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;
}
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::StructuralElement2D::internal_residual (bool request_jacobian,
RealVectorX& f,
RealMatrixX& jac,
bool if_ignore_ho_jac)
{
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_A_mat,
material_B_mat,
material_D_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),
stress_l = 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_n3 = RealVectorX::Zero(n3),
vec5_n3 = RealVectorX::Zero(n3),
local_f = RealVectorX::Zero(n2);
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 > >
mat_stiff_A = _property.stiffness_A_matrix(*this),
mat_stiff_B = _property.stiffness_B_matrix(*this),
mat_stiff_D = _property.stiffness_D_matrix(*this);
libMesh::Point p;
for (unsigned int qp=0; qp<JxW.size(); qp++) {
this->local_elem().global_coordinates_location(xyz[qp], p);
// get the material matrix
(*mat_stiff_A)(p, _time, material_A_mat);
if (if_bending) {
(*mat_stiff_B)(p, _time, material_B_mat);
(*mat_stiff_D)(p, _time, material_D_mat);
}
// now calculte the quantity for these matrices
_internal_residual_operation(if_bending, if_vk, n2, qp, JxW,
request_jacobian, if_ignore_ho_jac,
local_f, local_jac,
Bmat_mem, Bmat_bend, Bmat_vk,
stress, stress_l, vk_dwdxi_mat, material_A_mat,
material_B_mat, material_D_mat, vec1_n1,
vec2_n1, vec3_n2, vec4_n3,
vec5_n3, mat1_n1n2, mat2_n2n2,
mat3, mat4_n3n2);
}
// now calculate the transverse shear contribution if appropriate for the
// element
if (if_bending &&
_bending_operator->include_transverse_shear_energy())
_bending_operator->calculate_transverse_shear_residual(request_jacobian,
local_f,
local_jac,
NULL);
// now transform to the global coorodinate system
transform_vector_to_global_system(local_f, vec3_n2);
f += vec3_n2;
if (request_jacobian) {
// for 2D elements
if (_elem.dim() == 2) {
// add small values to the diagonal of the theta_z dofs
for (unsigned int i=0; i<n_phi; i++)
local_jac(5*n_phi+i, 5*n_phi+i) = -1.0e-8;
}
transform_matrix_to_global_system(local_jac, mat2_n2n2);
jac += mat2_n2n2;
}
return request_jacobian;
}