bool
MAST::StructuralElement2D::thermal_residual (bool request_jacobian,
RealVectorX& f,
RealMatrixX& jac,
MAST::BoundaryConditionBase& bc)
{
FEMOperatorMatrix Bmat_mem, Bmat_bend, Bmat_vk;
const std::vector<Real>& JxW = _fe->get_JxW();
const std::vector<libMesh::Point>& xyz = _fe->get_xyz();
const unsigned int n_phi = (unsigned int)_fe->get_phi().size();
const unsigned int n1= this->n_direct_strain_components(), n2=6*n_phi,
n3 = this->n_von_karman_strain_components();
RealMatrixX
material_exp_A_mat,
material_exp_B_mat,
mat1_n1n2 = RealMatrixX::Zero(n1,n2),
mat2_n2n2 = RealMatrixX::Zero(n2,n2),
mat3,
mat4_n3n2 = RealMatrixX::Zero(n3,n2),
vk_dwdxi_mat = RealMatrixX::Zero(n1,n3),
stress = RealMatrixX::Zero(2,2),
local_jac = RealMatrixX::Zero(n2,n2);
RealVectorX
vec1_n1 = RealVectorX::Zero(n1),
vec2_n1 = RealVectorX::Zero(n1),
vec3_n2 = RealVectorX::Zero(n2),
vec4_2 = RealVectorX::Zero(2),
vec5_n3 = RealVectorX::Zero(n3),
local_f = RealVectorX::Zero(n2),
delta_t = RealVectorX::Zero(1);
local_f.setZero();
local_jac.setZero();
Bmat_mem.reinit(n1, _system.n_vars(), n_phi); // three stress-strain components
Bmat_bend.reinit(n1, _system.n_vars(), n_phi);
Bmat_vk.reinit(n3, _system.n_vars(), n_phi); // only dw/dx and dw/dy
bool if_vk = (_property.strain_type() == MAST::VON_KARMAN_STRAIN),
if_bending = (_property.bending_model(_elem, _fe->get_fe_type()) != MAST::NO_BENDING);
std::auto_ptr<MAST::FieldFunction<RealMatrixX > >
expansion_A = _property.thermal_expansion_A_matrix(*this),
expansion_B = _property.thermal_expansion_B_matrix(*this);
const MAST::FieldFunction<Real>
&temp_func = bc.get<MAST::FieldFunction<Real> >("temperature"),
&ref_temp_func = bc.get<MAST::FieldFunction<Real> >("ref_temperature");
Real t, t0;
libMesh::Point pt;
for (unsigned int qp=0; qp<JxW.size(); qp++) {
this->local_elem().global_coordinates_location(xyz[qp], pt);
// this is moved inside the domain since
(*expansion_A)(pt, _time, material_exp_A_mat);
(*expansion_B)(pt, _time, material_exp_B_mat);
// get the temperature function
temp_func(pt, _time, t);
ref_temp_func(pt, _time, t0);
delta_t(0) = t-t0;
vec1_n1 = material_exp_A_mat * delta_t; // [C]{alpha (T - T0)} (with membrane strain)
vec2_n1 = material_exp_B_mat * delta_t; // [C]{alpha (T - T0)} (with bending strain)
stress(0,0) = vec1_n1(0); // sigma_xx
stress(0,1) = vec1_n1(2); // sigma_xy
stress(1,0) = vec1_n1(2); // sigma_yx
stress(1,1) = vec1_n1(1); // sigma_yy
this->initialize_direct_strain_operator(qp, Bmat_mem);
// membrane strain
Bmat_mem.vector_mult_transpose(vec3_n2, vec1_n1);
local_f += JxW[qp] * vec3_n2;
if (if_bending) {
// bending strain
_bending_operator->initialize_bending_strain_operator(qp, Bmat_bend);
Bmat_bend.vector_mult_transpose(vec3_n2, vec2_n1);
local_f += JxW[qp] * vec3_n2;
// von Karman strain
if (if_vk) {
// get the vonKarman strain operator if needed
this->initialize_von_karman_strain_operator(qp,
vec2_n1, // epsilon_vk
vk_dwdxi_mat,
Bmat_vk);
// von Karman strain
vec4_2 = vk_dwdxi_mat.transpose() * vec1_n1;
Bmat_vk.vector_mult_transpose(vec3_n2, vec4_2);
local_f += JxW[qp] * vec3_n2;
}
if (request_jacobian && if_vk) { // Jacobian only for vk strain
// vk - vk
mat3 = RealMatrixX::Zero(2, n2);
Bmat_vk.left_multiply(mat3, stress);
Bmat_vk.right_multiply_transpose(mat2_n2n2, mat3);
local_jac += JxW[qp] * mat2_n2n2;
}
}
}
// now transform to the global coorodinate system
transform_vector_to_global_system(local_f, vec3_n2);
f -= vec3_n2;
if (request_jacobian && if_vk) {
transform_matrix_to_global_system(local_jac, mat2_n2n2);
jac -= mat2_n2n2;
}
// Jacobian contribution from von Karman strain
return request_jacobian && if_vk;
}
double sigma_func(double x) {
return sigma0 * pow(temp_func(x),polyn);
}
double sigma_func(double x) {
double sig_ref = temp_func(x)* pow(center,-sigma_index-1.5)/( M_PI*Qmin*(1+amplitude));
double exp_fac = exp(-(x-center)*(x-center)/(2*width*width));
return sig_ref * pow(x, sigma_index) * (1 + amplitude*exp_fac);
}
