void
MAST::StructuralElement2D::
initialize_direct_strain_operator(const unsigned int qp,
MAST::FEMOperatorMatrix& Bmat) {
const std::vector<std::vector<libMesh::RealVectorValue> >& dphi = _fe->get_dphi();
unsigned int n_phi = (unsigned int)dphi.size();
RealVectorX phi = RealVectorX::Zero(n_phi);
libmesh_assert_equal_to(Bmat.m(), 3);
libmesh_assert_equal_to(Bmat.n(), 6*n_phi);
// now set the shape function values
// dN/dx
for ( unsigned int i_nd=0; i_nd<n_phi; i_nd++ )
phi(i_nd) = dphi[i_nd][qp](0);
Bmat.set_shape_function(0, 0, phi); // epsilon_xx = du/dx
Bmat.set_shape_function(2, 1, phi); // gamma_xy = dv/dx + ...
// dN/dy
for ( unsigned int i_nd=0; i_nd<n_phi; i_nd++ )
phi(i_nd) = dphi[i_nd][qp](1);
Bmat.set_shape_function(1, 1, phi); // epsilon_yy = dv/dy
Bmat.set_shape_function(2, 0, phi); // gamma_xy = du/dy + ...
}
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)
}