The ElementTemplate class illustrates the basic formulation a typical Element class used in FEM analysis. More...

#include <ElementTemplate.h>

Inheritance diagram for ElementTemplate:

Collaboration diagram for ElementTemplate:

Public Member Functions
	ElementTemplate (unsigned, uvec &&, unsigned, double=1.)
	Here we target our ElementTemplate class to fulfill the functionality of a constant stress triangular element, viz., CPS3, in Abaqus notation. More...

int	initialize (const shared_ptr< DomainBase > &) override
	As explained before, this method get all necessary information, which includes getting copies of Material objects and other operations, from the Domain object. More...

int	update_status () override
	Now we handle the status update method. We get trial displacement via build-in method and pass trial strain to the material model. Then get updated stiffness and stress back to form element stiffness and resistance. More...

int	commit_status () override
	Simply call corresponding methods in material objects. If the element itself has history variables, they should also be updated/modified in following methods. More...

int	clear_status () override

int	reset_status () override

Public Member Functions inherited from MaterialElement2D
	MaterialElement2D (unsigned, unsigned, unsigned, uvec &&, uvec &&, bool, vector< DOF > &&={})

Public Member Functions inherited from MaterialElement
	MaterialElement (unsigned, unsigned, unsigned, uvec &&, uvec &&, bool, MaterialType, vector< DOF > &&)

Public Member Functions inherited from Element
	Element (unsigned, unsigned, unsigned, uvec &&, std::vector< DOF > &&)

	Element (unsigned, unsigned, unsigned, uvec &&, uvec &&, bool, MaterialType, std::vector< DOF > &&)

	Element (unsigned, unsigned, unsigned, uvec &&, uvec &&, bool, SectionType, std::vector< DOF > &&)

	Element (unsigned, unsigned, uvec &&)

	Element (unsigned, unsigned, unsigned, unsigned)

	Element (const Element &)=delete

	Element (Element &&)=delete

Element &	operator= (const Element &)=delete

Element &	operator= (Element &&)=delete

	~Element () override=default

int	initialize_base (const shared_ptr< DomainBase > &) final

void	set_initialized (bool) const override

void	set_symmetric (bool) const override

bool	is_initialized () const override

bool	is_symmetric () const override

bool	is_nlgeom () const override

void	update_dof_encoding () override

bool	if_update_mass () const override

bool	if_update_viscous () const override

bool	if_update_nonviscous () const override

bool	if_update_stiffness () const override

bool	if_update_geometry () const override

bool	allow_modify_mass () const override

bool	allow_modify_viscous () const override

bool	allow_modify_nonviscous () const override

const uvec &	get_dof_encoding () const override

const uvec &	get_node_encoding () const override

const std::vector< MappingDOF > &	get_dof_mapping () const override

const uvec &	get_material_tag () const override

const uvec &	get_section_tag () const override

unsigned	get_dof_number () const override

unsigned	get_node_number () const override

unsigned	get_total_number () const override

void	clear_node_ptr () override

const std::vector< weak_ptr< Node > > &	get_node_ptr () const override

vec	get_incre_displacement () const override

vec	get_incre_velocity () const override

vec	get_incre_acceleration () const override

vec	get_trial_displacement () const override

vec	get_trial_velocity () const override

vec	get_trial_acceleration () const override

vec	get_current_displacement () const override

vec	get_current_velocity () const override

vec	get_current_acceleration () const override

const vec &	get_trial_resistance () const override

const vec &	get_current_resistance () const override

const vec &	get_trial_damping_force () const override

const vec &	get_current_damping_force () const override

const cx_mat &	get_trial_nonviscous_force () const override

const cx_mat &	get_current_nonviscous_force () const override

const vec &	get_trial_inertial_force () override

const vec &	get_current_inertial_force () override

const vec &	get_trial_body_force () const override

const vec &	get_current_body_force () const override

const vec &	get_trial_traction () const override

const vec &	get_current_traction () const override

const mat &	get_trial_mass () const override

const mat &	get_trial_viscous () const override

const mat &	get_trial_nonviscous () const override

const mat &	get_trial_stiffness () const override

const mat &	get_trial_geometry () const override

const mat &	get_trial_secant () const override

const mat &	get_current_mass () const override

const mat &	get_current_viscous () const override

const mat &	get_current_nonviscous () const override

const mat &	get_current_stiffness () const override

const mat &	get_current_geometry () const override

const mat &	get_current_secant () const override

const mat &	get_initial_mass () const override

const mat &	get_initial_viscous () const override

const mat &	get_initial_nonviscous () const override

const mat &	get_initial_stiffness () const override

const mat &	get_initial_geometry () const override

const mat &	get_initial_secant () const override

const mat &	get_mass_container () const override

const mat &	get_stiffness_container () const override

int	clear_status () override=0

int	commit_status () override=0

int	reset_status () override=0

const vec &	update_body_force (const vec &) override

const vec &	update_traction (const vec &) override

std::vector< vec >	record (OutputType) override

double	get_strain_energy () const override

double	get_complementary_energy () const override

double	get_kinetic_energy () const override

double	get_viscous_energy () const override

double	get_nonviscous_energy () const override

const vec &	get_momentum () const override

double	get_momentum_component (DOF) const override

double	get_characteristic_length () const override

mat	compute_shape_function (const mat &, unsigned) const override

Public Member Functions inherited from ElementBase
	ElementBase (const unsigned T)

	ElementBase (const ElementBase &)=delete

	ElementBase (ElementBase &&)=delete

ElementBase &	operator= (const ElementBase &)=delete

ElementBase &	operator= (ElementBase &&)=delete

	~ElementBase () override=default

virtual int	initialize_base (const shared_ptr< DomainBase > &)=0

virtual int	initialize (const shared_ptr< DomainBase > &)=0

virtual void	set_initialized (bool) const =0

virtual void	set_symmetric (bool) const =0

virtual bool	is_initialized () const =0

virtual bool	is_symmetric () const =0

virtual bool	is_nlgeom () const =0

virtual void	update_dof_encoding ()=0

virtual bool	if_update_mass () const =0

virtual bool	if_update_viscous () const =0

virtual bool	if_update_nonviscous () const =0

virtual bool	if_update_stiffness () const =0

virtual bool	if_update_geometry () const =0

virtual bool	allow_modify_mass () const =0

virtual bool	allow_modify_viscous () const =0

virtual bool	allow_modify_nonviscous () const =0

virtual const uvec &	get_dof_encoding () const =0

virtual const uvec &	get_node_encoding () const =0

virtual const std::vector< MappingDOF > &	get_dof_mapping () const =0

virtual const uvec &	get_material_tag () const =0

virtual const uvec &	get_section_tag () const =0

virtual unsigned	get_dof_number () const =0

virtual unsigned	get_node_number () const =0

virtual unsigned	get_total_number () const =0

virtual void	clear_node_ptr ()=0

virtual const std::vector< weak_ptr< Node > > &	get_node_ptr () const =0

virtual vec	get_incre_displacement () const =0

virtual vec	get_incre_velocity () const =0

virtual vec	get_incre_acceleration () const =0

virtual vec	get_trial_displacement () const =0

virtual vec	get_trial_velocity () const =0

virtual vec	get_trial_acceleration () const =0

virtual vec	get_current_displacement () const =0

virtual vec	get_current_velocity () const =0

virtual vec	get_current_acceleration () const =0

virtual const vec &	get_trial_resistance () const =0

virtual const vec &	get_current_resistance () const =0

virtual const vec &	get_trial_damping_force () const =0

virtual const vec &	get_current_damping_force () const =0

virtual const cx_mat &	get_trial_nonviscous_force () const =0

virtual const cx_mat &	get_current_nonviscous_force () const =0

virtual const vec &	get_trial_inertial_force ()=0

virtual const vec &	get_current_inertial_force ()=0

virtual const vec &	get_trial_body_force () const =0

virtual const vec &	get_current_body_force () const =0

virtual const vec &	get_trial_traction () const =0

virtual const vec &	get_current_traction () const =0

virtual const mat &	get_trial_mass () const =0

virtual const mat &	get_trial_viscous () const =0

virtual const mat &	get_trial_nonviscous () const =0

virtual const mat &	get_trial_stiffness () const =0

virtual const mat &	get_trial_geometry () const =0

virtual const mat &	get_trial_secant () const =0

virtual const mat &	get_current_mass () const =0

virtual const mat &	get_current_viscous () const =0

virtual const mat &	get_current_nonviscous () const =0

virtual const mat &	get_current_stiffness () const =0

virtual const mat &	get_current_geometry () const =0

virtual const mat &	get_current_secant () const =0

virtual const mat &	get_initial_mass () const =0

virtual const mat &	get_initial_viscous () const =0

virtual const mat &	get_initial_nonviscous () const =0

virtual const mat &	get_initial_stiffness () const =0

virtual const mat &	get_initial_geometry () const =0

virtual const mat &	get_initial_secant () const =0

virtual const mat &	get_mass_container () const =0

virtual const mat &	get_stiffness_container () const =0

virtual int	update_status ()=0

virtual int	clear_status ()=0

virtual int	commit_status ()=0

virtual int	reset_status ()=0

virtual const vec &	update_body_force (const vec &)=0

virtual const vec &	update_traction (const vec &)=0

virtual std::vector< vec >	record (OutputType)=0

virtual double	get_strain_energy () const =0

virtual double	get_complementary_energy () const =0

virtual double	get_kinetic_energy () const =0

virtual double	get_viscous_energy () const =0

virtual double	get_nonviscous_energy () const =0

virtual const vec &	get_momentum () const =0

virtual double	get_momentum_component (DOF) const =0

virtual double	get_characteristic_length () const =0

virtual mat	compute_shape_function (const mat &, unsigned) const =0

Public Member Functions inherited from Tag
	Tag (unsigned=0)

	Tag (const Tag &)=default

	Tag (Tag &&)=default

Tag &	operator= (const Tag &)=delete

Tag &	operator= (Tag &&)=delete

virtual	~Tag ()=default

void	set_tag (unsigned) const

unsigned	get_tag () const

void	enable ()

void	disable ()

void	guard ()

void	unguard ()

bool	is_active () const

bool	is_guarded () const

virtual void	print ()

Additional Inherited Members
Protected Member Functions inherited from Element
mat	get_coordinate (unsigned) const override
	generate a matrix that contains coordinates of connected nodes More...

vec	get_node_incre_resistance () const override

vec	get_node_trial_resistance () const override

vec	get_node_current_resistance () const override

std::vector< shared_ptr< Material > >	get_material (const shared_ptr< DomainBase > &) const override

std::vector< shared_ptr< Section > >	get_section (const shared_ptr< DomainBase > &) const override

virtual mat	get_coordinate (unsigned) const =0

virtual vec	get_node_incre_resistance () const =0

virtual vec	get_node_trial_resistance () const =0

virtual vec	get_node_current_resistance () const =0

virtual std::vector< shared_ptr< Material > >	get_material (const shared_ptr< DomainBase > &) const =0

virtual std::vector< shared_ptr< Section > >	get_section (const shared_ptr< DomainBase > &) const =0

	ElementBase (const unsigned T)

	ElementBase (const ElementBase &)=delete

	ElementBase (ElementBase &&)=delete

ElementBase &	operator= (const ElementBase &)=delete

ElementBase &	operator= (ElementBase &&)=delete

	~ElementBase () override=default

virtual int	initialize_base (const shared_ptr< DomainBase > &)=0

virtual int	initialize (const shared_ptr< DomainBase > &)=0

virtual void	set_initialized (bool) const =0

virtual void	set_symmetric (bool) const =0

virtual bool	is_initialized () const =0

virtual bool	is_symmetric () const =0

virtual bool	is_nlgeom () const =0

virtual void	update_dof_encoding ()=0

virtual bool	if_update_mass () const =0

virtual bool	if_update_viscous () const =0

virtual bool	if_update_nonviscous () const =0

virtual bool	if_update_stiffness () const =0

virtual bool	if_update_geometry () const =0

virtual bool	allow_modify_mass () const =0

virtual bool	allow_modify_viscous () const =0

virtual bool	allow_modify_nonviscous () const =0

virtual const uvec &	get_dof_encoding () const =0

virtual const uvec &	get_node_encoding () const =0

virtual const std::vector< MappingDOF > &	get_dof_mapping () const =0

virtual const uvec &	get_material_tag () const =0

virtual const uvec &	get_section_tag () const =0

virtual unsigned	get_dof_number () const =0

virtual unsigned	get_node_number () const =0

virtual unsigned	get_total_number () const =0

virtual void	clear_node_ptr ()=0

virtual const std::vector< weak_ptr< Node > > &	get_node_ptr () const =0

virtual vec	get_incre_displacement () const =0

virtual vec	get_incre_velocity () const =0

virtual vec	get_incre_acceleration () const =0

virtual vec	get_trial_displacement () const =0

virtual vec	get_trial_velocity () const =0

virtual vec	get_trial_acceleration () const =0

virtual vec	get_current_displacement () const =0

virtual vec	get_current_velocity () const =0

virtual vec	get_current_acceleration () const =0

virtual const vec &	get_trial_resistance () const =0

virtual const vec &	get_current_resistance () const =0

virtual const vec &	get_trial_damping_force () const =0

virtual const vec &	get_current_damping_force () const =0

virtual const cx_mat &	get_trial_nonviscous_force () const =0

virtual const cx_mat &	get_current_nonviscous_force () const =0

virtual const vec &	get_trial_inertial_force ()=0

virtual const vec &	get_current_inertial_force ()=0

virtual const vec &	get_trial_body_force () const =0

virtual const vec &	get_current_body_force () const =0

virtual const vec &	get_trial_traction () const =0

virtual const vec &	get_current_traction () const =0

virtual const mat &	get_trial_mass () const =0

virtual const mat &	get_trial_viscous () const =0

virtual const mat &	get_trial_nonviscous () const =0

virtual const mat &	get_trial_stiffness () const =0

virtual const mat &	get_trial_geometry () const =0

virtual const mat &	get_trial_secant () const =0

virtual const mat &	get_current_mass () const =0

virtual const mat &	get_current_viscous () const =0

virtual const mat &	get_current_nonviscous () const =0

virtual const mat &	get_current_stiffness () const =0

virtual const mat &	get_current_geometry () const =0

virtual const mat &	get_current_secant () const =0

virtual const mat &	get_initial_mass () const =0

virtual const mat &	get_initial_viscous () const =0

virtual const mat &	get_initial_nonviscous () const =0

virtual const mat &	get_initial_stiffness () const =0

virtual const mat &	get_initial_geometry () const =0

virtual const mat &	get_initial_secant () const =0

virtual const mat &	get_mass_container () const =0

virtual const mat &	get_stiffness_container () const =0

virtual int	update_status ()=0

virtual int	clear_status ()=0

virtual int	commit_status ()=0

virtual int	reset_status ()=0

virtual const vec &	update_body_force (const vec &)=0

virtual const vec &	update_traction (const vec &)=0

virtual std::vector< vec >	record (OutputType)=0

virtual double	get_strain_energy () const =0

virtual double	get_complementary_energy () const =0

virtual double	get_kinetic_energy () const =0

virtual double	get_viscous_energy () const =0

virtual double	get_nonviscous_energy () const =0

virtual const vec &	get_momentum () const =0

virtual double	get_momentum_component (DOF) const =0

virtual double	get_characteristic_length () const =0

virtual mat	compute_shape_function (const mat &, unsigned) const =0

Protected Member Functions inherited from Tag
	Tag (unsigned=0)

	Tag (const Tag &)=default

	Tag (Tag &&)=default

Tag &	operator= (const Tag &)=delete

Tag &	operator= (Tag &&)=delete

virtual	~Tag ()=default

void	set_tag (unsigned) const

unsigned	get_tag () const

void	enable ()

void	disable ()

void	guard ()

void	unguard ()

bool	is_active () const

bool	is_guarded () const

virtual void	print ()

Protected Attributes inherited from Element
std::vector< weak_ptr< Node > >	node_ptr

Protected Attributes inherited from DataElement
const uvec	node_encoding

const uvec	material_tag

const uvec	section_tag

const bool	nlgeom = false

bool	update_mass = true

bool	update_viscous = true

bool	update_nonviscous = true

bool	update_stiffness = true

bool	update_geometry = true

bool	modify_mass = true

bool	modify_viscous = true

bool	modify_nonviscous = true

uvec	dof_encoding {}

mat	initial_mass {}

mat	initial_viscous {}

mat	initial_nonviscous {}

mat	initial_stiffness {}

mat	initial_geometry {}

mat	trial_mass {}

mat	trial_viscous {}

mat	trial_nonviscous {}

mat	trial_stiffness {}

mat	trial_geometry {}

mat	current_mass {}

mat	current_viscous {}

mat	current_nonviscous {}

mat	current_stiffness {}

mat	current_geometry {}

vec	trial_resistance {}

vec	current_resistance {}

vec	trial_viscous_force {}

vec	current_viscous_force {}

cx_mat	trial_nonviscous_force {}

cx_mat	current_nonviscous_force {}

vec	trial_inertial_force {}

vec	current_inertial_force {}

vec	trial_body_force {}

vec	current_body_force {}

vec	trial_traction {}

vec	current_traction {}

mat	body_force {}

mat	traction {}

mat	stiffness_container {}

mat	mass_container {}

double	strain_energy = 0.

double	kinetic_energy = 0.

double	viscous_energy = 0.

double	nonviscous_energy = 0.

double	complementary_energy = 0.

vec	momentum {}

const double	characteristic_length = 1.

Detailed Description

The ElementTemplate class illustrates the basic formulation a typical Element class used in FEM analysis.

Author: tlc

Date: 05/01/2020

Version: 0.1.3

Constructor & Destructor Documentation

◆ ElementTemplate()

ElementTemplate::ElementTemplate	(	unsigned	T,
		uvec &&	NT,
		unsigned	MT,
		double	TH = `1.`
	)

Here we target our ElementTemplate class to fulfill the functionality of a constant stress triangular element, viz., CPS3, in Abaqus notation.

The example element is derived from the MaterialElement2D class, hence it is a 2D element using material models (instead of sections).

The constructor of MaterialElement2D class asks for six parameters:

Unique Element Object Tag (T)
Number of Nodes (NN)
Number of DoFs (ND)
Node Encoding Tags (NT)
Material Tag (MT)
Nonlinear Switch (F)

In our example, CT and F will be constants, NN is 3 and ND is 2. So we have three parameters plus thickness for our derived element. Except for initializing private member variables, we do not have to do anything. All other initializations will be handled by the Element and Domain class. As simple as this.

Member Function Documentation

◆ clear_status()

int ElementTemplate::clear_status ( )

overridevirtual

Implements Element.

◆ commit_status()

int ElementTemplate::commit_status ( )

overridevirtual

Simply call corresponding methods in material objects. If the element itself has history variables, they should also be updated/modified in following methods.

Implements Element.

◆ initialize()

int ElementTemplate::initialize ( const shared_ptr< DomainBase > & D )

overridevirtual

As explained before, this method get all necessary information, which includes getting copies of Material objects and other operations, from the Domain object.

Please note that we do not have to check the existence of any objects which are used in the element. The validity of the connected node objects and the material models is checked in the base initialisation before calling this method. The execution of this initialize() method automatically implies that this is a valid Element object with valid material model.

The displacement mode is

\begin{gather}\phi=\begin{bmatrix}1&x&y\end{bmatrix}.\end{gather}

The strain matrix is calculated as

\begin{gather}B=\partial{}N=\partial{}\left(\phi{}C^{-1}\right),\end{gather}

where

\begin{gather}C=\begin{bmatrix}1&x_i&y_i\\1&x_j&y_j\\1&x_k&y_k\end{bmatrix}.\end{gather}

One can also initialize stiffness matrix and/or other build-in matrices from Element class (check the definition for details) in the initialize() method. However, this it not necessary, as the Solver will always call update_status() method with a zero trial displacement to update current stiffness and resistance before running iterations.

As CPS3 is a constant stress/strain element, one integration point at the center of the element is enough. Hence we only have one material model defined. First we get a reference of the Material object from the Domain and then call the get_copy() method to get a local copy. Direct assignment is allowed, the move semantics will automatically be invoked. There is no need to check if the material model is a 2D one. The validation is done in base Element class initialisation.

The node pointers are handled in the base Element class, we do not have to set it manually. Now we could fill in the ele_coor matrix. The area/natural coordinate is another version of implementation. Please refer to FEM textbooks for theories. This will be used for the computation of the shape function.

The area is half of the determinant of the above matrix. The area of 2D polygons can also be computed by the shoelace function.

A standard way to construct the strain mat is to derive from the partial derivative of the shape function N. For CP3, as it is a constant stress/strain element, the derivatives are constants which can be directly obtained from above matrix.

We use function ConstantMass() to indicate the mass matrix will not change so that trial_mass, current_mass and initial_mass matrices can point to the same memory location. This avoids unnecessary allocation of memory. It is not compulsory to call ConstantMass(), ConstantStiffness() and ConstantDamping() but highly recommended to do so when one or some matrices indeed remain unchanged for the whole analysis.

Implements ElementBase.

◆ reset_status()

int ElementTemplate::reset_status ( )

overridevirtual

Implements Element.

◆ update_status()

int ElementTemplate::update_status ( )

overridevirtual

Now we handle the status update method. We get trial displacement via build-in method and pass trial strain to the material model. Then get updated stiffness and stress back to form element stiffness and resistance.

For a static analysis, stiffness and resistance have to be formulated. Apart from this, there is nothing you have to do. They will be send to global assembler by methods in base Element class, which can also be overridden to be customized.

Implements ElementBase.

Here is the call graph for this function:

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

Element/ElementTemplate.h
Element/ElementTemplate.cpp

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ ElementTemplate()

Member Function Documentation

◆ clear_status()

◆ commit_status()

◆ initialize()

◆ reset_status()

◆ update_status()