // gamma-xy : dw/dy
}
void
MAST::StructuralElement2D::_convert_prestress_B_mat_to_vector(const RealMatrixX& mat,
RealVectorX& vec) const {
libmesh_assert_equal_to(mat.rows(), 2);
libmesh_assert_equal_to(mat.cols(), 2);
vec = RealVectorX::Zero(3);
vec(0) = mat(0,0); // sigma x
vec(1) = mat(1,1); // sigma y
vec(2) = mat(0,1); // tau xy
}
virtual void operator() (const libMesh::Point& p,
const Real t,
RealMatrixX& m) const {
// add the values of each matrix to get the integrated value
RealMatrixX mi;
for (unsigned int i=0; i<_layer_mats.size(); i++) {
(*_layer_mats[i])(p, t, mi);
// use the size of the layer matrix to resize the output
// all other layers should return the same sized matrices
if (i==0)
m = RealMatrixX::Zero(mi.rows(), mi.cols());
m += mi;
}
}
virtual void derivative ( const MAST::FunctionBase& f,
const libMesh::Point& p,
const Real t,
RealMatrixX& m) const {
// add the values of each matrix to get the integrated value
RealMatrixX mi;
m = RealMatrixX::Zero(2,2);
for (unsigned int i=0; i<_layer_mats.size(); i++) {
_layer_mats[i]->derivative( f, p, t, mi);
// use the size of the layer matrix to resize the output
// all other layers should return the same sized matrices
if (i==0)
m = RealMatrixX::Zero(mi.rows(), mi.cols());
m += mi;
}
}
void
MAST::StructuralElement2D::
initialize_von_karman_strain_operator(const unsigned int qp,
RealVectorX& vk_strain,
RealMatrixX& vk_dwdxi_mat,
MAST::FEMOperatorMatrix& Bmat_vk) {
const std::vector<std::vector<libMesh::RealVectorValue> >& dphi = _fe->get_dphi();
const unsigned int n_phi = (unsigned int)dphi.size();
libmesh_assert_equal_to(vk_strain.size(), 3);
libmesh_assert_equal_to(vk_dwdxi_mat.rows(), 3);
libmesh_assert_equal_to(vk_dwdxi_mat.cols(), 2);
libmesh_assert_equal_to(Bmat_vk.m(), 2);
libmesh_assert_equal_to(Bmat_vk.n(), 6*n_phi);
Real dw=0.;
vk_strain.setConstant(0.);
vk_dwdxi_mat.setConstant(0.);
RealVectorX phi_vec = RealVectorX::Zero(n_phi);
dw = 0.;
for ( unsigned int i_nd=0; i_nd<n_phi; i_nd++ ) {
phi_vec(i_nd) = dphi[i_nd][qp](0); // dphi/dx
dw += phi_vec(i_nd)*_local_sol(2*n_phi+i_nd); // dw/dx
}
Bmat_vk.set_shape_function(0, 2, phi_vec); // dw/dx
vk_dwdxi_mat(0, 0) = dw; // epsilon-xx : dw/dx
vk_dwdxi_mat(2, 1) = dw; // gamma-xy : dw/dx
vk_strain(0) = 0.5*dw*dw; // 1/2 * (dw/dx)^2
vk_strain(2) = dw; // (dw/dx)*(dw/dy) only dw/dx is provided here
dw = 0.;
for ( unsigned int i_nd=0; i_nd<n_phi; i_nd++ ) {
phi_vec(i_nd) = dphi[i_nd][qp](1); // dphi/dy
dw += phi_vec(i_nd)*_local_sol(2*n_phi+i_nd); // dw/dy
}
Bmat_vk.set_shape_function(1, 2, phi_vec); // dw/dy
vk_dwdxi_mat(1, 1) = dw; // epsilon-yy : dw/dy
vk_dwdxi_mat(2, 0) = dw; // gamma-xy : dw/dy
vk_strain(1) = 0.5*dw*dw; // 1/2 * (dw/dy)^2
vk_strain(2) *= dw; // (dw/dx)*(dw/dy)
}
void
MAST::LAPACK_DGGEV::compute(const RealMatrixX &A,
const RealMatrixX &B,
bool computeEigenvectors) {
libmesh_assert(A.cols() == A.rows() &&
B.cols() == A.rows() &&
B.cols() == B.rows());
_A = A;
_B = B;
RealMatrixX
Amat = A,
Bmat = B;
int n = (int)A.cols();
char L='N',R='N';
if (computeEigenvectors) {
L = 'V'; R = 'V';
VL.setZero(n, n);
VR.setZero(n, n);
}
int
lwork=16*n;
info_val=-1;
alpha.setZero(n);
beta.setZero(n);
RealVectorX
work,
aval_r,
aval_i,
bval;
RealMatrixX
vecl,
vecr;
work.setZero(lwork);
aval_r.setZero(n);
aval_i.setZero(n);
bval.setZero(n);
vecl.setZero(n,n);
vecr.setZero(n,n);
Real
*a_vals = Amat.data(),
*b_vals = Bmat.data(),
*alpha_r_v = aval_r.data(),
*alpha_i_v = aval_i.data(),
*beta_v = bval.data(),
*vecl_v = vecl.data(),
*vecr_v = vecr.data(),
*work_v = work.data();
dggev_(&L, &R, &n,
&(a_vals[0]), &n,
&(b_vals[0]), &n,
&(alpha_r_v[0]), &(alpha_i_v[0]), &(beta_v[0]),
&(vecl_v[0]), &n, &(vecr_v[0]), &n,
&(work_v[0]), &lwork,
&info_val);
// now sort the eigenvalues for complex conjugates
unsigned int n_located = 0;
while (n_located < n) {
// if the imaginary part of the eigenvalue is non-zero, it is a
// complex conjugate
if (aval_i(n_located) != 0.) { // complex conjugate
alpha( n_located) = std::complex<double>(aval_r(n_located), aval_i(n_located));
alpha(1+n_located) = std::complex<double>(aval_r(n_located), -aval_i(n_located));
beta ( n_located) = bval(n_located);
beta (1+n_located) = bval(n_located);
// copy the eigenvectors if they were requested
if (computeEigenvectors) {
std::complex<double> iota = std::complex<double>(0, 1.);
VL.col( n_located) = (vecl.col( n_located).cast<Complex>() +
vecl.col(1+n_located).cast<Complex>() * iota);
VL.col(1+n_located) = (vecl.col( n_located).cast<Complex>() -
vecl.col(1+n_located).cast<Complex>() * iota);
VR.col( n_located) = (vecr.col( n_located).cast<Complex>() +
vecr.col(1+n_located).cast<Complex>() * iota);
VR.col(1+n_located) = (vecr.col( n_located).cast<Complex>() -
vecr.col(1+n_located).cast<Complex>() * iota);
}
// two complex conjugate roots were found
n_located +=2;
}
else {
alpha( n_located) = std::complex<double>(aval_r(n_located), 0.);
beta ( n_located) = bval(n_located);
// copy the eigenvectors if they were requested
if (computeEigenvectors) {
VL.col(n_located) = vecl.col(n_located).cast<Complex>();
VR.col(n_located) = vecr.col(n_located).cast<Complex>();
}
// only one real root was found
n_located++;
}
}
if (info_val != 0)
libMesh::out
<< "Warning!! DGGEV returned with nonzero info = "
<< info_val << std::endl;
}