#include <axisym_solid_elements.h>

Inheritance diagram for oomph::AxisymmetricPVDEquationsWithPressure:

Public Member Functions
	AxisymmetricPVDEquationsWithPressure ()
	Constructor, by default the element is not incompressible. More...

ConstitutiveLaw *&	constitutive_law_pt ()
	Return the constitutive law pointer. More...

void	get_stress (const DenseMatrix< double > &g, const DenseMatrix< double > &G, DenseMatrix< double > &sigma, DenseMatrix< double > &Gup, double &pressure_stress, double &kappa)

void	get_stress (const DenseMatrix< double > &g, const DenseMatrix< double > &G, DenseMatrix< double > &sigma, DenseMatrix< double > &Gup, double &detG)

bool	is_incompressible () const
	Return whether the material is incompressible. More...

void	set_incompressible ()
	Set the material to be incompressible. More...

void	set_compressible ()
	Set the material to be compressible. More...

virtual unsigned	nsolid_pres () const =0
	Return the number of solid pressure degrees of freedom. More...

virtual double	solid_p (const unsigned &l)=0
	Return the lth solid pressures. More...

void	fill_in_contribution_to_residuals (Vector< double > &residuals)
	Return the residuals. More...

void	fill_in_contribution_to_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	Return the residuals and the jacobian. More...

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

double	compute_physical_size () const
	Overload/implement the size function. More...

double	interpolated_solid_p (const Vector< double > &s)
	Return the interpolated_solid_pressure. More...

void	output (std::ostream &outfile)
	Overload the output function. More...

void	output (std::ostream &outfile, const unsigned &n_plot)
	Output function. More...

void	output (FILE *file_pt)
	Overload the output function. More...

void	output (FILE *file_pt, const unsigned &n_plot)
	Output function. More...

Public Member Functions inherited from oomph::SolidFiniteElement
void	set_lagrangian_dimension (const unsigned &lagrangian_dimension)

virtual bool	has_internal_solid_data ()

	SolidFiniteElement ()
	Constructor: Set defaults. More...

virtual	~SolidFiniteElement ()
	Destructor to clean up any allocated memory. More...

	SolidFiniteElement (const SolidFiniteElement &)=delete
	Broken copy constructor. More...

unsigned	ngeom_data () const
	Broken assignment operator. More...

Data *	geom_data_pt (const unsigned &j)

void	identify_geometric_data (std::set< Data * > &geometric_data_pt)

double	zeta_nodal (const unsigned &n, const unsigned &k, const unsigned &i) const

virtual void	get_x_and_xi (const Vector< double > &s, Vector< double > &x_fe, Vector< double > &x, Vector< double > &xi_fe, Vector< double > &xi) const

virtual void	set_macro_elem_pt (MacroElement *macro_elem_pt)

virtual void	set_macro_elem_pt (MacroElement macro_elem_pt, MacroElement undeformed_macro_elem_pt)

void	set_undeformed_macro_elem_pt (MacroElement *undeformed_macro_elem_pt)

MacroElement *	undeformed_macro_elem_pt ()
	Access function to pointer to "undeformed" macro element. More...

double	dshape_lagrangian (const Vector< double > &s, Shape &psi, DShape &dpsidxi) const

virtual double	dshape_lagrangian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidxi) const

double	d2shape_lagrangian (const Vector< double > &s, Shape &psi, DShape &dpsidxi, DShape &d2psidxi) const

virtual double	d2shape_lagrangian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidxi, DShape &d2psidxi) const

unsigned	lagrangian_dimension () const

unsigned	nnodal_lagrangian_type () const

Node *	construct_node (const unsigned &n)
	Construct the local node n and return a pointer to it. More...

Node *	construct_node (const unsigned &n, TimeStepper *const &time_stepper_pt)

Node *	construct_boundary_node (const unsigned &n)

Node *	construct_boundary_node (const unsigned &n, TimeStepper *const &time_stepper_pt)

virtual void	assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)

void	describe_local_dofs (std::ostream &out, const std::string &current_string) const

double	raw_lagrangian_position (const unsigned &n, const unsigned &i) const

double	raw_lagrangian_position_gen (const unsigned &n, const unsigned &k, const unsigned &i) const

double	lagrangian_position (const unsigned &n, const unsigned &i) const
	Return i-th Lagrangian coordinate at local node n. More...

double	lagrangian_position_gen (const unsigned &n, const unsigned &k, const unsigned &i) const

virtual double	interpolated_xi (const Vector< double > &s, const unsigned &i) const

virtual void	interpolated_xi (const Vector< double > &s, Vector< double > &xi) const

virtual void	interpolated_dxids (const Vector< double > &s, DenseMatrix< double > &dxids) const

virtual void	J_lagrangian (const Vector< double > &s) const

virtual double	J_lagrangian_at_knot (const unsigned &ipt) const

SolidInitialCondition *&	solid_ic_pt ()
	Pointer to object that describes the initial condition. More...

void	enable_solve_for_consistent_newmark_accel ()

void	disable_solve_for_consistent_newmark_accel ()
	Set to reset the problem being solved to be the standard problem. More...

MultiplierFctPt &	multiplier_fct_pt ()

MultiplierFctPt	multiplier_fct_pt () const

virtual void	get_residuals_for_solid_ic (Vector< double > &residuals)

void	fill_in_residuals_for_solid_ic (Vector< double > &residuals)

void	fill_in_jacobian_for_solid_ic (Vector< double > &residuals, DenseMatrix< double > &jacobian)

void	fill_in_jacobian_for_newmark_accel (DenseMatrix< double > &jacobian)

void	compute_norm (double &el_norm)

int	position_local_eqn (const unsigned &n, const unsigned &k, const unsigned &j) 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)

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_nodal_local_dofs (std::ostream &out, const std::string &current_string) const

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 ()

virtual unsigned	required_nvalue (const unsigned &n) const

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

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)

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)

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 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 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, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
	Output an exact solution over the element. More...

virtual void	output_fct (std::ostream &outfile, const unsigned &n_plot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt)
	Output a time-dependent exact solution over the element. More...

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, double &error, double &norm)

virtual void	compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, 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 unsigned	ndof_types () const

virtual void	get_dof_numbers_for_unknowns (std::list< std::pair< unsigned long, unsigned >> &dof_lookup_list) const

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

Protected Member Functions
virtual int	solid_p_local_eqn (const unsigned &i)=0

virtual void	solid_pshape (const Vector< double > &s, Shape &psi) const =0
	Return the solid pressure shape functions. More...

void	solid_pshape_at_knot (const unsigned &ipt, Shape &psi) const
	Return the stored solid shape functions at the knots. More...

Protected Member Functions inherited from oomph::SolidFiniteElement
void	fill_in_generic_jacobian_for_solid_ic (Vector< double > &residuals, DenseMatrix< double > &jacobian, const unsigned &flag)

void	set_nnodal_lagrangian_type (const unsigned &nlagrangian_type)

virtual double	local_to_lagrangian_mapping (const DShape &dpsids, DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const

double	local_to_lagrangian_mapping (const DShape &dpsids, DenseMatrix< double > &inverse_jacobian) const

virtual double	local_to_lagrangian_mapping_diagonal (const DShape &dpsids, DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const

virtual void	assign_solid_local_eqn_numbers (const bool &store_local_dof)
	Assign local equation numbers for the solid equations in the element. More...

void	describe_solid_local_dofs (std::ostream &out, const std::string &current_string) const
	Classifies dofs locally for solid specific aspects. More...

void	fill_in_contribution_to_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)

virtual void	fill_in_jacobian_from_solid_position_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian)

void	fill_in_jacobian_from_solid_position_by_fd (DenseMatrix< double > &jacobian)

virtual void	update_before_solid_position_fd ()

virtual void	reset_after_solid_position_fd ()

virtual void	update_in_solid_position_fd (const unsigned &i)

virtual void	reset_in_solid_position_fd (const unsigned &i)

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)

Private Attributes
ConstitutiveLaw *	Constitutive_law_pt
	Pointer to constitutive law. More...

bool	Incompressible
	Boolean to determine whether the solid is incompressible or not. More...

Additional Inherited Members
Public Types inherited from oomph::SolidFiniteElement
typedef double(*	MultiplierFctPt) (const Vector< double > &xi)

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 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 Attributes inherited from oomph::SolidFiniteElement
MacroElement *	Undeformed_macro_elem_pt
	Pointer to the element's "undeformed" macro element (NULL by default) More...

SolidInitialCondition *	Solid_ic_pt
	Pointer to object that specifies the initial condition. More...

bool	Solve_for_consistent_newmark_accel_flag

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::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

A class for elements that solve the equations of solid mechanics, based on the principle of virtual displacements in axisymmetric coordinates in a formulation that allows for incompressibility or near incompressibility.

Constructor & Destructor Documentation

◆ AxisymmetricPVDEquationsWithPressure()

oomph::AxisymmetricPVDEquationsWithPressure::AxisymmetricPVDEquationsWithPressure ( )

inline

Constructor, by default the element is not incompressible.

       : Constitutive_law_pt(0), Incompressible(false)
     {
     }

Member Function Documentation

◆ compute_physical_size()

double oomph::AxisymmetricPVDEquationsWithPressure::compute_physical_size ( ) const

inlinevirtual

Overload/implement the size function.

Reimplemented from oomph::FiniteElement.

     {
       unsigned n_node = nnode();
       unsigned n_position_type = 1;
  
       // Set up memory for the shape functions
       Shape psi(n_node, n_position_type);
       DShape dpsidxi(n_node, n_position_type, 2);
  
       // Set sum to zero
       double sum = 0.0;
       // Set the value of n_intpt
       unsigned n_intpt = integral_pt()->nweight();
  
       // Loop over the integration points
       // Loop in s1 direction*
       for (unsigned ipt = 0; ipt < n_intpt; ipt++)
       {
         // Get the integral weight
         double w = integral_pt()->weight(ipt);
         // Call the derivatives of the shape function wrt lagrangian coordinates
         double J = dshape_lagrangian_at_knot(ipt, psi, dpsidxi);
         // Premultiply the weights and the Jacobian
         double W = w * J;
  
         // Calculate the local Lagrangian coordinates, position components
         // and the derivatives of global position components
         // wrt lagrangian coordinates
         double interpolated_xi[2] = {0.0, 0.0};
         double interpolated_X[2] = {0.0, 0.0};
         double interpolated_dXdxi[2][2];
  
         // Initialise interpolated_dXdxi to zero
         for (unsigned i = 0; i < 2; i++)
         {
           for (unsigned j = 0; j < 2; j++)
           {
             interpolated_dXdxi[i][j] = 0.0;
           }
         }
  
         // Calculate displacements and derivatives
         for (unsigned l = 0; l < n_node; l++)
         {
           // Loop over positional dofs
           for (unsigned k = 0; k < n_position_type; k++)
           {
             // Loop over displacement components (deformed position)
             for (unsigned i = 0; i < 2; i++)
             {
               // Set the value of the lagrangian coordinate
               interpolated_xi[i] +=
                 lagrangian_position_gen(l, k, i) * psi(l, k);
               // Set the value of the position component
               interpolated_X[i] += nodal_position_gen(l, k, i) * psi(l, k);
               // Loop over Lagrangian derivative directions
               for (unsigned j = 0; j < 2; j++)
               {
                 // Calculate dX[i]/dxi_{j}
                 interpolated_dXdxi[i][j] +=
                   nodal_position_gen(l, k, i) * dpsidxi(l, k, j);
               }
             }
           }
         }
  
         // Now calculate the deformed metric tensor
         DenseMatrix<double> G(3);
         // r row
         G(0, 0) = interpolated_dXdxi[0][0] * interpolated_dXdxi[0][0] +
                   interpolated_dXdxi[1][0] * interpolated_dXdxi[1][0];
         G(0, 1) = interpolated_dXdxi[0][0] *
                     (interpolated_dXdxi[0][1] - interpolated_X[1]) +
                   interpolated_dXdxi[1][0] *
                     (interpolated_dXdxi[1][1] + interpolated_X[0]);
         G(0, 2) = 0.0;
         // theta row
         G(1, 0) = G(0, 1);
         G(1, 1) = (interpolated_dXdxi[0][1] - interpolated_X[1]) *
                     (interpolated_dXdxi[0][1] - interpolated_X[1]) +
                   (interpolated_dXdxi[1][1] + interpolated_X[0]) *
                     (interpolated_dXdxi[1][1] + interpolated_X[0]);
         G(1, 2) = 0.0;
         // phi row
         G(2, 0) = 0.0;
         G(2, 1) = 0.0;
         G(2, 2) = (interpolated_X[0] * sin(interpolated_xi[1]) +
                    interpolated_X[1] * cos(interpolated_xi[1])) *
                   (interpolated_X[0] * sin(interpolated_xi[1]) +
                    interpolated_X[1] * cos(interpolated_xi[1]));
  
         // Calculate the determinant of the metric tensor
         double detG = G(0, 0) * G(1, 1) * G(2, 2) - G(0, 1) * G(1, 0) * G(2, 2);
  
         // Add the appropriate weight to the integral, i.e. sqrt of metric
         // tensor
         sum += W * sqrt(detG);
       }
  
       // Return the volume
       return (2.0 * MathematicalConstants::Pi * sum);
     }

References cos(), oomph::SolidFiniteElement::dshape_lagrangian_at_knot(), G, i, oomph::FiniteElement::integral_pt(), oomph::SolidFiniteElement::interpolated_xi(), J, j, k, oomph::SolidFiniteElement::lagrangian_position_gen(), oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_position_gen(), oomph::Integral::nweight(), oomph::MathematicalConstants::Pi, sin(), sqrt(), w, oomph::QuadTreeNames::W, and oomph::Integral::weight().

◆ constitutive_law_pt()

ConstitutiveLaw*& oomph::AxisymmetricPVDEquationsWithPressure::constitutive_law_pt ( )

inline

Return the constitutive law pointer.

     {
       return Constitutive_law_pt;
     }

References Constitutive_law_pt.

◆ fill_in_contribution_to_jacobian()

void oomph::AxisymmetricPVDEquationsWithPressure::fill_in_contribution_to_jacobian	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian
	)

inlinevirtual

Return the residuals and the jacobian.

Reimplemented from oomph::GeneralisedElement.

     {
       // Call the generic routine with the flag set to 1
       fill_in_generic_residual_contribution_axisym_pvd_with_pressure(
         residuals, jacobian, 1);
       // Call the finite difference routine for the displacements
       SolidFiniteElement::fill_in_jacobian_from_solid_position_by_fd(jacobian);
     }

References fill_in_generic_residual_contribution_axisym_pvd_with_pressure(), and oomph::SolidFiniteElement::fill_in_jacobian_from_solid_position_by_fd().

◆ fill_in_contribution_to_residuals()

void oomph::AxisymmetricPVDEquationsWithPressure::fill_in_contribution_to_residuals ( Vector< double > & residuals )

inlinevirtual

Return the residuals.

Reimplemented from oomph::GeneralisedElement.

     {
       // Call the generic residuals function with flag set to 0
       // using a dummy matrix argument
       fill_in_generic_residual_contribution_axisym_pvd_with_pressure(
         residuals, GeneralisedElement::Dummy_matrix, 0);
     }

References oomph::GeneralisedElement::Dummy_matrix, and fill_in_generic_residual_contribution_axisym_pvd_with_pressure().

◆ fill_in_generic_residual_contribution_axisym_pvd_with_pressure()

void oomph::AxisymmetricPVDEquationsWithPressure::fill_in_generic_residual_contribution_axisym_pvd_with_pressure	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian,
		unsigned	flag
	)

inline

Return the residuals for the equations of solid mechanics formulated in the incompressible case!

     {
       // Set the number of Lagrangian coordinates
       unsigned n_lagrangian = 2;
       // Find out how many nodes there are
       unsigned n_node = nnode();
       // Find out how many positional dofs there are
       unsigned n_position_type = nnodal_position_type();
       // Find out how many pressure dofs there are
       unsigned n_solid_pres = nsolid_pres();
  
       // Integers to store the local equation and unknown numbers
       int local_eqn = 0, local_unknown = 0;
  
       // Set up memory for the shape functions
       Shape psi(n_node, n_position_type);
       DShape dpsidxi(n_node, n_position_type, n_lagrangian);
  
       // Set up memory for the pressure shape functions
       Shape psisp(n_solid_pres);
  
       // Set the value of n_intpt
       unsigned n_intpt = integral_pt()->nweight();
  
       // Loop over the integration points
       for (unsigned ipt = 0; ipt < n_intpt; ipt++)
       {
         // Get the integral weight
         double w = integral_pt()->weight(ipt);
         // Call the derivatives of the shape functions
         double J = dshape_lagrangian_at_knot(ipt, psi, dpsidxi);
         // Call the pressure shape functions
         solid_pshape_at_knot(ipt, psisp);
  
         // Premultiply the weights and the Jacobian
         double W = w * J;
  
         // Calculate the local Lagrangian coordinates, position components
         // and the derivatives of global position components
         // wrt lagrangian coordinates
         double interpolated_xi[2] = {0.0, 0.0};
         double interpolated_X[2] = {0.0, 0.0};
         double interpolated_dXdxi[2][2];
         double interpolated_solid_p = 0.0;
  
         // Initialise interpolated_dXdxi to zero
         for (unsigned i = 0; i < 2; i++)
         {
           for (unsigned j = 0; j < 2; j++)
           {
             interpolated_dXdxi[i][j] = 0.0;
           }
         }
  
         // Calculate displacements and derivatives
         for (unsigned l = 0; l < n_node; l++)
         {
           // Loop over positional dofs
           for (unsigned k = 0; k < n_position_type; k++)
           {
             // Loop over displacement components (deformed position)
             for (unsigned i = 0; i < 2; i++)
             {
               // Set the value of the lagrangian coordinate
               interpolated_xi[i] +=
                 lagrangian_position_gen(l, k, i) * psi(l, k);
               // Set the value of the position component
               interpolated_X[i] += nodal_position_gen(l, k, i) * psi(l, k);
               // Loop over Lagrangian derivative directions
               for (unsigned j = 0; j < 2; j++)
               {
                 // Calculate dX[i]/dxi_{j}
                 interpolated_dXdxi[i][j] +=
                   nodal_position_gen(l, k, i) * dpsidxi(l, k, j);
               }
             }
           }
         }
  
         // Calculate the local internal pressure
         for (unsigned l = 0; l < n_solid_pres; l++)
         {
           interpolated_solid_p += solid_p(l) * psisp[l];
         }
  
         // We are now in a position to calculate the undeformed metric tensor
         DenseMatrix<double> g(3);
         // r row
         g(0, 0) = 1.0;
         g(0, 1) = 0.0;
         g(0, 2) = 0.0;
         // theta row
         g(1, 0) = 0.0;
         g(1, 1) = interpolated_xi[0] * interpolated_xi[0];
         g(1, 2) = 0.0;
         // phi row
         g(2, 0) = 0.0;
         g(2, 1) = 0.0;
         g(2, 2) = interpolated_xi[0] * interpolated_xi[0] *
                   sin(interpolated_xi[1]) * sin(interpolated_xi[1]);
  
         // Find the determinant of the undeformed metric tensor
         double detg = g(0, 0) * g(1, 1) * g(2, 2);
  
         // Now multiply the weight by the square-root of the determinant of the
         // undeformed metric tensor r^2 sin(theta)
         W *= sqrt(detg);
  
         // Now calculate the deformed metric tensor
         DenseMatrix<double> G(3);
         // r row
         G(0, 0) = interpolated_dXdxi[0][0] * interpolated_dXdxi[0][0] +
                   interpolated_dXdxi[1][0] * interpolated_dXdxi[1][0];
         G(0, 1) = interpolated_dXdxi[0][0] *
                     (interpolated_dXdxi[0][1] - interpolated_X[1]) +
                   interpolated_dXdxi[1][0] *
                     (interpolated_dXdxi[1][1] + interpolated_X[0]);
         G(0, 2) = 0.0;
         // theta row
         G(1, 0) = G(0, 1);
         G(1, 1) = (interpolated_dXdxi[0][1] - interpolated_X[1]) *
                     (interpolated_dXdxi[0][1] - interpolated_X[1]) +
                   (interpolated_dXdxi[1][1] + interpolated_X[0]) *
                     (interpolated_dXdxi[1][1] + interpolated_X[0]);
         G(1, 2) = 0.0;
         // phi row
         G(2, 0) = 0.0;
         G(2, 1) = 0.0;
         G(2, 2) = (interpolated_X[0] * sin(interpolated_xi[1]) +
                    interpolated_X[1] * cos(interpolated_xi[1])) *
                   (interpolated_X[0] * sin(interpolated_xi[1]) +
                    interpolated_X[1] * cos(interpolated_xi[1]));
  
  
         // Now calculate the stress tensor from the constitutive law
         DenseMatrix<double> sigma(3), Gup(3);
         double detG = 0.0, pressure_stress = 0.0, kappa = 0.0;
         // If it's incompressible call one form of the constitutive law
         if (Incompressible)
         {
           get_stress(g, G, sigma, Gup, detG);
         }
         // Otherwise call another form
         else
         {
           get_stress(g, G, sigma, Gup, pressure_stress, kappa);
         }
  
  
         //=====EQUATIONS OF ELASTICITY FROM PRINCIPLE OF VIRTUAL
         // DISPLACEMENTS========
  
         // Loop over the test functions, nodes of the element
         for (unsigned l = 0; l < n_node; l++)
         {
           // Loop of types of dofs
           for (unsigned k = 0; k < n_position_type; k++)
           {
             // Radial displacemenet component
             unsigned i = 0;
             local_eqn = position_local_eqn(l, k, i);
             /*IF it's not a boundary condition*/
             if (local_eqn >= 0)
             {
               // Add the term for variations in radial position
               residuals[local_eqn] +=
                 ((sigma(0, 1) + interpolated_solid_p * Gup(0, 1)) *
                    interpolated_dXdxi[1][0] +
                  (sigma(1, 1) + interpolated_solid_p * Gup(1, 1)) *
                    (interpolated_dXdxi[1][1] + interpolated_X[0]) +
                  (sigma(2, 2) + interpolated_solid_p * Gup(2, 2)) *
                    sin(interpolated_xi[1]) *
                    (interpolated_X[0] * sin(interpolated_xi[1]) +
                     interpolated_X[1] * cos(interpolated_xi[1]))) *
                 psi(l, k) * W;
  
               // Add the terms for the variations in dX_{r}/dxi_{j}
               for (unsigned j = 0; j < 2; j++)
               {
                 residuals[local_eqn] +=
                   ((sigma(j, 0) + interpolated_solid_p * Gup(j, 0)) *
                      interpolated_dXdxi[0][0] +
                    (sigma(j, 1) + interpolated_solid_p * Gup(j, 1)) *
                      (interpolated_dXdxi[0][1] - interpolated_X[1])) *
                   dpsidxi(l, k, j) * W;
               }
  
               // Can add in the pressure jacobian terms
               if (flag)
               {
                 // Loop over the pressure nodes
                 for (unsigned l2 = 0; l2 < n_solid_pres; l2++)
                 {
                   local_unknown = solid_p_local_eqn(l2);
                   // If it's not a boundary condition
                   if (local_unknown >= 0)
                   {
                     jacobian(local_eqn, local_unknown) +=
                       (psisp[l2] * Gup(0, 1) * interpolated_dXdxi[1][0] +
                        psisp[l2] * Gup(1, 1) *
                          (interpolated_dXdxi[1][1] + interpolated_X[0]) +
                        psisp[l2] * Gup(2, 2) * sin(interpolated_xi[1]) *
                          (interpolated_X[0] * sin(interpolated_xi[1]) +
                           interpolated_X[1] * cos(interpolated_xi[1]))) *
                       psi(l, k) * W;
  
                     // Add the terms for the variations in dX_{r}/dxi_{j}
                     for (unsigned j = 0; j < 2; j++)
                     {
                       jacobian(local_eqn, local_unknown) +=
                         (psisp[l2] * Gup(j, 0) * interpolated_dXdxi[0][0] +
                          psisp[l2] * Gup(j, 1) *
                            (interpolated_dXdxi[0][1] - interpolated_X[1])) *
                         dpsidxi(l, k, j) * W;
                     }
                   } // End of if not boundary condition
                 }
               } // End of if(flag)
             } // End of if Position_local_eqn
  
             // Theta displacement component
             i = 1;
             local_eqn = position_local_eqn(l, k, i);
             /*IF it's not a boundary condition*/
             if (local_eqn >= 0)
             {
               // Add the term for variations in azimuthal position
               residuals[local_eqn] +=
                 (-(sigma(0, 1) + interpolated_solid_p * Gup(0, 1)) *
                    interpolated_dXdxi[0][0] -
                  (sigma(1, 1) + interpolated_solid_p * Gup(1, 1)) *
                    (interpolated_dXdxi[0][1] - interpolated_X[1]) +
                  (sigma(2, 2) + interpolated_solid_p * Gup(2, 2)) *
                    cos(interpolated_xi[1]) *
                    (interpolated_X[0] * sin(interpolated_xi[1]) +
                     interpolated_X[1] * cos(interpolated_xi[1]))) *
                 psi(l, k) * W;
  
               // Add the terms for the variations in dX_{theta}/dxi_{j}
               for (unsigned j = 0; j < 2; j++)
               {
                 residuals[local_eqn] +=
                   ((sigma(j, 0) + interpolated_solid_p * Gup(j, 0)) *
                      interpolated_dXdxi[1][0] +
                    (sigma(j, 1) + interpolated_solid_p * Gup(j, 1)) *
                      (interpolated_dXdxi[1][1] + interpolated_X[0])) *
                   dpsidxi(l, k, j) * W;
               }
  
               // Can add in the pressure jacobian terms
               if (flag)
               {
                 // Loop over the pressure nodes
                 for (unsigned l2 = 0; l2 < n_solid_pres; l2++)
                 {
                   local_unknown = solid_p_local_eqn(l2);
                   // If it's not a boundary condition
                   if (local_unknown >= 0)
                   {
                     // Add the term for variations in azimuthal position
                     jacobian(local_eqn, local_unknown) +=
                       (-psisp[l2] * Gup(0, 1) * interpolated_dXdxi[0][0] -
                        psisp[l2] * Gup(1, 1) *
                          (interpolated_dXdxi[0][1] - interpolated_X[1]) +
                        psisp[l2] * Gup(2, 2) * cos(interpolated_xi[1]) *
                          (interpolated_X[0] * sin(interpolated_xi[1]) +
                           interpolated_X[1] * cos(interpolated_xi[1]))) *
                       psi(l, k) * W;
  
                     // Add the terms for the variations in dX_{theta}/dxi_{j}
                     for (unsigned j = 0; j < 2; j++)
                     {
                       jacobian(local_eqn, local_unknown) +=
                         (psisp[l2] * Gup(j, 0) * interpolated_dXdxi[1][0] +
                          psisp[l2] * Gup(j, 1) *
                            (interpolated_dXdxi[1][1] + interpolated_X[0])) *
                         dpsidxi(l, k, j) * W;
                     }
                   }
                 }
               } // End of if(flag)
             } // End of Position_local_eqn
           } // End of loop over type of dof
         } // End of loop over shape functions
  
  
         //======================CONSTRAINT EQUATIONS FOR THE PRESSURE===========
  
  
         // Now loop over the pressure degrees of freedom
         for (unsigned l = 0; l < n_solid_pres; l++)
         {
           local_eqn = solid_p_local_eqn(l);
           // If it's not a bondary condition
           if (local_eqn >= 0)
           {
             // For true incompressibility we need the ratio of determinants of
             // the metric tensors to be exactly 1.0
             if (Incompressible)
             {
               residuals[local_eqn] += (detG / detg - 1.0) * psisp[l] * W;
  
               // No Jacobian terms since the pressure does not feature
               // in the incompressibility constraint
             }
             else
             {
               // Otherwise the pressure must be that calculated by the
               // constitutive law
               residuals[local_eqn] +=
                 (kappa * interpolated_solid_p - pressure_stress) * psisp[l] * W;
  
               // Add in the jacobian terms
               if (flag)
               {
                 // Loop over the pressure nodes again
                 for (unsigned l2 = 0; l2 < n_solid_pres; l2++)
                 {
                   local_unknown = solid_p_local_eqn(l2);
                   // If not a boundary condition
                   if (local_unknown >= 0)
                   {
                     jacobian(local_eqn, local_unknown) +=
                       kappa * psisp[l2] * psisp[l] * W;
                   }
                 }
               } // End of jacobian terms
             } // End of else
  
           } // End of if not boundary condition
         }
  
       } // End of loop over integration points
     }

References cos(), oomph::SolidFiniteElement::dshape_lagrangian_at_knot(), G, get_stress(), i, Incompressible, oomph::FiniteElement::integral_pt(), interpolated_solid_p(), oomph::SolidFiniteElement::interpolated_xi(), J, j, k, oomph::SolidFiniteElement::lagrangian_position_gen(), oomph::FiniteElement::nnodal_position_type(), oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_position_gen(), nsolid_pres(), oomph::Integral::nweight(), oomph::SolidFiniteElement::position_local_eqn(), calibrate::sigma, sin(), solid_p(), solid_p_local_eqn(), solid_pshape_at_knot(), sqrt(), w, oomph::QuadTreeNames::W, and oomph::Integral::weight().

Referenced by fill_in_contribution_to_jacobian(), and fill_in_contribution_to_residuals().

◆ get_stress() [1/2]

void oomph::AxisymmetricPVDEquationsWithPressure::get_stress	(	const DenseMatrix< double > &	g,
		const DenseMatrix< double > &	G,
		DenseMatrix< double > &	sigma,
		DenseMatrix< double > &	Gup,
		double &	detG
	)

inline

Return the stress tensor, as calculated from the constitutive law in the "true" incompresible formulation

     {
 #ifdef PARANOID
       // If the pointer to the constitutive law hasn't been set, issue an error
       if (Constitutive_law_pt == 0)
       {
         std::string error_message =
           "Elements derived from AxisymmetricPVDEquationsWithPressure";
         error_message += " must have a constitutive law :\n ";
         error_message +=
           "set one using the constitutive_law_pt() member function\n";
  
         throw OomphLibError(
           error_message, OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
       }
 #endif
       Constitutive_law_pt->calculate_second_piola_kirchhoff_stress(
         g, G, sigma, Gup, detG);
     }

References oomph::ConstitutiveLaw::calculate_second_piola_kirchhoff_stress(), Constitutive_law_pt, G, OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, calibrate::sigma, and oomph::Global_string_for_annotation::string().

◆ get_stress() [2/2]

void oomph::AxisymmetricPVDEquationsWithPressure::get_stress	(	const DenseMatrix< double > &	g,
		const DenseMatrix< double > &	G,
		DenseMatrix< double > &	sigma,
		DenseMatrix< double > &	Gup,
		double &	pressure_stress,
		double &	kappa
	)

inline

Return the stress tensor, as calculated from the constitutive law in the Near-incompresible formulation

     {
 #ifdef PARANOID
       // If the pointer to the constitutive law hasn't been set, issue an error
       if (Constitutive_law_pt == 0)
       {
         std::string error_message =
           "Elements derived from AxisymmetricPVDEquationsWithPressure";
         error_message += " must have a constitutive law :\n ";
         error_message +=
           "set one using the constitutive_law_pt() member function\n";
  
         throw OomphLibError(
           error_message, OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
       }
 #endif
       Constitutive_law_pt->calculate_second_piola_kirchhoff_stress(
         g, G, sigma, Gup, pressure_stress, kappa);
     }

References oomph::ConstitutiveLaw::calculate_second_piola_kirchhoff_stress(), Constitutive_law_pt, G, OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, calibrate::sigma, and oomph::Global_string_for_annotation::string().

Referenced by fill_in_generic_residual_contribution_axisym_pvd_with_pressure().

◆ interpolated_solid_p()

double oomph::AxisymmetricPVDEquationsWithPressure::interpolated_solid_p ( const Vector< double > & s )

inline

Return the interpolated_solid_pressure.

     {
       // Find number of nodes
       unsigned n_solid_pres = nsolid_pres();
       // Local shape function
       Shape psisp(n_solid_pres);
       // Find values of shape function
       solid_pshape(s, psisp);
  
       // Initialise value of solid_p
       double interpolated_solid_p = 0.0;
       // Loop over the local nodes and sum
       for (unsigned l = 0; l < n_solid_pres; l++)
       {
         interpolated_solid_p += solid_p(l) * psisp[l];
       }
  
       return (interpolated_solid_p);
     }

References nsolid_pres(), s, solid_p(), and solid_pshape().

Referenced by fill_in_generic_residual_contribution_axisym_pvd_with_pressure(), and output().

◆ is_incompressible()

bool oomph::AxisymmetricPVDEquationsWithPressure::is_incompressible ( ) const

inline

Return whether the material is incompressible.

     {
       return Incompressible;
     }

References Incompressible.

◆ nsolid_pres()

virtual unsigned oomph::AxisymmetricPVDEquationsWithPressure::nsolid_pres ( ) const

pure virtual

Return the number of solid pressure degrees of freedom.

Implemented in oomph::AxisymQPVDElementWithPressure.

Referenced by fill_in_generic_residual_contribution_axisym_pvd_with_pressure(), and interpolated_solid_p().

◆ output() [1/4]

void oomph::AxisymmetricPVDEquationsWithPressure::output ( FILE * file_pt )

inlinevirtual

Overload the output function.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::AxisymQPVDElementWithPressure.

     {
       FiniteElement::output(file_pt);
     }

References oomph::FiniteElement::output().

◆ output() [2/4]

void oomph::AxisymmetricPVDEquationsWithPressure::output	(	FILE *	file_pt,
		const unsigned &	n_plot
	)

inlinevirtual

Output function.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::AxisymQPVDElementWithPressure.

     {
       // Set the output Vector
       Vector<double> s(2);
  
       // Tecplot header info
       fprintf(file_pt, "ZONE I=%i, J=%i\n", n_plot, n_plot);
  
       // Loop over element nodes
       for (unsigned l2 = 0; l2 < n_plot; l2++)
       {
         s[1] = -1.0 + l2 * 2.0 / (n_plot - 1);
         for (unsigned l1 = 0; l1 < n_plot; l1++)
         {
           s[0] = -1.0 + l1 * 2.0 / (n_plot - 1);
  
           double x_r = interpolated_x(s, 0), x_theta = interpolated_x(s, 1);
           double theta = interpolated_xi(s, 1);
           // Output the x,y,u,v
           // First output x and y assuming phi = 0
           // outfile << x_r*sin(theta) + x_theta*cos(theta) << " " <<
           // x_r*cos(theta) - x_theta*sin(theta) << " ";
           fprintf(file_pt,
                   "%g %g ",
                   x_r * sin(theta) + x_theta * cos(theta),
                   x_r * cos(theta) - x_theta * sin(theta));
  
           // Now output the true variables
           for (unsigned i = 0; i < 2; i++)
             fprintf(file_pt, "%g ", interpolated_x(s, i));
           for (unsigned i = 0; i < 2; i++)
             fprintf(file_pt, "%g ", interpolated_xi(s, i));
           fprintf(file_pt, "\n");
         }
       }
       fprintf(file_pt, "\n");
     }

References cos(), i, oomph::FiniteElement::interpolated_x(), oomph::SolidFiniteElement::interpolated_xi(), s, sin(), and BiharmonicTestFunctions2::theta.

◆ output() [3/4]

void oomph::AxisymmetricPVDEquationsWithPressure::output ( std::ostream & outfile )

inlinevirtual

Overload the output function.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::AxisymQPVDElementWithPressure.

     {
       FiniteElement::output(outfile);
     }

References oomph::FiniteElement::output().

Referenced by oomph::AxisymQPVDElementWithPressure::output().

◆ output() [4/4]

void oomph::AxisymmetricPVDEquationsWithPressure::output	(	std::ostream &	outfile,
		const unsigned &	n_plot
	)

inlinevirtual

Output function.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::AxisymQPVDElementWithPressure.

     {
       // Set the output Vector
       Vector<double> s(2);
  
       // Tecplot header info
       outfile << "ZONE I=" << n_plot << ", J=" << n_plot << std::endl;
  
       // Loop over element nodes
       for (unsigned l2 = 0; l2 < n_plot; l2++)
       {
         s[1] = -1.0 + l2 * 2.0 / (n_plot - 1);
         for (unsigned l1 = 0; l1 < n_plot; l1++)
         {
           s[0] = -1.0 + l1 * 2.0 / (n_plot - 1);
  
           double x_r = interpolated_x(s, 0), x_theta = interpolated_x(s, 1);
           double theta = interpolated_xi(s, 1);
           // Output the x,y,u,v
           // First output x and y assuming phi = 0
           outfile << x_r * sin(theta) + x_theta * cos(theta) << " "
                   << x_r * cos(theta) - x_theta * sin(theta) << " ";
           outfile << interpolated_solid_p(s) << " ";
           // Now output the true variables
           for (unsigned i = 0; i < 2; i++)
             outfile << interpolated_x(s, i) << " ";
           for (unsigned i = 0; i < 2; i++)
             outfile << interpolated_xi(s, i) << " ";
           outfile << std::endl;
         }
       }
       outfile << std::endl;
     }

References cos(), i, interpolated_solid_p(), oomph::FiniteElement::interpolated_x(), oomph::SolidFiniteElement::interpolated_xi(), s, sin(), and BiharmonicTestFunctions2::theta.

◆ set_compressible()

void oomph::AxisymmetricPVDEquationsWithPressure::set_compressible ( )

inline

Set the material to be compressible.

     {
       Incompressible = false;
     }

References Incompressible.

◆ set_incompressible()

void oomph::AxisymmetricPVDEquationsWithPressure::set_incompressible ( )

inline

Set the material to be incompressible.

     {
       Incompressible = true;
     }

References Incompressible.

◆ solid_p()

virtual double oomph::AxisymmetricPVDEquationsWithPressure::solid_p ( const unsigned & l )

pure virtual

Return the lth solid pressures.

Implemented in oomph::AxisymQPVDElementWithPressure.

Referenced by fill_in_generic_residual_contribution_axisym_pvd_with_pressure(), and interpolated_solid_p().

◆ solid_p_local_eqn()

virtual int oomph::AxisymmetricPVDEquationsWithPressure::solid_p_local_eqn ( const unsigned & i )

protectedpure virtual

Access function that returns the local equation number for the n-th solid pressure value.

Implemented in oomph::AxisymQPVDElementWithPressure.

Referenced by fill_in_generic_residual_contribution_axisym_pvd_with_pressure().

◆ solid_pshape()

virtual void oomph::AxisymmetricPVDEquationsWithPressure::solid_pshape	(	const Vector< double > &	s,
		Shape &	psi
	)		const

protectedpure virtual

Return the solid pressure shape functions.

Implemented in oomph::AxisymQPVDElementWithPressure.

Referenced by interpolated_solid_p(), and solid_pshape_at_knot().

◆ solid_pshape_at_knot()

void oomph::AxisymmetricPVDEquationsWithPressure::solid_pshape_at_knot	(	const unsigned &	ipt,
		Shape &	psi
	)		const

protected

Return the stored solid shape functions at the knots.

Solid pressure shape function evaluated at integration point.

   {
     // Storage for local coordinates of the integration point
     Vector<double> s(2);
     // Set the local coordinates
     for (unsigned i = 0; i < 2; i++)
     {
       s[i] = this->integral_pt()->knot(ipt, i);
     }
     // Get the shape function
     solid_pshape(s, psi);
   }

References i, oomph::FiniteElement::integral_pt(), oomph::Integral::knot(), s, and solid_pshape().

Referenced by fill_in_generic_residual_contribution_axisym_pvd_with_pressure().

Member Data Documentation

◆ Constitutive_law_pt

ConstitutiveLaw* oomph::AxisymmetricPVDEquationsWithPressure::Constitutive_law_pt

private

Pointer to constitutive law.

Referenced by constitutive_law_pt(), and get_stress().

◆ Incompressible

bool oomph::AxisymmetricPVDEquationsWithPressure::Incompressible

private

Boolean to determine whether the solid is incompressible or not.

Referenced by fill_in_generic_residual_contribution_axisym_pvd_with_pressure(), is_incompressible(), set_compressible(), and set_incompressible().

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

Public Member Functions

Protected Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ AxisymmetricPVDEquationsWithPressure()

Member Function Documentation

◆ compute_physical_size()

◆ constitutive_law_pt()

◆ fill_in_contribution_to_jacobian()

◆ fill_in_contribution_to_residuals()

◆ fill_in_generic_residual_contribution_axisym_pvd_with_pressure()

◆ get_stress() [1/2]

◆ get_stress() [2/2]

◆ interpolated_solid_p()

◆ is_incompressible()

◆ nsolid_pres()

◆ output() [1/4]

◆ output() [2/4]

◆ output() [3/4]

◆ output() [4/4]

◆ set_compressible()

◆ set_incompressible()

◆ solid_p()

◆ solid_p_local_eqn()

◆ solid_pshape()

◆ solid_pshape_at_knot()

Member Data Documentation

◆ Constitutive_law_pt

◆ Incompressible