void
MAST::MindlinBendingOperator::
initialize_bending_strain_operator_for_z(const MAST::FEBase& fe,
const unsigned int qp,
const Real z,
MAST::FEMOperatorMatrix& Bmat_bend) {
const std::vector<std::vector<libMesh::RealVectorValue> >& dphi = fe.get_dphi();
const std::vector<std::vector<Real> >& phi = fe.get_phi();
const unsigned int n_phi = (unsigned int)phi.size();
RealVectorX phi_vec = RealVectorX::Zero(n_phi);
for ( unsigned int i_nd=0; i_nd<n_phi; i_nd++ )
phi_vec(i_nd) = dphi[i_nd][qp](0); // dphi/dx
phi_vec *= z;
Bmat_bend.set_shape_function(0, 4, phi_vec); // epsilon-x: thetay
phi_vec *= -1.0;
Bmat_bend.set_shape_function(2, 3, phi_vec); // gamma-xy : thetax
for ( unsigned int i_nd=0; i_nd<n_phi; i_nd++ )
phi_vec(i_nd) = dphi[i_nd][qp](1); // dphi/dy
phi_vec *= z;
Bmat_bend.set_shape_function(2, 4, phi_vec); // gamma-xy : thetay
//Bmat_trans.set_shape_function(1, 2, phi_vec); // gamma-yz : w
phi_vec *= -1.0;
Bmat_bend.set_shape_function(1, 3, phi_vec); // epsilon-y: thetax
}
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 + ...
}
bool
MAST::HeatConductionElementBase::
surface_convection_residual(bool request_jacobian,
RealVectorX& f,
RealMatrixX& jac,
const unsigned int s,
MAST::BoundaryConditionBase& p) {
// prepare the side finite element
std::auto_ptr<libMesh::FEBase> fe;
std::auto_ptr<libMesh::QBase> qrule;
_get_side_fe_and_qrule(get_elem_for_quadrature(), s, fe, qrule);
// get the function from this boundary condition
const MAST::FieldFunction<Real>
&coeff = p.get<MAST::FieldFunction<Real> >("convection_coeff"),
&T_amb = p.get<MAST::FieldFunction<Real> >("ambient_temperature");
const std::vector<Real> &JxW = fe->get_JxW();
const std::vector<libMesh::Point>& qpoint = fe->get_xyz();
const std::vector<std::vector<Real> >& phi = fe->get_phi();
const unsigned int n_phi = (unsigned int)phi.size();
RealVectorX phi_vec = RealVectorX::Zero(n_phi);
RealMatrixX mat = RealMatrixX::Zero(n_phi, n_phi);
Real temp, amb_temp, h_coeff;
libMesh::Point pt;
MAST::FEMOperatorMatrix Bmat;
for (unsigned int qp=0; qp<qpoint.size(); qp++) {
_local_elem->global_coordinates_location (qpoint[qp], pt);
// now set the shape function values
for ( unsigned int i_nd=0; i_nd<n_phi; i_nd++ )
phi_vec(i_nd) = phi[i_nd][qp];
// value of flux
coeff(pt, _time, h_coeff);
T_amb(pt, _time, amb_temp);
temp = phi_vec.dot(_sol);
// normal flux is given as:
// qi_ni = h_coeff * (T - T_amb)
//
f += JxW[qp] * phi_vec * h_coeff * (temp - amb_temp);
if (request_jacobian) {
Bmat.reinit(1, phi_vec);
Bmat.right_multiply_transpose(mat, Bmat);
jac += JxW[qp] * mat * h_coeff;
}
}
return request_jacobian;
}
bool
MAST::HeatConductionElementBase::
surface_radiation_residual(bool request_jacobian,
RealVectorX& f,
RealMatrixX& jac,
MAST::BoundaryConditionBase& p) {
// get the function from this boundary condition
const MAST::FieldFunction<Real>
&emissivity = p.get<MAST::FieldFunction<Real> >("emissivity");
const MAST::Parameter
&T_amb = p.get<MAST::Parameter>("ambient_temperature"),
&T_ref_zero = p.get<MAST::Parameter>("reference_zero_temperature"),
&sb_const = p.get<MAST::Parameter>("stefan_bolzmann_constant");
const std::vector<Real> &JxW = _fe->get_JxW();
const std::vector<libMesh::Point>& qpoint = _fe->get_xyz();
const std::vector<std::vector<Real> >& phi = _fe->get_phi();
const unsigned int n_phi = (unsigned int)phi.size();
RealVectorX phi_vec = RealVectorX::Zero(n_phi);
RealMatrixX mat = RealMatrixX::Zero(n_phi, n_phi);
const Real
sbc = sb_const(),
amb_temp = T_amb(),
zero_ref = T_ref_zero();
Real temp, emiss;
libMesh::Point pt;
MAST::FEMOperatorMatrix Bmat;
for (unsigned int qp=0; qp<qpoint.size(); qp++) {
_local_elem->global_coordinates_location (qpoint[qp], pt);
// now set the shape function values
for ( unsigned int i_nd=0; i_nd<n_phi; i_nd++ )
phi_vec(i_nd) = phi[i_nd][qp];
// value of flux
emissivity(pt, _time, emiss);
temp = phi_vec.dot(_sol);
f += JxW[qp] * phi_vec * sbc * emiss *
(pow(temp-zero_ref, 4.) - pow(amb_temp-zero_ref, 4.));
if (request_jacobian) {
Bmat.reinit(1, phi_vec);
Bmat.right_multiply_transpose(mat, Bmat);
jac += JxW[qp] * mat * sbc * emiss * 4. * pow(temp-zero_ref, 3.);
}
}
return request_jacobian;
}
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::HeatConductionElementBase::
_initialize_mass_fem_operator(const unsigned int qp,
MAST::FEMOperatorMatrix& Bmat) {
const std::vector<std::vector<Real> >& phi_fe = _fe->get_phi();
const unsigned int n_phi = (unsigned int)phi_fe.size();
RealVectorX phi = RealVectorX::Zero(n_phi);
// shape function values
// N
for ( unsigned int i_nd=0; i_nd<n_phi; i_nd++ )
phi(i_nd) = phi_fe[i_nd][qp];
Bmat.reinit(1, phi);
}
bool
MAST::HeatConductionElementBase::internal_residual (bool request_jacobian,
RealVectorX& f,
RealMatrixX& jac) {
const std::vector<Real>& JxW = _fe->get_JxW();
const std::vector<libMesh::Point>& xyz = _fe->get_xyz();
const unsigned int
n_phi = _fe->n_shape_functions(),
dim = _elem.dim();
RealMatrixX
material_mat = RealMatrixX::Zero(dim, dim),
dmaterial_mat = RealMatrixX::Zero(dim, dim), // for calculation of Jac when k is temp. dep.
mat_n2n2 = RealMatrixX::Zero(n_phi, n_phi);
RealVectorX
vec1 = RealVectorX::Zero(1),
vec2_n2 = RealVectorX::Zero(n_phi),
flux = RealVectorX::Zero(dim);
std::auto_ptr<MAST::FieldFunction<RealMatrixX> > conductance =
_property.thermal_conductance_matrix(*this);
libMesh::Point p;
std::vector<MAST::FEMOperatorMatrix> dBmat(dim);
MAST::FEMOperatorMatrix Bmat; // for calculation of Jac when k is temp. dep.
for (unsigned int qp=0; qp<JxW.size(); qp++) {
// initialize the Bmat operator for this term
_initialize_mass_fem_operator(qp, Bmat);
Bmat.right_multiply(vec1, _sol);
if (_active_sol_function)
dynamic_cast<MAST::MeshFieldFunction<RealVectorX>*>
(_active_sol_function)->set_element_quadrature_point_solution(vec1);
_local_elem->global_coordinates_location(xyz[qp], p);
(*conductance)(p, _time, material_mat);
_initialize_flux_fem_operator(qp, dBmat);
// calculate the flux for each dimension and add its weighted
// component to the residual
flux.setZero();
for (unsigned int j=0; j<dim; j++) {
dBmat[j].right_multiply(vec1, _sol); // dT_dxj
for (unsigned int i=0; i<dim; i++)
flux(i) += vec1(0) * material_mat(i,j); // q_i = k_ij dT_dxj
}
// now add to the residual vector
for (unsigned int i=0; i<dim; i++) {
vec1(0) = flux(i);
dBmat[i].vector_mult_transpose(vec2_n2, vec1);
f += JxW[qp] * vec2_n2;
}
if (request_jacobian) {
// Jacobian contribution from int_omega dB_dxi^T k_ij dB_dxj
for (unsigned int i=0; i<dim; i++)
for (unsigned int j=0; j<dim; j++) {
dBmat[i].right_multiply_transpose(mat_n2n2, dBmat[j]);
jac += JxW[qp] * material_mat(i,j) * mat_n2n2;
}
// Jacobian contribution from int_omega dB_dxi dT_dxj dk_ij/dT B
if (_active_sol_function) {
// get derivative of the conductance matrix wrt temperature
conductance->derivative(MAST::PARTIAL_DERIVATIVE,
*_active_sol_function,
p,
_time, dmaterial_mat);
for (unsigned int j=0; j<dim; j++) {
dBmat[j].right_multiply(vec1, _sol); // dT_dxj
for (unsigned int i=0; i<dim; i++)
if (dmaterial_mat(i,j) != 0.) { // no need to process for zero terms
// dB_dxi^T B
dBmat[i].right_multiply_transpose(mat_n2n2, Bmat);
// dB_dxi^T (dT_dxj dk_ij/dT) B
jac += JxW[qp] * vec1(0) * dmaterial_mat(i,j) * mat_n2n2;
}
}
}
}
}
if (_active_sol_function)
dynamic_cast<MAST::MeshFieldFunction<RealVectorX>*>
(_active_sol_function)->clear_element_quadrature_point_solution();
return request_jacobian;
}
bool
MAST::HeatConductionElementBase::velocity_residual (bool request_jacobian,
RealVectorX& f,
RealMatrixX& jac_xdot,
RealMatrixX& jac) {
MAST::FEMOperatorMatrix Bmat;
const std::vector<Real>& JxW = _fe->get_JxW();
const std::vector<libMesh::Point>& xyz = _fe->get_xyz();
const unsigned int
n_phi = _fe->n_shape_functions(),
dim = _elem.dim();
RealMatrixX
material_mat = RealMatrixX::Zero(dim, dim),
mat_n2n2 = RealMatrixX::Zero(n_phi, n_phi);
RealVectorX
vec1 = RealVectorX::Zero(1),
vec2_n2 = RealVectorX::Zero(n_phi);
std::auto_ptr<MAST::FieldFunction<RealMatrixX> > capacitance =
_property.thermal_capacitance_matrix(*this);
libMesh::Point p;
for (unsigned int qp=0; qp<JxW.size(); qp++) {
_initialize_mass_fem_operator(qp, Bmat);
Bmat.right_multiply(vec1, _sol); // B * T
if (_active_sol_function)
dynamic_cast<MAST::MeshFieldFunction<RealVectorX>*>
(_active_sol_function)->set_element_quadrature_point_solution(vec1);
_local_elem->global_coordinates_location(xyz[qp], p);
(*capacitance)(p, _time, material_mat);
Bmat.right_multiply(vec1, _vel); // B * T_dot
Bmat.vector_mult_transpose(vec2_n2, vec1); // B^T * B * T_dot
f += JxW[qp] * material_mat(0,0) * vec2_n2; // (rho*cp)*JxW B^T B T_dot
if (request_jacobian) {
Bmat.right_multiply_transpose(mat_n2n2, Bmat); // B^T B
jac_xdot += JxW[qp] * material_mat(0,0) * mat_n2n2; // B^T B * JxW (rho*cp)
// Jacobian contribution from int_omega B T d(rho*cp)/dT B
if (_active_sol_function) {
// get derivative of the conductance matrix wrt temperature
capacitance->derivative(MAST::PARTIAL_DERIVATIVE,
*_active_sol_function,
p,
_time, material_mat);
if (material_mat(0,0) != 0.) { // no need to process for zero terms
// B^T (T d(rho cp)/dT) B
jac += JxW[qp] * vec1(0) * material_mat(0,0) * mat_n2n2;
}
}
}
}
if (_active_sol_function)
dynamic_cast<MAST::MeshFieldFunction<RealVectorX>*>
(_active_sol_function)->clear_element_quadrature_point_solution();
return request_jacobian;
}