Public Member Functions | Private Member Functions | List of all members
oomph::LinearElasticityEquations< DIM > Class Template Reference

#include <linear_elasticity_elements.h>

+ Inheritance diagram for oomph::LinearElasticityEquations< DIM >:

Public Member Functions

 LinearElasticityEquations ()
 Constructor. More...
 
unsigned required_nvalue (const unsigned &n) const
 Number of values required at node n. More...
 
void fill_in_contribution_to_residuals (Vector< double > &residuals)
 
void fill_in_contribution_to_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)
 
void get_stress (const Vector< double > &s, DenseMatrix< double > &sigma) const
 
void output_fct (std::ostream &outfile, const unsigned &nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
 Output exact solution x,y,[z],u,v,[w]. More...
 
void output_fct (std::ostream &outfile, const unsigned &nplot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt)
 Output exact solution x,y,[z],u,v,[w] (unsteady version) More...
 
void output (std::ostream &outfile)
 Output: x,y,[z],u,v,[w]. More...
 
void output (std::ostream &outfile, const unsigned &n_plot)
 Output: x,y,[z],u,v,[w]. More...
 
void output (FILE *file_pt)
 C-style output: x,y,[z],u,v,[w]. More...
 
void output (FILE *file_pt, const unsigned &n_plot)
 Output: x,y,[z],u,v,[w]. More...
 
void compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)
 
void compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm)
 
- Public Member Functions inherited from oomph::LinearElasticityEquationsBase< DIM >
virtual unsigned u_index_linear_elasticity (const unsigned i) const
 
double d2u_dt2_linear_elasticity (const unsigned &n, const unsigned &i) const
 d^2u/dt^2 at local node n More...
 
void interpolated_u_linear_elasticity (const Vector< double > &s, Vector< double > &disp) const
 Compute vector of FE interpolated displacement u at local coordinate s. More...
 
double interpolated_u_linear_elasticity (const Vector< double > &s, const unsigned &i) const
 Return FE interpolated displacement u[i] at local coordinate s. More...
 
 LinearElasticityEquationsBase ()
 
ElasticityTensor *& elasticity_tensor_pt ()
 Return the pointer to the elasticity_tensor. More...
 
double E (const unsigned &i, const unsigned &j, const unsigned &k, const unsigned &l) const
 Access function to the entries in the elasticity tensor. More...
 
const double & lambda_sq () const
 Access function for timescale ratio (nondim density) More...
 
double *& lambda_sq_pt ()
 Access function for pointer to timescale ratio (nondim density) More...
 
BodyForceFctPt & body_force_fct_pt ()
 Access function: Pointer to body force function. More...
 
BodyForceFctPt body_force_fct_pt () const
 Access function: Pointer to body force function (const version) More...
 
void enable_inertia ()
 Switch on solid inertia. More...
 
void disable_inertia ()
 Switch off solid inertia. More...
 
bool is_inertia_enabled () const
 Access function to flag that switches inertia on/off (const version) More...
 
virtual void pin_elemental_redundant_nodal_solid_pressures ()
 Pin the element's redundant solid pressures (needed for refinement) More...
 
void get_strain (const Vector< double > &s, DenseMatrix< double > &strain) const
 Return the strain tensor. More...
 
void body_force (const Vector< double > &x, Vector< double > &b) const
 
unsigned ndof_types () const
 
void get_dof_numbers_for_unknowns (std::list< std::pair< unsigned long, unsigned >> &dof_lookup_list) const
 
- Public Member Functions inherited from oomph::FiniteElement
void set_dimension (const unsigned &dim)
 
void set_nodal_dimension (const unsigned &nodal_dim)
 
void set_nnodal_position_type (const unsigned &nposition_type)
 Set the number of types required to interpolate the coordinate. More...
 
void set_n_node (const unsigned &n)
 
int nodal_local_eqn (const unsigned &n, const unsigned &i) const
 
double dJ_eulerian_at_knot (const unsigned &ipt, Shape &psi, DenseMatrix< double > &djacobian_dX) const
 
 FiniteElement ()
 Constructor. More...
 
virtual ~FiniteElement ()
 
 FiniteElement (const FiniteElement &)=delete
 Broken copy constructor. More...
 
virtual bool local_coord_is_valid (const Vector< double > &s)
 Broken assignment operator. More...
 
virtual void move_local_coord_back_into_element (Vector< double > &s) const
 
void get_centre_of_gravity_and_max_radius_in_terms_of_zeta (Vector< double > &cog, double &max_radius) const
 
virtual void local_coordinate_of_node (const unsigned &j, Vector< double > &s) const
 
virtual void local_fraction_of_node (const unsigned &j, Vector< double > &s_fraction)
 
virtual double local_one_d_fraction_of_node (const unsigned &n1d, const unsigned &i)
 
virtual void set_macro_elem_pt (MacroElement *macro_elem_pt)
 
MacroElement * macro_elem_pt ()
 Access function to pointer to macro element. More...
 
void get_x (const Vector< double > &s, Vector< double > &x) const
 
void get_x (const unsigned &t, const Vector< double > &s, Vector< double > &x)
 
virtual void get_x_from_macro_element (const Vector< double > &s, Vector< double > &x) const
 
virtual void get_x_from_macro_element (const unsigned &t, const Vector< double > &s, Vector< double > &x)
 
virtual void set_integration_scheme (Integral *const &integral_pt)
 Set the spatial integration scheme. More...
 
Integral *const & integral_pt () const
 Return the pointer to the integration scheme (const version) More...
 
virtual void shape (const Vector< double > &s, Shape &psi) const =0
 
virtual void shape_at_knot (const unsigned &ipt, Shape &psi) const
 
virtual void dshape_local (const Vector< double > &s, Shape &psi, DShape &dpsids) const
 
virtual void dshape_local_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsids) const
 
virtual void d2shape_local (const Vector< double > &s, Shape &psi, DShape &dpsids, DShape &d2psids) const
 
virtual void d2shape_local_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsids, DShape &d2psids) const
 
virtual double J_eulerian (const Vector< double > &s) const
 
virtual double J_eulerian_at_knot (const unsigned &ipt) const
 
void check_J_eulerian_at_knots (bool &passed) const
 
void check_jacobian (const double &jacobian) const
 
double dshape_eulerian (const Vector< double > &s, Shape &psi, DShape &dpsidx) const
 
virtual double dshape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidx) const
 
virtual double dshape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsi, DenseMatrix< double > &djacobian_dX, RankFourTensor< double > &d_dpsidx_dX) const
 
double d2shape_eulerian (const Vector< double > &s, Shape &psi, DShape &dpsidx, DShape &d2psidx) const
 
virtual double d2shape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidx, DShape &d2psidx) const
 
virtual void assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt)
 
virtual void describe_local_dofs (std::ostream &out, const std::string &current_string) const
 
virtual void describe_nodal_local_dofs (std::ostream &out, const std::string &current_string) const
 
virtual void assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)
 
Node *& node_pt (const unsigned &n)
 Return a pointer to the local node n. More...
 
Node *const & node_pt (const unsigned &n) const
 Return a pointer to the local node n (const version) More...
 
unsigned nnode () const
 Return the number of nodes. More...
 
virtual unsigned nnode_1d () const
 
double raw_nodal_position (const unsigned &n, const unsigned &i) const
 
double raw_nodal_position (const unsigned &t, const unsigned &n, const unsigned &i) const
 
double raw_dnodal_position_dt (const unsigned &n, const unsigned &i) const
 
double raw_dnodal_position_dt (const unsigned &n, const unsigned &j, const unsigned &i) const
 
double raw_nodal_position_gen (const unsigned &n, const unsigned &k, const unsigned &i) const
 
double raw_nodal_position_gen (const unsigned &t, const unsigned &n, const unsigned &k, const unsigned &i) const
 
double raw_dnodal_position_gen_dt (const unsigned &n, const unsigned &k, const unsigned &i) const
 
double raw_dnodal_position_gen_dt (const unsigned &j, const unsigned &n, const unsigned &k, const unsigned &i) const
 
double nodal_position (const unsigned &n, const unsigned &i) const
 
double nodal_position (const unsigned &t, const unsigned &n, const unsigned &i) const
 
double dnodal_position_dt (const unsigned &n, const unsigned &i) const
 Return the i-th component of nodal velocity: dx/dt at local node n. More...
 
double dnodal_position_dt (const unsigned &n, const unsigned &j, const unsigned &i) const
 
double nodal_position_gen (const unsigned &n, const unsigned &k, const unsigned &i) const
 
double nodal_position_gen (const unsigned &t, const unsigned &n, const unsigned &k, const unsigned &i) const
 
double dnodal_position_gen_dt (const unsigned &n, const unsigned &k, const unsigned &i) const
 
double dnodal_position_gen_dt (const unsigned &j, const unsigned &n, const unsigned &k, const unsigned &i) const
 
virtual void get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)
 
virtual void disable_ALE ()
 
virtual void enable_ALE ()
 
unsigned nnodal_position_type () const
 
bool has_hanging_nodes () const
 
unsigned nodal_dimension () const
 Return the required Eulerian dimension of the nodes in this element. More...
 
virtual unsigned nvertex_node () const
 
virtual Node * vertex_node_pt (const unsigned &j) const
 
virtual Node * construct_node (const unsigned &n)
 
virtual Node * construct_node (const unsigned &n, TimeStepper *const &time_stepper_pt)
 
virtual Node * construct_boundary_node (const unsigned &n)
 
virtual Node * construct_boundary_node (const unsigned &n, TimeStepper *const &time_stepper_pt)
 
int get_node_number (Node *const &node_pt) const
 
virtual Node * get_node_at_local_coordinate (const Vector< double > &s) const
 
double raw_nodal_value (const unsigned &n, const unsigned &i) const
 
double raw_nodal_value (const unsigned &t, const unsigned &n, const unsigned &i) const
 
double nodal_value (const unsigned &n, const unsigned &i) const
 
double nodal_value (const unsigned &t, const unsigned &n, const unsigned &i) const
 
unsigned dim () const
 
virtual ElementGeometry::ElementGeometry element_geometry () const
 Return the geometry type of the element (either Q or T usually). More...
 
virtual double interpolated_x (const Vector< double > &s, const unsigned &i) const
 Return FE interpolated coordinate x[i] at local coordinate s. More...
 
virtual double interpolated_x (const unsigned &t, const Vector< double > &s, const unsigned &i) const
 
virtual void interpolated_x (const Vector< double > &s, Vector< double > &x) const
 Return FE interpolated position x[] at local coordinate s as Vector. More...
 
virtual void interpolated_x (const unsigned &t, const Vector< double > &s, Vector< double > &x) const
 
virtual double interpolated_dxdt (const Vector< double > &s, const unsigned &i, const unsigned &t)
 
virtual void interpolated_dxdt (const Vector< double > &s, const unsigned &t, Vector< double > &dxdt)
 
unsigned ngeom_data () const
 
Data * geom_data_pt (const unsigned &j)
 
void position (const Vector< double > &zeta, Vector< double > &r) const
 
void position (const unsigned &t, const Vector< double > &zeta, Vector< double > &r) const
 
void dposition_dt (const Vector< double > &zeta, const unsigned &t, Vector< double > &drdt)
 
virtual double zeta_nodal (const unsigned &n, const unsigned &k, const unsigned &i) const
 
void interpolated_zeta (const Vector< double > &s, Vector< double > &zeta) const
 
void locate_zeta (const Vector< double > &zeta, GeomObject *&geom_object_pt, Vector< double > &s, const bool &use_coordinate_as_initial_guess=false)
 
virtual void node_update ()
 
virtual void identify_field_data_for_interactions (std::set< std::pair< Data *, unsigned >> &paired_field_data)
 
virtual void identify_geometric_data (std::set< Data * > &geometric_data_pt)
 
virtual double s_min () const
 Min value of local coordinate. More...
 
virtual double s_max () const
 Max. value of local coordinate. More...
 
double size () const
 
virtual double compute_physical_size () const
 
virtual void point_output_data (const Vector< double > &s, Vector< double > &data)
 
void point_output (std::ostream &outfile, const Vector< double > &s)
 
virtual unsigned nplot_points_paraview (const unsigned &nplot) const
 
virtual unsigned nsub_elements_paraview (const unsigned &nplot) const
 
void output_paraview (std::ofstream &file_out, const unsigned &nplot) const
 
virtual void write_paraview_output_offset_information (std::ofstream &file_out, const unsigned &nplot, unsigned &counter) const
 
virtual void write_paraview_type (std::ofstream &file_out, const unsigned &nplot) const
 
virtual void write_paraview_offsets (std::ofstream &file_out, const unsigned &nplot, unsigned &offset_sum) const
 
virtual unsigned nscalar_paraview () const
 
virtual void scalar_value_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot) const
 
virtual void scalar_value_fct_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt) const
 
virtual void scalar_value_fct_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt) const
 
virtual std::string scalar_name_paraview (const unsigned &i) const
 
virtual void output (const unsigned &t, std::ostream &outfile, const unsigned &n_plot) const
 
virtual void output_fct (std::ostream &outfile, const unsigned &n_plot, const double &time, const SolutionFunctorBase &exact_soln) const
 Output a time-dependent exact solution over the element. More...
 
virtual void get_s_plot (const unsigned &i, const unsigned &nplot, Vector< double > &s, const bool &shifted_to_interior=false) const
 
virtual std::string tecplot_zone_string (const unsigned &nplot) const
 
virtual void write_tecplot_zone_footer (std::ostream &outfile, const unsigned &nplot) const
 
virtual void write_tecplot_zone_footer (FILE *file_pt, const unsigned &nplot) const
 
virtual unsigned nplot_points (const unsigned &nplot) const
 
virtual void compute_error (FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)
 Calculate the norm of the error and that of the exact solution. More...
 
virtual void compute_error (FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm)
 Calculate the norm of the error and that of the exact solution. More...
 
virtual void compute_error (FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, Vector< double > &error, Vector< double > &norm)
 
virtual void compute_error (FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, Vector< double > &error, Vector< double > &norm)
 
virtual void compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, Vector< double > &error, Vector< double > &norm)
 
virtual void compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, Vector< double > &error, Vector< double > &norm)
 
virtual void compute_abs_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error)
 
void integrate_fct (FiniteElement::SteadyExactSolutionFctPt integrand_fct_pt, Vector< double > &integral)
 Integrate Vector-valued function over element. More...
 
void integrate_fct (FiniteElement::UnsteadyExactSolutionFctPt integrand_fct_pt, const double &time, Vector< double > &integral)
 Integrate Vector-valued time-dep function over element. More...
 
virtual void build_face_element (const int &face_index, FaceElement *face_element_pt)
 
virtual unsigned self_test ()
 
virtual unsigned get_bulk_node_number (const int &face_index, const unsigned &i) const
 
virtual int face_outer_unit_normal_sign (const int &face_index) const
 Get the sign of the outer unit normal on the face given by face_index. More...
 
virtual unsigned nnode_on_face () const
 
void face_node_number_error_check (const unsigned &i) const
 Range check for face node numbers. More...
 
virtual CoordinateMappingFctPt face_to_bulk_coordinate_fct_pt (const int &face_index) const
 
virtual BulkCoordinateDerivativesFctPt bulk_coordinate_derivatives_fct_pt (const int &face_index) const
 
- Public Member Functions inherited from oomph::GeneralisedElement
 GeneralisedElement ()
 Constructor: Initialise all pointers and all values to zero. More...
 
virtual ~GeneralisedElement ()
 Virtual destructor to clean up any memory allocated by the object. More...
 
 GeneralisedElement (const GeneralisedElement &)=delete
 Broken copy constructor. More...
 
void operator= (const GeneralisedElement &)=delete
 Broken assignment operator. More...
 
Data *& internal_data_pt (const unsigned &i)
 Return a pointer to i-th internal data object. More...
 
Data *const & internal_data_pt (const unsigned &i) const
 Return a pointer to i-th internal data object (const version) More...
 
Data *& external_data_pt (const unsigned &i)
 Return a pointer to i-th external data object. More...
 
Data *const & external_data_pt (const unsigned &i) const
 Return a pointer to i-th external data object (const version) More...
 
unsigned long eqn_number (const unsigned &ieqn_local) const
 
int local_eqn_number (const unsigned long &ieqn_global) const
 
unsigned add_external_data (Data *const &data_pt, const bool &fd=true)
 
bool external_data_fd (const unsigned &i) const
 
void exclude_external_data_fd (const unsigned &i)
 
void include_external_data_fd (const unsigned &i)
 
void flush_external_data ()
 Flush all external data. More...
 
void flush_external_data (Data *const &data_pt)
 Flush the object addressed by data_pt from the external data array. More...
 
unsigned ninternal_data () const
 Return the number of internal data objects. More...
 
unsigned nexternal_data () const
 Return the number of external data objects. More...
 
unsigned ndof () const
 Return the number of equations/dofs in the element. More...
 
void dof_vector (const unsigned &t, Vector< double > &dof)
 Return the vector of dof values at time level t. More...
 
void dof_pt_vector (Vector< double * > &dof_pt)
 Return the vector of pointers to dof values. More...
 
void set_internal_data_time_stepper (const unsigned &i, TimeStepper *const &time_stepper_pt, const bool &preserve_existing_data)
 
void assign_internal_eqn_numbers (unsigned long &global_number, Vector< double * > &Dof_pt)
 
void describe_dofs (std::ostream &out, const std::string &current_string) const
 
void add_internal_value_pt_to_map (std::map< unsigned, double * > &map_of_value_pt)
 
virtual void assign_local_eqn_numbers (const bool &store_local_dof_pt)
 
virtual void complete_setup_of_dependencies ()
 
virtual void get_residuals (Vector< double > &residuals)
 
virtual void get_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)
 
virtual void get_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &mass_matrix)
 
virtual void get_jacobian_and_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix)
 
virtual void get_dresiduals_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam)
 
virtual void get_djacobian_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam)
 
virtual void get_djacobian_and_dmass_matrix_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam, DenseMatrix< double > &dmass_matrix_dparam)
 
virtual void get_hessian_vector_products (Vector< double > const &Y, DenseMatrix< double > const &C, DenseMatrix< double > &product)
 
virtual void get_inner_products (Vector< std::pair< unsigned, unsigned >> const &history_index, Vector< double > &inner_product)
 
virtual void get_inner_product_vectors (Vector< unsigned > const &history_index, Vector< Vector< double >> &inner_product_vector)
 
virtual void compute_norm (Vector< double > &norm)
 
virtual void compute_norm (double &norm)
 
- Public Member Functions inherited from oomph::GeomObject
 GeomObject ()
 Default constructor. More...
 
 GeomObject (const unsigned &ndim)
 
 GeomObject (const unsigned &nlagrangian, const unsigned &ndim)
 
 GeomObject (const unsigned &nlagrangian, const unsigned &ndim, TimeStepper *time_stepper_pt)
 
 GeomObject (const GeomObject &dummy)=delete
 Broken copy constructor. More...
 
void operator= (const GeomObject &)=delete
 Broken assignment operator. More...
 
virtual ~GeomObject ()
 (Empty) destructor More...
 
unsigned nlagrangian () const
 Access function to # of Lagrangian coordinates. More...
 
unsigned ndim () const
 Access function to # of Eulerian coordinates. More...
 
void set_nlagrangian_and_ndim (const unsigned &n_lagrangian, const unsigned &n_dim)
 Set # of Lagrangian and Eulerian coordinates. More...
 
TimeStepper *& time_stepper_pt ()
 
TimeStepper * time_stepper_pt () const
 
virtual void position (const double &t, const Vector< double > &zeta, Vector< double > &r) const
 
virtual void dposition (const Vector< double > &zeta, DenseMatrix< double > &drdzeta) const
 
virtual void d2position (const Vector< double > &zeta, RankThreeTensor< double > &ddrdzeta) const
 
virtual void d2position (const Vector< double > &zeta, Vector< double > &r, DenseMatrix< double > &drdzeta, RankThreeTensor< double > &ddrdzeta) const
 

Private Member Functions

virtual void fill_in_generic_contribution_to_residuals_linear_elasticity (Vector< double > &residuals, DenseMatrix< double > &jacobian, unsigned flag)
 

Additional Inherited Members

- Public Types inherited from oomph::LinearElasticityEquationsBase< DIM >
typedef void(* BodyForceFctPt) (const double &t, const Vector< double > &x, Vector< double > &b)
 
- Public Types inherited from oomph::FiniteElement
typedef void(* SteadyExactSolutionFctPt) (const Vector< double > &, Vector< double > &)
 
typedef void(* UnsteadyExactSolutionFctPt) (const double &, const Vector< double > &, Vector< double > &)
 
- Static Public Member Functions inherited from oomph::LinearElasticityEquationsBase< DIM >
static void pin_redundant_nodal_solid_pressures (const Vector< GeneralisedElement * > &element_pt)
 
- Static Public Attributes inherited from oomph::FiniteElement
static double Tolerance_for_singular_jacobian = 1.0e-16
 Tolerance below which the jacobian is considered singular. More...
 
static bool Accept_negative_jacobian = false
 
static bool Suppress_output_while_checking_for_inverted_elements
 
- Static Public Attributes inherited from oomph::GeneralisedElement
static bool Suppress_warning_about_repeated_internal_data
 
static bool Suppress_warning_about_repeated_external_data = true
 
static double Default_fd_jacobian_step = 1.0e-8
 
- Protected Member Functions inherited from oomph::FiniteElement
virtual void assemble_local_to_eulerian_jacobian (const DShape &dpsids, DenseMatrix< double > &jacobian) const
 
virtual void assemble_local_to_eulerian_jacobian2 (const DShape &d2psids, DenseMatrix< double > &jacobian2) const
 
virtual void assemble_eulerian_base_vectors (const DShape &dpsids, DenseMatrix< double > &interpolated_G) const
 
template<unsigned DIM>
double invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
 
virtual double invert_jacobian_mapping (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
 
virtual double local_to_eulerian_mapping (const DShape &dpsids, DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
 
double local_to_eulerian_mapping (const DShape &dpsids, DenseMatrix< double > &inverse_jacobian) const
 
virtual double local_to_eulerian_mapping_diagonal (const DShape &dpsids, DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
 
virtual void dJ_eulerian_dnodal_coordinates (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
 
template<unsigned DIM>
void dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
 
virtual void d_dshape_eulerian_dnodal_coordinates (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
 
template<unsigned DIM>
void d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
 
virtual void transform_derivatives (const DenseMatrix< double > &inverse_jacobian, DShape &dbasis) const
 
void transform_derivatives_diagonal (const DenseMatrix< double > &inverse_jacobian, DShape &dbasis) const
 
virtual void transform_second_derivatives (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
 
template<unsigned DIM>
void transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
 
template<unsigned DIM>
void transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
 
virtual void fill_in_jacobian_from_nodal_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian)
 
void fill_in_jacobian_from_nodal_by_fd (DenseMatrix< double > &jacobian)
 
virtual void update_before_nodal_fd ()
 
virtual void reset_after_nodal_fd ()
 
virtual void update_in_nodal_fd (const unsigned &i)
 
virtual void reset_in_nodal_fd (const unsigned &i)
 
template<>
double invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
 Zero-d specialisation of function to calculate inverse of jacobian mapping. More...
 
template<>
double invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
 One-d specialisation of function to calculate inverse of jacobian mapping. More...
 
template<>
double invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
 Two-d specialisation of function to calculate inverse of jacobian mapping. More...
 
template<>
double invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
 
template<>
void dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
 
template<>
void dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
 
template<>
void dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
 
template<>
void dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
 
template<>
void d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
 
template<>
void d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
 
template<>
void d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
 
template<>
void d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
 
template<>
void transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
 
template<>
void transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
 
template<>
void transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
 
template<>
void transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
 
- Protected Member Functions inherited from oomph::GeneralisedElement
unsigned add_internal_data (Data *const &data_pt, const bool &fd=true)
 
bool internal_data_fd (const unsigned &i) const
 
void exclude_internal_data_fd (const unsigned &i)
 
void include_internal_data_fd (const unsigned &i)
 
void clear_global_eqn_numbers ()
 
void add_global_eqn_numbers (std::deque< unsigned long > const &global_eqn_numbers, std::deque< double * > const &global_dof_pt)
 
virtual void assign_internal_and_external_local_eqn_numbers (const bool &store_local_dof_pt)
 
virtual void assign_additional_local_eqn_numbers ()
 
int internal_local_eqn (const unsigned &i, const unsigned &j) const
 
int external_local_eqn (const unsigned &i, const unsigned &j)
 
void fill_in_jacobian_from_internal_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian, const bool &fd_all_data=false)
 
void fill_in_jacobian_from_internal_by_fd (DenseMatrix< double > &jacobian, const bool &fd_all_data=false)
 
void fill_in_jacobian_from_external_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian, const bool &fd_all_data=false)
 
void fill_in_jacobian_from_external_by_fd (DenseMatrix< double > &jacobian, const bool &fd_all_data=false)
 
virtual void update_before_internal_fd ()
 
virtual void reset_after_internal_fd ()
 
virtual void update_in_internal_fd (const unsigned &i)
 
virtual void reset_in_internal_fd (const unsigned &i)
 
virtual void update_before_external_fd ()
 
virtual void reset_after_external_fd ()
 
virtual void update_in_external_fd (const unsigned &i)
 
virtual void reset_in_external_fd (const unsigned &i)
 
virtual void fill_in_contribution_to_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &mass_matrix)
 
virtual void fill_in_contribution_to_jacobian_and_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix)
 
virtual void fill_in_contribution_to_dresiduals_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam)
 
virtual void fill_in_contribution_to_djacobian_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam)
 
virtual void fill_in_contribution_to_djacobian_and_dmass_matrix_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam, DenseMatrix< double > &dmass_matrix_dparam)
 
virtual void fill_in_contribution_to_hessian_vector_products (Vector< double > const &Y, DenseMatrix< double > const &C, DenseMatrix< double > &product)
 
virtual void fill_in_contribution_to_inner_products (Vector< std::pair< unsigned, unsigned >> const &history_index, Vector< double > &inner_product)
 
virtual void fill_in_contribution_to_inner_product_vectors (Vector< unsigned > const &history_index, Vector< Vector< double >> &inner_product_vector)
 
- Protected Attributes inherited from oomph::LinearElasticityEquationsBase< DIM >
ElasticityTensor * Elasticity_tensor_pt
 Pointer to the elasticity tensor. More...
 
double * Lambda_sq_pt
 Timescale ratio (non-dim. density) More...
 
bool Unsteady
 Flag that switches inertia on/off. More...
 
BodyForceFctPt Body_force_fct_pt
 Pointer to body force function. More...
 
- Protected Attributes inherited from oomph::FiniteElement
MacroElement * Macro_elem_pt
 Pointer to the element's macro element (NULL by default) More...
 
- Protected Attributes inherited from oomph::GeomObject
unsigned NLagrangian
 Number of Lagrangian (intrinsic) coordinates. More...
 
unsigned Ndim
 Number of Eulerian coordinates. More...
 
TimeStepper * Geom_object_time_stepper_pt
 
- Static Protected Attributes inherited from oomph::LinearElasticityEquationsBase< DIM >
static double Default_lambda_sq_value = 1.0
 Static default value for timescale ratio (1.0 – for natural scaling) More...
 
- Static Protected Attributes inherited from oomph::FiniteElement
static const unsigned Default_Initial_Nvalue = 0
 Default value for the number of values at a node. More...
 
static const double Node_location_tolerance = 1.0e-14
 
static const unsigned N2deriv [] = {0, 1, 3, 6}
 
- Static Protected Attributes inherited from oomph::GeneralisedElement
static DenseMatrix< double > Dummy_matrix
 
static std::deque< double * > Dof_pt_deque
 

Detailed Description

template<unsigned DIM>
class oomph::LinearElasticityEquations< DIM >

//////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////// A class for elements that solve the equations of linear elasticity in cartesian coordinates.

Constructor & Destructor Documentation

◆ LinearElasticityEquations()

template<unsigned DIM>
oomph::LinearElasticityEquations< DIM >::LinearElasticityEquations ( )
inline

Constructor.

383 {}

Member Function Documentation

◆ compute_error() [1/2]

template<unsigned DIM>
void oomph::LinearElasticityEquations< DIM >::compute_error ( std::ostream &  outfile,
FiniteElement::SteadyExactSolutionFctPt  exact_soln_pt,
double &  error,
double &  norm 
)
virtual

Validate against exact solution. Solution is provided via function pointer. Plot at a given number of plot points and compute L2 error and L2 norm of displacement solution over element

Validate against exact velocity solution Solution is provided via function pointer. Plot at a given number of plot points and compute L2 error and L2 norm of velocity solution over element.

Reimplemented from oomph::FiniteElement.

573  {
574  error = 0.0;
575  norm = 0.0;
576 
577  // Vector of local coordinates
578  Vector<double> s(DIM);
579 
580  // Vector for coordinates
581  Vector<double> x(DIM);
582 
583  // Set the value of n_intpt
584  unsigned n_intpt = this->integral_pt()->nweight();
585 
586  outfile << "ZONE" << std::endl;
587 
588  // Exact solution Vector (u,v,[w])
589  Vector<double> exact_soln(DIM);
590 
591  // Loop over the integration points
592  for (unsigned ipt = 0; ipt < n_intpt; ipt++)
593  {
594  // Assign values of s
595  for (unsigned i = 0; i < DIM; i++)
596  {
597  s[i] = this->integral_pt()->knot(ipt, i);
598  }
599 
600  // Get the integral weight
601  double w = this->integral_pt()->weight(ipt);
602 
603  // Get jacobian of mapping
604  double J = this->J_eulerian(s);
605 
606  // Premultiply the weights and the Jacobian
607  double W = w * J;
608 
609  // Get x position as Vector
610  this->interpolated_x(s, x);
611 
612  // Get exact solution at this point
613  (*exact_soln_pt)(x, exact_soln);
614 
615  // Displacement error
616  for (unsigned i = 0; i < DIM; i++)
617  {
618  norm += exact_soln[i] * exact_soln[i] * W;
619  error +=
620  (exact_soln[i] - this->interpolated_u_linear_elasticity(s, i)) *
621  (exact_soln[i] - this->interpolated_u_linear_elasticity(s, i)) * W;
622  }
623 
624  // Output x,y,[z]
625  for (unsigned i = 0; i < DIM; i++)
626  {
627  outfile << x[i] << " ";
628  }
629 
630  // Output u_error,v_error,[w_error]
631  for (unsigned i = 0; i < DIM; i++)
632  {
633  outfile << exact_soln[i] - this->interpolated_u_linear_elasticity(s, i)
634  << " ";
635  }
636  outfile << std::endl;
637  }
638  }
i
int i
Definition: BiCGSTAB_step_by_step.cpp:9
J
JacobiRotation< float > J
Definition: Jacobi_makeJacobi.cpp:3
w
RowVector3d w
Definition: Matrix_resize_int.cpp:3
oomph::FiniteElement::interpolated_x
virtual double interpolated_x(const Vector< double > &s, const unsigned &i) const
Return FE interpolated coordinate x[i] at local coordinate s.
Definition: elements.cc:3962
oomph::FiniteElement::integral_pt
Integral *const & integral_pt() const
Return the pointer to the integration scheme (const version)
Definition: elements.h:1963
oomph::FiniteElement::J_eulerian
virtual double J_eulerian(const Vector< double > &s) const
Definition: elements.cc:4103
oomph::Integral::knot
virtual double knot(const unsigned &i, const unsigned &j) const =0
Return local coordinate s[j] of i-th integration point.
oomph::Integral::nweight
virtual unsigned nweight() const =0
Return the number of integration points of the scheme.
oomph::Integral::weight
virtual double weight(const unsigned &i) const =0
Return weight of i-th integration point.
oomph::LinearElasticityEquationsBase::interpolated_u_linear_elasticity
void interpolated_u_linear_elasticity(const Vector< double > &s, Vector< double > &disp) const
Compute vector of FE interpolated displacement u at local coordinate s.
Definition: linear_elasticity_elements.h:98
s
RealScalar s
Definition: level1_cplx_impl.h:130
DIM
#define DIM
Definition: linearised_navier_stokes_elements.h:44
ProblemParameters::exact_soln
void exact_soln(const double &time, const Vector< double > &x, Vector< double > &soln)
Definition: unstructured_two_d_curved.cc:301
calibrate.error
int error
Definition: calibrate.py:297
oomph::QuadTreeNames::W
@ W
Definition: quadtree.h:63
plotDoE.x
list x
Definition: plotDoE.py:28

References DIM, calibrate::error, ProblemParameters::exact_soln(), i, J, s, w, oomph::QuadTreeNames::W, and plotDoE::x.

◆ compute_error() [2/2]

template<unsigned DIM>
void oomph::LinearElasticityEquations< DIM >::compute_error ( std::ostream &  outfile,
FiniteElement::UnsteadyExactSolutionFctPt  exact_soln_pt,
const double &  time,
double &  error,
double &  norm 
)
virtual

Validate against exact solution. Solution is provided via function pointer. Plot at a given number of plot points and compute L2 error and L2 norm of displacement solution over element (unsteady version)

Validate against exact velocity solution Solution is provided via function pointer. Plot at a given number of plot points and compute L2 error and L2 norm of velocity solution over element. Unsteady version

Reimplemented from oomph::FiniteElement.

653  {
654  error = 0.0;
655  norm = 0.0;
656 
657  // Vector of local coordinates
658  Vector<double> s(DIM);
659 
660  // Vector for coordinates
661  Vector<double> x(DIM);
662 
663  // Set the value of n_intpt
664  unsigned n_intpt = this->integral_pt()->nweight();
665 
666  outfile << "ZONE" << std::endl;
667 
668  // Exact solution Vector (u,v,[w])
669  Vector<double> exact_soln(DIM);
670 
671  // Loop over the integration points
672  for (unsigned ipt = 0; ipt < n_intpt; ipt++)
673  {
674  // Assign values of s
675  for (unsigned i = 0; i < DIM; i++)
676  {
677  s[i] = this->integral_pt()->knot(ipt, i);
678  }
679 
680  // Get the integral weight
681  double w = this->integral_pt()->weight(ipt);
682 
683  // Get jacobian of mapping
684  double J = this->J_eulerian(s);
685 
686  // Premultiply the weights and the Jacobian
687  double W = w * J;
688 
689  // Get x position as Vector
690  this->interpolated_x(s, x);
691 
692  // Get exact solution at this point
693  (*exact_soln_pt)(time, x, exact_soln);
694 
695  // Displacement error
696  for (unsigned i = 0; i < DIM; i++)
697  {
698  norm += exact_soln[i] * exact_soln[i] * W;
699  error +=
700  (exact_soln[i] - this->interpolated_u_linear_elasticity(s, i)) *
701  (exact_soln[i] - this->interpolated_u_linear_elasticity(s, i)) * W;
702  }
703 
704  // Output x,y,[z]
705  for (unsigned i = 0; i < DIM; i++)
706  {
707  outfile << x[i] << " ";
708  }
709 
710  // Output u_error,v_error,[w_error]
711  for (unsigned i = 0; i < DIM; i++)
712  {
713  outfile << exact_soln[i] - this->interpolated_u_linear_elasticity(s, i)
714  << " ";
715  }
716  outfile << std::endl;
717  }
718  }

References DIM, calibrate::error, ProblemParameters::exact_soln(), i, J, s, w, oomph::QuadTreeNames::W, and plotDoE::x.

◆ fill_in_contribution_to_jacobian()

template<unsigned DIM>
void oomph::LinearElasticityEquations< DIM >::fill_in_contribution_to_jacobian ( Vector< double > &  residuals,
DenseMatrix< double > &  jacobian 
)
inlinevirtual

The jacobian is calculated by finite differences by default, We need only to take finite differences w.r.t. positional variables For this element

Reimplemented from oomph::FiniteElement.

404  {
405  // Add the contribution to the residuals
406  this->fill_in_generic_contribution_to_residuals_linear_elasticity(
407  residuals, jacobian, 1);
408  }
oomph::LinearElasticityEquations::fill_in_generic_contribution_to_residuals_linear_elasticity
virtual void fill_in_generic_contribution_to_residuals_linear_elasticity(Vector< double > &residuals, DenseMatrix< double > &jacobian, unsigned flag)
Definition: linear_elasticity_elements.cc:190

References oomph::LinearElasticityEquations< DIM >::fill_in_generic_contribution_to_residuals_linear_elasticity().

◆ fill_in_contribution_to_residuals()

template<unsigned DIM>
void oomph::LinearElasticityEquations< DIM >::fill_in_contribution_to_residuals ( Vector< double > &  residuals)
inlinevirtual

Return the residuals for the solid equations (the discretised principle of virtual displacements)

Reimplemented from oomph::GeneralisedElement.

394  {
395  fill_in_generic_contribution_to_residuals_linear_elasticity(
396  residuals, GeneralisedElement::Dummy_matrix, 0);
397  }
oomph::GeneralisedElement::Dummy_matrix
static DenseMatrix< double > Dummy_matrix
Definition: elements.h:227

References oomph::GeneralisedElement::Dummy_matrix, and oomph::LinearElasticityEquations< DIM >::fill_in_generic_contribution_to_residuals_linear_elasticity().

◆ fill_in_generic_contribution_to_residuals_linear_elasticity()

template<unsigned DIM>
void oomph::LinearElasticityEquations< DIM >::fill_in_generic_contribution_to_residuals_linear_elasticity ( Vector< double > &  residuals,
DenseMatrix< double > &  jacobian,
unsigned  flag 
)
privatevirtual

Private helper function to compute residuals and (if requested via flag) also the Jacobian matrix.

Compute the residuals for the linear elasticity equations in cartesian coordinates. Flag indicates if we want Jacobian too.

Reimplemented in oomph::RefineableLinearElasticityEquations< DIM >.

192  {
193  // Find out how many nodes there are
194  unsigned n_node = this->nnode();
195 
196 #ifdef PARANOID
197  // Find out how many positional dofs there are
198  unsigned n_position_type = this->nnodal_position_type();
199 
200  if (n_position_type != 1)
201  {
202  throw OomphLibError("LinearElasticity is not yet implemented for more "
203  "than one position type",
204  OOMPH_CURRENT_FUNCTION,
205  OOMPH_EXCEPTION_LOCATION);
206  }
207 
208  // Throw and error if an elasticity tensor has not been set
209  if (this->Elasticity_tensor_pt == 0)
210  {
211  throw OomphLibError("No elasticity tensor set.",
212  OOMPH_CURRENT_FUNCTION,
213  OOMPH_EXCEPTION_LOCATION);
214  }
215 #endif
216 
217  // Find the indices at which the local displacements are stored
218  unsigned u_nodal_index[DIM];
219  for (unsigned i = 0; i < DIM; i++)
220  {
221  u_nodal_index[i] = this->u_index_linear_elasticity(i);
222  }
223 
224  // Timescale ratio (non-dim density)
225  double Lambda_sq = this->lambda_sq();
226 
227  // Set up memory for the shape functions
228  Shape psi(n_node);
229  DShape dpsidx(n_node, DIM);
230 
231  // Set the value of Nintpt -- the number of integration points
232  unsigned n_intpt = this->integral_pt()->nweight();
233 
234  // Set the vector to hold the local coordinates in the element
235  Vector<double> s(DIM);
236 
237  // Integer to store the local equation number
238  int local_eqn = 0, local_unknown = 0;
239 
240  // Loop over the integration points
241  for (unsigned ipt = 0; ipt < n_intpt; ipt++)
242  {
243  // Assign the values of s
244  for (unsigned i = 0; i < DIM; ++i)
245  {
246  s[i] = this->integral_pt()->knot(ipt, i);
247  }
248 
249  // Get the integral weight
250  double w = this->integral_pt()->weight(ipt);
251 
252  // Call the derivatives of the shape functions (and get Jacobian)
253  double J = this->dshape_eulerian_at_knot(ipt, psi, dpsidx);
254 
255  // Storage for Eulerian coordinates (initialised to zero)
256  Vector<double> interpolated_x(DIM, 0.0);
257 
258  // Calculate interpolated values of the derivative of global position
259  // wrt lagrangian coordinates
260  DenseMatrix<double> interpolated_dudx(DIM, DIM, 0.0);
261 
262  // Setup memory for accelerations (initialised to zero)
263  Vector<double> accel(DIM, 0.0);
264 
265  // Calculate displacements and derivatives and lagrangian coordinates
266  for (unsigned l = 0; l < n_node; l++)
267  {
268  // Loop over displacement components (deformed position)
269  for (unsigned i = 0; i < DIM; i++)
270  {
271  // Calculate the Lagrangian coordinates and the accelerations
272  interpolated_x[i] += this->raw_nodal_position(l, i) * psi(l);
273 
274  // Only compute accelerations if inertia is switched on
275  if (this->Unsteady)
276  {
277  accel[i] += this->d2u_dt2_linear_elasticity(l, i) * psi(l);
278  }
279 
280  // Get the nodal displacements
281  const double u_value = this->raw_nodal_value(l, u_nodal_index[i]);
282 
283  // Loop over derivative directions
284  for (unsigned j = 0; j < DIM; j++)
285  {
286  interpolated_dudx(i, j) += u_value * dpsidx(l, j);
287  }
288  }
289  }
290 
291  // Get body force at current time
292  Vector<double> b(DIM);
293  this->body_force(interpolated_x, b);
294 
295  // Premultiply the weights and the Jacobian
296  double W = w * J;
297 
298  //=====EQUATIONS OF LINEAR ELASTICITY ========
299 
300  // Loop over the test functions, nodes of the element
301  for (unsigned l = 0; l < n_node; l++)
302  {
303  // Loop over the displacement components
304  for (unsigned a = 0; a < DIM; a++)
305  {
306  // Get the equation number
307  local_eqn = this->nodal_local_eqn(l, u_nodal_index[a]);
308  /*IF it's not a boundary condition*/
309  if (local_eqn >= 0)
310  {
311  // Acceleration and body force
312  residuals[local_eqn] += (Lambda_sq * accel[a] - b[a]) * psi(l) * W;
313 
314  // Stress term
315  for (unsigned b = 0; b < DIM; b++)
316  {
317  for (unsigned c = 0; c < DIM; c++)
318  {
319  for (unsigned d = 0; d < DIM; d++)
320  {
321  // Add the stress terms to the residuals
322  residuals[local_eqn] += this->E(a, b, c, d) *
323  interpolated_dudx(c, d) *
324  dpsidx(l, b) * W;
325  }
326  }
327  }
328 
329  // Jacobian entries
330  if (flag)
331  {
332  // Loop over the displacement basis functions again
333  for (unsigned l2 = 0; l2 < n_node; l2++)
334  {
335  // Loop over the displacement components again
336  for (unsigned c = 0; c < DIM; c++)
337  {
338  local_unknown = this->nodal_local_eqn(l2, u_nodal_index[c]);
339  // If it's not pinned
340  if (local_unknown >= 0)
341  {
342  // Inertial term
343  if (a == c)
344  {
345  jacobian(local_eqn, local_unknown) +=
346  Lambda_sq *
347  this->node_pt(l2)->time_stepper_pt()->weight(2, 0) *
348  psi(l) * psi(l2) * W;
349  }
350 
351  for (unsigned b = 0; b < DIM; b++)
352  {
353  for (unsigned d = 0; d < DIM; d++)
354  {
355  // Add the contribution to the Jacobian matrix
356  jacobian(local_eqn, local_unknown) +=
357  this->E(a, b, c, d) * dpsidx(l2, d) * dpsidx(l, b) *
358  W;
359  }
360  }
361  } // End of if not boundary condition
362  }
363  }
364  } // End of jacobian calculation
365 
366  } // End of if not boundary condition
367  } // End of loop over coordinate directions
368  } // End of loop over shape functions
369  } // End of loop over integration points
370  }
b
Scalar * b
Definition: benchVecAdd.cpp:17
oomph::Data::time_stepper_pt
TimeStepper *& time_stepper_pt()
Return the pointer to the timestepper.
Definition: nodes.h:238
oomph::FiniteElement::node_pt
Node *& node_pt(const unsigned &n)
Return a pointer to the local node n.
Definition: elements.h:2175
oomph::FiniteElement::nnodal_position_type
unsigned nnodal_position_type() const
Definition: elements.h:2463
oomph::FiniteElement::nodal_local_eqn
int nodal_local_eqn(const unsigned &n, const unsigned &i) const
Definition: elements.h:1432
oomph::FiniteElement::nnode
unsigned nnode() const
Return the number of nodes.
Definition: elements.h:2210
oomph::FiniteElement::dshape_eulerian_at_knot
virtual double dshape_eulerian_at_knot(const unsigned &ipt, Shape &psi, DShape &dpsidx) const
Definition: elements.cc:3325
oomph::FiniteElement::raw_nodal_value
double raw_nodal_value(const unsigned &n, const unsigned &i) const
Definition: elements.h:2576
oomph::FiniteElement::raw_nodal_position
double raw_nodal_position(const unsigned &n, const unsigned &i) const
Definition: elements.cc:1686
oomph::LinearElasticityEquationsBase::Elasticity_tensor_pt
ElasticityTensor * Elasticity_tensor_pt
Pointer to the elasticity tensor.
Definition: linear_elasticity_elements.h:352
oomph::LinearElasticityEquationsBase::lambda_sq
const double & lambda_sq() const
Access function for timescale ratio (nondim density)
Definition: linear_elasticity_elements.h:189
oomph::LinearElasticityEquationsBase::body_force
void body_force(const Vector< double > &x, Vector< double > &b) const
Definition: linear_elasticity_elements.h:270
oomph::LinearElasticityEquationsBase::Unsteady
bool Unsteady
Flag that switches inertia on/off.
Definition: linear_elasticity_elements.h:358
oomph::LinearElasticityEquationsBase::E
double E(const unsigned &i, const unsigned &j, const unsigned &k, const unsigned &l) const
Access function to the entries in the elasticity tensor.
Definition: linear_elasticity_elements.h:180
oomph::LinearElasticityEquationsBase::u_index_linear_elasticity
virtual unsigned u_index_linear_elasticity(const unsigned i) const
Definition: linear_elasticity_elements.h:62
oomph::LinearElasticityEquationsBase::d2u_dt2_linear_elasticity
double d2u_dt2_linear_elasticity(const unsigned &n, const unsigned &i) const
d^2u/dt^2 at local node n
Definition: linear_elasticity_elements.h:68
oomph::TimeStepper::weight
virtual double weight(const unsigned &i, const unsigned &j) const
Access function for j-th weight for the i-th derivative.
Definition: timesteppers.h:594
a
const Scalar * a
Definition: level2_cplx_impl.h:32
Global_Physical_Variables::Lambda_sq
double Lambda_sq
Pseudo-solid mass density.
Definition: pressure_driven_torus.cc:62
calibrate.c
int c
Definition: calibrate.py:100
OOMPH_EXCEPTION_LOCATION
#define OOMPH_EXCEPTION_LOCATION
Definition: oomph_definitions.h:61
OOMPH_CURRENT_FUNCTION
#define OOMPH_CURRENT_FUNCTION
Definition: oomph_definitions.h:86
j
std::ptrdiff_t j
Definition: tut_arithmetic_redux_minmax.cpp:2

References a, b, Global_Parameters::body_force(), calibrate::c, DIM, Global_Physical_Variables::E, i, J, j, Global_Physical_Variables::Lambda_sq, OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, s, w, and oomph::QuadTreeNames::W.

Referenced by oomph::LinearElasticityEquations< DIM >::fill_in_contribution_to_jacobian(), and oomph::LinearElasticityEquations< DIM >::fill_in_contribution_to_residuals().

◆ get_stress()

template<unsigned DIM>
void oomph::LinearElasticityEquations< DIM >::get_stress ( const Vector< double > &  s,
DenseMatrix< double > &  stress 
) const
virtual

Return the Cauchy stress tensor, as calculated from the elasticity tensor at specified local coordinate

Compute the Cauchy stress tensor at local coordinate s for displacement formulation.

Implements oomph::LinearElasticityEquationsBase< DIM >.

147  {
148 #ifdef PARANOID
149  if ((stress.ncol() != DIM) || (stress.nrow() != DIM))
150  {
151  std::ostringstream error_message;
152  error_message << "Stress matrix is " << stress.ncol() << " x "
153  << stress.nrow() << ", but dimension of the equations is "
154  << DIM << std::endl;
155  throw OomphLibError(
156  error_message.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
157  }
158 #endif
159 
160  // Get strain
161  DenseMatrix<double> strain(DIM, DIM);
162  this->get_strain(s, strain);
163 
164  // Now fill in the entries of the stress tensor without exploiting
165  // symmetry -- sorry too lazy. This fct is only used for
166  // postprocessing anyway...
167  for (unsigned i = 0; i < DIM; i++)
168  {
169  for (unsigned j = 0; j < DIM; j++)
170  {
171  stress(i, j) = 0.0;
172  for (unsigned k = 0; k < DIM; k++)
173  {
174  for (unsigned l = 0; l < DIM; l++)
175  {
176  stress(i, j) += this->E(i, j, k, l) * strain(k, l);
177  }
178  }
179  }
180  }
181  }
oomph::DenseMatrix::nrow
unsigned long nrow() const
Return the number of rows of the matrix.
Definition: matrices.h:485
oomph::DenseMatrix::ncol
unsigned long ncol() const
Return the number of columns of the matrix.
Definition: matrices.h:491
oomph::LinearElasticityEquationsBase::get_strain
void get_strain(const Vector< double > &s, DenseMatrix< double > &strain) const
Return the strain tensor.
Definition: linear_elasticity_elements.cc:47
k
char char char int int * k
Definition: level2_impl.h:374

References DIM, Global_Physical_Variables::E, i, j, k, oomph::DenseMatrix< T >::ncol(), oomph::DenseMatrix< T >::nrow(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, and s.

◆ output() [1/4]

template<unsigned DIM>
void oomph::LinearElasticityEquations< DIM >::output ( FILE *  file_pt)
inlinevirtual

C-style output: x,y,[z],u,v,[w].

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::TLinearElasticityElement< DIM, NNODE_1D >, oomph::QLinearElasticityElement< DIM, NNODE_1D >, oomph::QLinearElasticityElement< DIM, 2 >, and oomph::QLinearElasticityElement< DIM, 3 >.

439  {
440  unsigned n_plot = 5;
441  output(file_pt, n_plot);
442  }
oomph::LinearElasticityEquations::output
void output(std::ostream &outfile)
Output: x,y,[z],u,v,[w].
Definition: linear_elasticity_elements.h:427

References oomph::LinearElasticityEquations< DIM >::output().

◆ output() [2/4]

template<unsigned DIM>
void oomph::LinearElasticityEquations< DIM >::output ( FILE *  file_pt,
const unsigned &  n_plot 
)
virtual

Output: x,y,[z],u,v,[w].

C-style output: x,y,[z],u,v,[w].

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::TLinearElasticityElement< DIM, NNODE_1D >, oomph::QLinearElasticityElement< DIM, NNODE_1D >, oomph::QLinearElasticityElement< DIM, 2 >, and oomph::QLinearElasticityElement< DIM, 3 >.

528  {
529  // Vector of local coordinates
530  Vector<double> s(DIM);
531 
532  // Tecplot header info
533  fprintf(file_pt, "%s", this->tecplot_zone_string(nplot).c_str());
534 
535  // Loop over plot points
536  unsigned num_plot_points = this->nplot_points(nplot);
537  for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
538  {
539  // Get local coordinates of plot point
540  this->get_s_plot(iplot, nplot, s);
541 
542  // Coordinates
543  for (unsigned i = 0; i < DIM; i++)
544  {
545  fprintf(file_pt, "%g ", this->interpolated_x(s, i));
546  }
547 
548  // Displacement
549  for (unsigned i = 0; i < DIM; i++)
550  {
551  fprintf(file_pt, "%g ", this->interpolated_u_linear_elasticity(s, i));
552  }
553  }
554  fprintf(file_pt, "\n");
555 
556  // Write tecplot footer (e.g. FE connectivity lists)
557  this->write_tecplot_zone_footer(file_pt, nplot);
558  }
oomph::FiniteElement::tecplot_zone_string
virtual std::string tecplot_zone_string(const unsigned &nplot) const
Definition: elements.h:3161
oomph::FiniteElement::get_s_plot
virtual void get_s_plot(const unsigned &i, const unsigned &nplot, Vector< double > &s, const bool &shifted_to_interior=false) const
Definition: elements.h:3148
oomph::FiniteElement::nplot_points
virtual unsigned nplot_points(const unsigned &nplot) const
Definition: elements.h:3186
oomph::FiniteElement::write_tecplot_zone_footer
virtual void write_tecplot_zone_footer(std::ostream &outfile, const unsigned &nplot) const
Definition: elements.h:3174

References DIM, i, and s.

◆ output() [3/4]

template<unsigned DIM>
void oomph::LinearElasticityEquations< DIM >::output ( std::ostream &  outfile)
inlinevirtual

Output: x,y,[z],u,v,[w].

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::TLinearElasticityElement< DIM, NNODE_1D >, oomph::QLinearElasticityElement< DIM, NNODE_1D >, oomph::QLinearElasticityElement< DIM, 2 >, and oomph::QLinearElasticityElement< DIM, 3 >.

428  {
429  unsigned n_plot = 5;
430  output(outfile, n_plot);
431  }

Referenced by oomph::LinearElasticityEquations< DIM >::output(), oomph::QLinearElasticityElement< DIM, NNODE_1D >::output(), and oomph::TLinearElasticityElement< DIM, NNODE_1D >::output().

◆ output() [4/4]

template<unsigned DIM>
void oomph::LinearElasticityEquations< DIM >::output ( std::ostream &  outfile,
const unsigned &  n_plot 
)
virtual

Output: x,y,[z],u,v,[w].

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::TLinearElasticityElement< DIM, NNODE_1D >, oomph::QLinearElasticityElement< DIM, NNODE_1D >, oomph::QLinearElasticityElement< DIM, 2 >, and oomph::QLinearElasticityElement< DIM, 3 >.

482  {
483  // Set output Vector
484  Vector<double> s(DIM);
485  Vector<double> x(DIM);
486  Vector<double> u(DIM);
487 
488  // Tecplot header info
489  outfile << this->tecplot_zone_string(nplot);
490 
491  // Loop over plot points
492  unsigned num_plot_points = this->nplot_points(nplot);
493  for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
494  {
495  // Get local coordinates of plot point
496  this->get_s_plot(iplot, nplot, s);
497 
498  // Get Eulerian coordinates and displacements
499  this->interpolated_x(s, x);
500  this->interpolated_u_linear_elasticity(s, u);
501 
502  // Output the x,y,..
503  for (unsigned i = 0; i < DIM; i++)
504  {
505  outfile << x[i] << " ";
506  }
507 
508  // Output u,v,..
509  for (unsigned i = 0; i < DIM; i++)
510  {
511  outfile << u[i] << " ";
512  }
513 
514  outfile << std::endl;
515  }
516 
517  // Write tecplot footer (e.g. FE connectivity lists)
518  this->write_tecplot_zone_footer(outfile, nplot);
519  }

References DIM, i, s, and plotDoE::x.

◆ output_fct() [1/2]

template<unsigned DIM>
void oomph::LinearElasticityEquations< DIM >::output_fct ( std::ostream &  outfile,
const unsigned &  nplot,
const double &  time,
FiniteElement::UnsteadyExactSolutionFctPt  exact_soln_pt 
)
virtual

Output exact solution x,y,[z],u,v,[w] (unsteady version)

Reimplemented from oomph::FiniteElement.

433  {
434  // Vector of local coordinates
435  Vector<double> s(DIM);
436 
437  // Vector for coordintes
438  Vector<double> x(DIM);
439 
440  // Tecplot header info
441  outfile << this->tecplot_zone_string(nplot);
442 
443  // Exact solution Vector
444  Vector<double> exact_soln(DIM);
445 
446  // Loop over plot points
447  unsigned num_plot_points = this->nplot_points(nplot);
448  for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
449  {
450  // Get local coordinates of plot point
451  this->get_s_plot(iplot, nplot, s);
452 
453  // Get x position as Vector
454  this->interpolated_x(s, x);
455 
456  // Get exact solution at this point
457  (*exact_soln_pt)(time, x, exact_soln);
458 
459  // Output x,y,...,u_exact,...
460  for (unsigned i = 0; i < DIM; i++)
461  {
462  outfile << x[i] << " ";
463  }
464  for (unsigned i = 0; i < DIM; i++)
465  {
466  outfile << exact_soln[i] << " ";
467  }
468  outfile << std::endl;
469  }
470 
471  // Write tecplot footer (e.g. FE connectivity lists)
472  this->write_tecplot_zone_footer(outfile, nplot);
473  }

References DIM, ProblemParameters::exact_soln(), i, s, and plotDoE::x.

◆ output_fct() [2/2]

template<unsigned DIM>
void oomph::LinearElasticityEquations< DIM >::output_fct ( std::ostream &  outfile,
const unsigned &  nplot,
FiniteElement::SteadyExactSolutionFctPt  exact_soln_pt 
)
virtual

Output exact solution x,y,[z],u,v,[w].

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::QLinearElasticityElement< DIM, NNODE_1D >, oomph::QLinearElasticityElement< DIM, 2 >, and oomph::QLinearElasticityElement< DIM, 3 >.

381  {
382  // Vector of local coordinates
383  Vector<double> s(DIM);
384 
385  // Vector for coordintes
386  Vector<double> x(DIM);
387 
388  // Tecplot header info
389  outfile << this->tecplot_zone_string(nplot);
390 
391  // Exact solution Vector
392  Vector<double> exact_soln(DIM);
393 
394  // Loop over plot points
395  unsigned num_plot_points = this->nplot_points(nplot);
396  for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
397  {
398  // Get local coordinates of plot point
399  this->get_s_plot(iplot, nplot, s);
400 
401  // Get x position as Vector
402  this->interpolated_x(s, x);
403 
404  // Get exact solution at this point
405  (*exact_soln_pt)(x, exact_soln);
406 
407  // Output x,y,...,u_exact,...
408  for (unsigned i = 0; i < DIM; i++)
409  {
410  outfile << x[i] << " ";
411  }
412  for (unsigned i = 0; i < DIM; i++)
413  {
414  outfile << exact_soln[i] << " ";
415  }
416  outfile << std::endl;
417  }
418 
419  // Write tecplot footer (e.g. FE connectivity lists)
420  this->write_tecplot_zone_footer(outfile, nplot);
421  }

References DIM, ProblemParameters::exact_soln(), i, s, and plotDoE::x.

Referenced by oomph::QLinearElasticityElement< DIM, NNODE_1D >::output_fct().

◆ required_nvalue()

template<unsigned DIM>
unsigned oomph::LinearElasticityEquations< DIM >::required_nvalue ( const unsigned &  n) const
inlinevirtual

Number of values required at node n.

Reimplemented from oomph::FiniteElement.

387  {
388  return DIM;
389  }

References DIM.

The documentation for this class was generated from the following files: