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_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
}
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)
}
bool
MAST::HeatConductionElementBase::
surface_flux_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>& func =
p.get<MAST::FieldFunction<Real> >("heat_flux");
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);
libMesh::Point pt;
Real flux;
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];
// get the value of flux = q_i . n_i
func(pt, _time, flux);
f += JxW[qp] * phi_vec * flux;
}
// calculation of the load vector is independent of solution
return false;
}
bool
MAST::StructuralElementBase::
small_disturbance_surface_pressure_force(bool request_jacobian,
DenseRealVector &f,
DenseRealMatrix &jac,
MAST::BoundaryCondition &p) {
libmesh_assert(_elem.dim() < 3); // only applicable for lower dimensional elements.
libmesh_assert(!follower_forces); // not implemented yet for follower forces
libmesh_assert_equal_to(p.type(), MAST::SMALL_DISTURBANCE_MOTION);
MAST::SmallDisturbanceMotion& sd_motion = dynamic_cast<MAST::SmallDisturbanceMotion&>(p);
MAST::SurfaceMotionBase& surf_motion = sd_motion.get_deformation();
MAST::SmallDisturbanceSurfacePressure& surf_press = sd_motion.get_pressure();
FEMOperatorMatrix Bmat;
// get the function from this boundary condition
const std::vector<Real> &JxW = _fe->get_JxW();
// Physical location of the quadrature points
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();
const unsigned int n1=3, n2=6*n_phi;
// normal for face integration
libMesh::Point normal;
// direction of pressure assumed to be normal (along local z-axis)
// to the element face for 2D and along local y-axis for 1D element.
normal(_elem.dim()) = -1.;
Real press;
ValType dpress;
DenseRealVector phi_vec;
libMesh::DenseVector<ValType> wtrans, utrans, dn_rot, force, local_f, vec_n2;
wtrans.resize(3); utrans.resize(3); dn_rot.resize(3);
phi_vec.resize(n_phi); force.resize(2*n1); local_f.resize(n2);
vec_n2.resize(n2);
libMesh::Point pt;
for (unsigned int qp=0; qp<qpoint.size(); qp++)
{
this->global_coordinates(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];
Bmat.reinit(2*n1, phi_vec);
// get pressure and deformation information
surf_press.surface_pressure<ValType>(_system.time, pt, press, dpress);
surf_motion.surface_velocity(_system.time, pt, normal,
wtrans, utrans, dn_rot);
// libMesh::out << std::setw(15) << pt(0)
// << std::setw(15) << std::real(press)
// << std::setw(15) << std::imag(press)
// << std::setw(15) << std::real(dpress)
// << std::setw(15) << std::imag(dpress)
// << std::setw(15) << std::real(utrans(1))
// << std::setw(15) << std::imag(utrans(1))
// << std::setw(15) << std::real(dn_rot(0))
// << std::setw(15) << std::imag(dn_rot(0)) << std::endl;
// calculate force
for (unsigned int i_dim=0; i_dim<n1; i_dim++)
force(i_dim) = ( press * dn_rot(i_dim) + // steady pressure
dpress * normal(i_dim)); // unsteady pressure
Bmat.vector_mult_transpose(vec_n2, force);
local_f.add(JxW[qp], vec_n2);
}
// now transform to the global system and add
transform_to_global_system(local_f, vec_n2);
MAST::add_to_assembled_vector(f, vec_n2);
return (request_jacobian && follower_forces);
}
bool
MAST::StructuralElementBase::inertial_force (bool request_jacobian,
DenseRealVector& f,
DenseRealMatrix& jac)
{
FEMOperatorMatrix Bmat;
const std::vector<Real>& JxW = _fe->get_JxW();
const std::vector<libMesh::Point>& xyz = _fe->get_xyz();
const std::vector<std::vector<Real> >& phi = _fe->get_phi();
const unsigned int n_phi = (unsigned int)phi.size(), n1=6, n2=6*n_phi;
DenseRealMatrix material_mat, mat1_n1n2, mat2_n2n2, local_jac;
DenseRealVector phi_vec, vec1_n1, vec2_n2, local_f;
mat1_n1n2.resize(n1, n2); mat2_n2n2.resize(n2, n2); local_jac.resize(n2, n2);
phi_vec.resize(n_phi); vec1_n1.resize(n1); vec2_n2.resize(n2);
local_f.resize(n2);
std::auto_ptr<MAST::FieldFunction<DenseRealMatrix > > mat_inertia
(_property.get_property(MAST::SECTION_INTEGRATED_MATERIAL_INERTIA_MATRIX,
*this).release());
if (_property.if_diagonal_mass_matrix()) {
// as an approximation, get matrix at the first quadrature point
(*mat_inertia)(xyz[0], _system.time, material_mat);
Real vol = 0.;
const unsigned int nshp = _fe->n_shape_functions();
for (unsigned int i=0; i<JxW.size(); i++)
vol += JxW[i];
vol /= (1.* nshp);
for (unsigned int i_var=0; i_var<6; i_var++)
for (unsigned int i=0; i<nshp; i++)
local_jac(i_var*nshp+i, i_var*nshp+i) =
vol*material_mat(i_var, i_var);
local_jac.vector_mult(local_f, local_acceleration);
}
else {
libMesh::Point p;
for (unsigned int qp=0; qp<JxW.size(); qp++) {
this->global_coordinates(xyz[qp], p);
(*mat_inertia)(p, _system.time, material_mat);
// 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];
Bmat.reinit(_system.n_vars(), phi_vec);
Bmat.left_multiply(mat1_n1n2, material_mat);
mat1_n1n2.vector_mult(vec1_n1, local_acceleration);
Bmat.vector_mult_transpose(vec2_n2, vec1_n1);
local_f.add(JxW[qp], vec2_n2);
if (request_jacobian) {
Bmat.right_multiply_transpose(mat2_n2n2,
mat1_n1n2);
local_jac.add(JxW[qp], mat2_n2n2);
}
}
}
// now transform to the global coorodinate system
if (_elem.dim() < 3) {
transform_to_global_system(local_f, vec2_n2);
f.add(1., vec2_n2);
if (request_jacobian) {
transform_to_global_system(local_jac, mat2_n2n2);
jac.add(1., mat2_n2n2);
}
}
else {
f.add(1., local_f);
if (request_jacobian)
jac.add(1., local_jac);
}
return request_jacobian;
}
bool
MAST::StructuralElementBase::small_disturbance_surface_pressure_force(bool request_jacobian,
DenseRealVector &f,
DenseRealMatrix &jac,
const unsigned int side,
MAST::BoundaryCondition &p) {
libmesh_assert(!follower_forces); // not implemented yet for follower forces
libmesh_assert_equal_to(p.type(), MAST::SMALL_DISTURBANCE_MOTION);
MAST::SmallDisturbanceMotion& sd_motion = dynamic_cast<MAST::SmallDisturbanceMotion&>(p);
MAST::SurfaceMotionBase& surf_motion = sd_motion.get_deformation();
MAST::SmallDisturbanceSurfacePressure& surf_press = sd_motion.get_pressure();
FEMOperatorMatrix Bmat;
// get the function from this boundary condition
std::auto_ptr<libMesh::FEBase> fe;
std::auto_ptr<libMesh::QBase> qrule;
_get_side_fe_and_qrule(this->local_elem().local_elem(), side, fe, qrule);
const std::vector<Real> &JxW = fe->get_JxW();
// Physical location of the quadrature points
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();
const unsigned int n1=3, n2=6*n_phi;
// boundary normals
const std::vector<libMesh::Point>& face_normals = fe->get_normals();
Real press;
ValType dpress;
DenseRealVector phi_vec;
libMesh::DenseVector<ValType> wtrans, utrans, dn_rot, force, local_f, vec_n2;
wtrans.resize(3); utrans.resize(3); dn_rot.resize(3);
phi_vec.resize(n_phi); force.resize(2*n1); local_f.resize(n2);
vec_n2.resize(n2);
libMesh::Point pt;
for (unsigned int qp=0; qp<qpoint.size(); qp++)
{
this->global_coordinates(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];
Bmat.reinit(2*n1, phi_vec);
// get pressure and deformation information
surf_press.surface_pressure<ValType>(_system.time, pt, press, dpress);
surf_motion.surface_velocity(_system.time, pt, face_normals[qp],
wtrans, utrans, dn_rot);
// press = 0.;
// dpress = Complex(2./4.*std::real(dn_rot(0)), 2./4./.1*std::imag(utrans(1)));
// libMesh::out << q_point[qp](0)
// << " " << std::real(utrans(1))
// << " " << std::imag(utrans(1))
// << " " << std::real(dn_rot(0))
// << " " << std::imag(dn_rot(0))
// << " " << std::real(press)
// << " " << std::imag(press)
// << " " << std::real(dpress)
// << " " << std::imag(dpress) << std::endl;
// calculate force
for (unsigned int i_dim=0; i_dim<n1; i_dim++)
force(i_dim) = ( press * dn_rot(i_dim) + // steady pressure
dpress * face_normals[qp](i_dim)); // unsteady pressure
Bmat.vector_mult_transpose(vec_n2, force);
local_f.add(JxW[qp], vec_n2);
}
// now transform to the global system and add
if (_elem.dim() < 3) {
transform_to_global_system(local_f, vec_n2);
MAST::add_to_assembled_vector(f, vec_n2);
}
else
MAST::add_to_assembled_vector(f, local_f);
return (request_jacobian && follower_forces);
}
bool
MAST::StructuralElementBase::surface_pressure_force(bool request_jacobian,
DenseRealVector &f,
DenseRealMatrix &jac,
MAST::BoundaryCondition &p) {
libmesh_assert(_elem.dim() < 3); // only applicable for lower dimensional elements
libmesh_assert(!follower_forces); // not implemented yet for follower forces
FEMOperatorMatrix Bmat;
// get the function from this boundary condition
MAST::FieldFunction<Real>& func =
dynamic_cast<MAST::FieldFunction<Real>&>(p.function());
const std::vector<Real> &JxW = _fe->get_JxW();
// Physical location of the quadrature points
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();
const unsigned int n1=3, n2=6*n_phi;
// normal for face integration
libMesh::Point normal;
// direction of pressure assumed to be normal (along local z-axis)
// to the element face for 2D and along local y-axis for 1D element.
normal(_elem.dim()) = -1.;
Real press;
DenseRealVector phi_vec, force, local_f, vec_n2;
phi_vec.resize(n_phi); force.resize(2*n1); local_f.resize(n2);
vec_n2.resize(n2);
libMesh::Point pt;
for (unsigned int qp=0; qp<qpoint.size(); qp++)
{
this->global_coordinates(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];
Bmat.reinit(2*n1, phi_vec);
// get pressure value
func(pt, _system.time, press);
// calculate force
for (unsigned int i_dim=0; i_dim<n1; i_dim++)
force(i_dim) = press * normal(i_dim);
Bmat.vector_mult_transpose(vec_n2, force);
local_f.add(JxW[qp], vec_n2);
}
// now transform to the global system and add
transform_to_global_system(local_f, vec_n2);
f.add(1., vec_n2);
return (request_jacobian && follower_forces);
}
bool
MAST::StructuralElementBase::surface_pressure_force(bool request_jacobian,
DenseRealVector &f,
DenseRealMatrix &jac,
const unsigned int side,
MAST::BoundaryCondition &p) {
libmesh_assert(!follower_forces); // not implemented yet for follower forces
FEMOperatorMatrix Bmat;
// get the function from this boundary condition
MAST::FieldFunction<Real>& func =
dynamic_cast<MAST::FieldFunction<Real>&>(p.function());
std::auto_ptr<libMesh::FEBase> fe;
std::auto_ptr<libMesh::QBase> qrule;
_get_side_fe_and_qrule(this->get_elem_for_quadrature(), side, fe, qrule);
const std::vector<Real> &JxW = fe->get_JxW();
// Physical location of the quadrature points
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();
const unsigned int n1=3, n2=6*n_phi;
// boundary normals
const std::vector<libMesh::Point>& face_normals = fe->get_normals();
Real press;
DenseRealVector phi_vec, force, local_f, vec_n2;
phi_vec.resize(n_phi); force.resize(2*n1); local_f.resize(n2);
vec_n2.resize(n2);
libMesh::Point pt;
for (unsigned int qp=0; qp<qpoint.size(); qp++)
{
this->global_coordinates(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];
Bmat.reinit(2*n1, phi_vec);
// get pressure value
func(pt, _system.time, press);
// calculate force
for (unsigned int i_dim=0; i_dim<n1; i_dim++)
force(i_dim) = press * face_normals[qp](i_dim);
Bmat.vector_mult_transpose(vec_n2, force);
local_f.add(JxW[qp], vec_n2);
}
// now transform to the global system and add
if (_elem.dim() < 3) {
transform_to_global_system(local_f, vec_n2);
f.add(1., vec_n2);
}
else
f.add(1., local_f);
return (request_jacobian && follower_forces);
}
bool
MAST::StructuralElementBase::inertial_force_sensitivity(bool request_jacobian,
DenseRealVector& f,
DenseRealMatrix& jac)
{
// this should be true if the function is called
libmesh_assert(this->sensitivity_param);
libmesh_assert(!this->sensitivity_param->is_shape_parameter()); // this is not implemented for now
// check if the material property or the provided exterior
// values, like temperature, are functions of the sensitivity parameter
bool calculate = false;
calculate = calculate || _property.depends_on(*(this->sensitivity_param));
// nothing to be calculated if the element does not depend on the
// sensitivity parameter.
if (!calculate)
return false;
FEMOperatorMatrix Bmat;
const std::vector<Real>& JxW = _fe->get_JxW();
const std::vector<libMesh::Point>& xyz = _fe->get_xyz();
const std::vector<std::vector<Real> >& phi = _fe->get_phi();
const unsigned int n_phi = (unsigned int)phi.size(), n1=6, n2=6*n_phi;
DenseRealMatrix material_mat, mat1_n1n2, mat2_n2n2, local_jac;
DenseRealVector phi_vec, vec1_n1, vec2_n2, local_f;
mat1_n1n2.resize(n1, n2); mat2_n2n2.resize(n2, n2); local_jac.resize(n2, n2);
phi_vec.resize(n_phi); vec1_n1.resize(n1); vec2_n2.resize(n2);
local_f.resize(n2);
std::auto_ptr<MAST::FieldFunction<DenseRealMatrix > > mat_inertia
(_property.get_property(MAST::SECTION_INTEGRATED_MATERIAL_INERTIA_MATRIX,
*this).release());
if (_property.if_diagonal_mass_matrix()) {
mat_inertia->total(*this->sensitivity_param,
xyz[0], _system.time, material_mat);
Real vol = 0.;
const unsigned int nshp = _fe->n_shape_functions();
for (unsigned int i=0; i<JxW.size(); i++)
vol += JxW[i];
vol /= (1.* nshp);
for (unsigned int i_var=0; i_var<6; i_var++)
for (unsigned int i=0; i<nshp; i++)
local_jac(i_var*nshp+i, i_var*nshp+i) =
vol*material_mat(i_var, i_var);
local_jac.vector_mult(local_f, local_acceleration);
}
else {
libMesh::Point p;
for (unsigned int qp=0; qp<JxW.size(); qp++) {
this->global_coordinates(xyz[qp], p);
mat_inertia->total(*this->sensitivity_param,
p, _system.time, material_mat);
// 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];
Bmat.reinit(_system.n_vars(), phi_vec);
Bmat.left_multiply(mat1_n1n2, material_mat);
mat1_n1n2.vector_mult(vec1_n1, local_acceleration);
Bmat.vector_mult_transpose(vec2_n2, vec1_n1);
local_f.add(JxW[qp], vec2_n2);
if (request_jacobian) {
Bmat.right_multiply_transpose(mat2_n2n2,
mat1_n1n2);
local_jac.add(JxW[qp], mat2_n2n2);
}
}
}
// now transform to the global coorodinate system
if (_elem.dim() < 3) {
transform_to_global_system(local_f, vec2_n2);
f.add(1., vec2_n2);
if (request_jacobian) {
transform_to_global_system(local_jac, mat2_n2n2);
jac.add(1., mat2_n2n2);
}
}
else {
f.add(1., local_f);
if (request_jacobian)
jac.add(1., local_jac);
}
return request_jacobian;
}
