Elas2DT3 Class Reference
[Solid Mechanics]

#include <Elas2DT3.h>

Inheritance diagram for Elas2DT3:

Detailed Description

To build element equations for 2-D linearized elasticity using 3-node triangles.

This class enables building finite element arrays for linearized isotropic elasticity problem in 2-D domains using 3-Node triangles.
Unilateral contact is handled using a penalty function.

Note that members calculating element arrays have as an argument a double coef that is multiplied by the contribution of the current element. This makes possible testing different algorithms.


Public Member Functions
T_ *	A ()
	Return element matrix as a C-array.
T_ *	b ()
	Return element right-hand side as a C-array.
void	BodyRHS (const NodeVect< double > &f, int opt=LOCAL_ARRAY)
	Add body right-hand side term to right hand side.
void	BodyRHS (UserData< double > &ud)
	Add body right-hand side term to right-hand side after multiplication by coef.
void	BoundaryRHS (SideVect< double > &f)
	Add boundary right-hand side term to right hand side.
void	BoundaryRHS (UserData< double > &ud)
	Add boundary right-hand side term to right hand side after multiplication by coef.
void	ContactPressure (const SideVect< double > &f, double penal, Point< double > &p)
	Calculate contact pressure.
void	Deviator (double coef=1.)
	Add element deviatoric matrix to left-hand side after multiplication by coef.
void	DeviatorToRHS (double coef=1.)
	Add element deviatoric contribution to right-hand side after multiplication by coef.
void	DiagBC (int dof_type=NODE_DOF, int dof=0)
	Update element matrix to impose bc by diagonalization technique.
void	Dilatation (double coef=1.)
	Add element dilatational contribution to left-hand side after multiplication by coef.
void	DilatationToRHS (double coef=1.)
	Add element dilatational contribution to right-hand side after multiplication by coef.
LocalMatrix< T_, NEE_, NEE_ > &	EA ()
	Return element matrix as a LocalMatrix instance.
LocalVect< T_, NEE_ > &	Eb ()
	Return element right-hand side as a LocalVect instance.
	Elas2DT3 (const Side *sd, const Vect< double > &u, double time, double deltat, int scheme)
	Constructor for a side (transient case) with specification of time integration scheme.
	Elas2DT3 (const Side *sd, const Vect< double > &u, double time=0.)
	Constructor using side, previous time solution u and time value.
	Elas2DT3 (const Element *el, const Vect< double > &u, double time, double deltat, int scheme)
	Constructor for an element (transient case) with specification of time integration scheme.
	Elas2DT3 (const Element *el, const Vect< double > &u, double time=0.)
	Constructor using element, previous time solution u and time value.
	Elas2DT3 (const Side *sd)
	Constructor using side data.
	Elas2DT3 (const Element *el)
	Constructor using element data.
	Elas2DT3 ()
	Default Constructor.
void	ElementSet (const Element *el)
	Element Settings.
void	ElementVector (const Vect< T_ > &b, int dof=0, int dof_type=NODE_DOF)
	Localize Element Vector.
LocalVect< T_, NEE_ > &	Ep ()
	Return element matrix as a C-array.
LinearSolver< T_ > &	getLinearSolver ()
	Return reference to linear solver instance.
size_t	getNbEq () const
	Return number of element equations.
size_t	getNbNodes () const
	Return number of element nodes.
void	LMass (double coef=1.)
	Add element lumped mass contribution to matrix and right-hand side after multiplication by coef.
void	LMassToLHS (double coef=1.)
	Add element lumped mass contribution to matrix after multiplication by coef.
void	LMassToRHS (double coef=1.)
	Add element lumped mass contribution to right-hand side after multiplication by coef.
void	LocalNodeVector (AbsVect< T_ > *b)
	Localize Element Vector from a NodeVect instance.
void	Mass (double coef=1.)
	Add element consistent mass contribution to matrix and right-hand side after multiplication by coef.
void	MassToLHS (double coef=1.)
	Add element consistent mass contribution to matrix after multiplication by coef.
void	MassToRHS (double coef=1.)
	Add element consistent mass contribution to right-hand side after multiplication by coef.
void	Media (double E, double nu, double rho)
	Set media properties.
void	Periodic (double coef=1.e20)
	Add contribution of periodic boundary condition (by a penalty technique).
void	PlaneStrain (double E, double nu)
	Set plane strain hypothesis by giving values of Young's modulus E and Poisson ratio nu.
void	PlaneStrain ()
	Set plane strain hypothesis.
void	PlaneStress (double E, double nu)
	Set plane stress hypothesis by giving values of Young's modulus E and Poisson ratio nu.
void	PlaneStress ()
	Set plane stress hypothesis.
T_ *	Prev ()
	Return element matrix as a C-array.
void	Reaction (SideVect< double > &r)
	Calculate reactions.
LocalMatrix< T_, NSE_, NSE_ > &	SA ()
	Return side matrix as a LocalMatrix instance.
void	setDeviator ()
	Add deviator matrix to left and/or right-hand side taking into account time integration scheme.
void	setInitialSolution (const Vect< T_ > &u)
	Set initial solution (previous time step).
void	setLumpedMass ()
	Add lumped mass contribution to left and right-hand sides taking into account time integration scheme.
void	setMass ()
	Add consistent mass contribution to left and right-hand sides taking into account time integration scheme.
double	setMaterialProperty (const string &exp, const string &prop)
	Define a material property by an algebraic expression.
void	setMesh (class Mesh &m)
	Define mesh and renumber DOFs after removing imposed ones.
void	setStiffness ()
	Add convection contribution to left and/or right-hand side taking into account time integration scheme.
void	SideSet (const Side *sd)
	Side Settings.
void	SideVector (const Vect< T_ > &b)
	Localize Side Vector.
int	SignoriniContact (SideVect< double > &f, double coef=1.e07)
	Penalty Signorini contact contribution to matrix and right-hand side.
int	SignoriniContact (UserData< double > &ud, double coef=1.e07)
	Penalty Signorini contact contribution to matrix and right-hand side.
virtual void	Stiffness (double coef=1)
	Add stiffness matrix to left-hand side taking into account time integration scheme.
virtual void	StiffnessToRHS (double coef=1)
	Add stiffness matrix to right-hand side taking into account time integration scheme.
void	Strain (Vect< double > &eps)
	Calculate strains in element.
void	Stress (Vect< double > &s, double &vm)
	Calculate principal stresses and Von-Mises stress in element.
void	updateBC (const Vect< T_ > &bc)
	Update Right-Hand side by taking into account essential boundary conditions.
	~Elas2DT3 ()
	Destructor.
Protected Member Functions
void	Density (const char *exp)
	Set density given by an algebraic expression.
void	Density (const double &rho)
	Set (constant) density.
void	Init (const Side *sd)
	Set side arrays to zero.
void	Init (const Element *el)
	Set element arrays to zero.
void	Poisson (const char *exp)
	Set Poisson ratio given by an algebraic expression.
void	Poisson (const double &nu)
	Set (constant) Poisson ratio.
void	setMaterial ()
	Set material properties.
void	Young (const char *exp)
	Set Young modulus given by an algebraic expression.
void	Young (const double &E)
	set (constant) Young modulus

Constructor & Destructor Documentation

Elas2DT3 ( )

Default Constructor.

Constructs an empty equation.

Elas2DT3	(	const Element *	el,
		const Vect< double > &	u,
		double	time = `0.`
	)

Constructor using element, previous time solution u and time value.

Parameters:

`[in]`	el	Pointer to element.
`[in]`	u	Vect instance that contains solution at previous time step.
`[in]`	time	Current time value (Default value is 0).

Elas2DT3	(	const Element *	el,
		const Vect< double > &	u,
		double	time,
		double	deltat,
		int	scheme
	)

Constructor for an element (transient case) with specification of time integration scheme.

Parameters:

`[in]`	el	Pointer to element.
`[in]`	u	Vect instance that contains solution at previous time step.
`[in]`	time	Current time value (Default value is 0).
`[in]`	deltat	Time step.
`[in]`	scheme	Time Integration Scheme ()

Elas2DT3	(	const Side *	sd,
		const Vect< double > &	u,
		double	time = `0.`
	)

Constructor using side, previous time solution u and time value.

Parameters:

`[in]`	sd	Pointer to side.
`[in]`	u	Vect instance that contains solution at previous time step.
`[in]`	time	Current time value (Default value is 0).

Elas2DT3	(	const Side *	sd,
		const Vect< double > &	u,
		double	time,
		double	deltat,
		int	scheme
	)

Constructor for a side (transient case) with specification of time integration scheme.

Parameters:

`[in]`	sd	Pointer to side.
`[in]`	u	Vect instance that contains solution at previous time step.
`[in]`	time	Current time value (Default value is 0).
`[in]`	deltat	Time step.
`[in]`	scheme	Time Integration Scheme

Member Function Documentation

void BodyRHS	(	const NodeVect< double > &	f,
		int	opt = `LOCAL_ARRAY`
	)

Add body right-hand side term to right hand side.

Parameters:

`[in]`	f	Vector containing source at element nodes (DOF by DOF).
`[in]`	opt	Vector is local (LOCAL_ARRAY) with size 6 or global (GLOBAL_ARRAY) with size = Number of element DOF.

void BodyRHS ( UserData< double > & ud )

Add body right-hand side term to right-hand side after multiplication by coef.

Body forces are deduced from UserData instance ud.

void BoundaryRHS ( UserData< double > & ud )

Add boundary right-hand side term to right hand side after multiplication by coef.

Parameters:

[in] ud UserData instance defining boundary forces

void ContactPressure	(	const SideVect< double > &	f,
		double	penal,
		Point< double > &	p
	)

Calculate contact pressure.

This function can be invoked in postprocessing.

void Deviator ( double coef = 1. ) [virtual]

Add element deviatoric matrix to left-hand side after multiplication by coef.

Parameters:

[in] coef Coefficient to multiply by added term [default=1].

Reimplemented from Equa_Solid< double, 3, 6, 2, 4 >.

void DeviatorToRHS ( double coef = 1. ) [virtual]

Add element deviatoric contribution to right-hand side after multiplication by coef.

Parameters:

[in] coef Coefficient to multiply by added term [default=1].

Reimplemented from Equa_Solid< double, 3, 6, 2, 4 >.

void DiagBC	(	int	dof_type = `NODE_DOF`,
		int	dof = `0`
	)			`[inherited]`

Update element matrix to impose bc by diagonalization technique.

Parameters:

`[in]`	dof_type	DOF type option. To choose among the enumerated values: = NODE_DOF, DOFs are supported by nodes [ default ] = ELEMENT_DOF, DOFs are supported by elements = SIDE_DOF, DOFs are supported by sides
`[in]`	dof	DOF setting: = 0, All DOFs are taken into account [ default ] != 0, Only DOF No. dof is handled in the sustem

References Side::getCode(), Node::getCode(), and Node::getLabel().

void Dilatation ( double coef = 1. )

Add element dilatational contribution to left-hand side after multiplication by coef.

Parameters:

[in] coef Coefficient to multiply by added term [default=1].

void DilatationToRHS ( double coef = 1. )

Add element dilatational contribution to right-hand side after multiplication by coef.

To use for explicit formulations.

Parameters:

[in] coef Coefficient to multiply by added term [default=1].

void ElementVector	(	const Vect< T_ > &	b,
		int	dof = `0`,
		int	dof_type = `NODE_DOF`
	)			`[inherited]`

Localize Element Vector.

Parameters:

`[in]`	b	Global vector to be localized
`[in]`	dof_type	DOF type option. To choose among the enumerated values: = NODE_DOF, DOFs are supported by nodes [ default ] = ELEMENT_DOF, DOFs are supported by elements = SIDE_DOF, DOFs are supported by sides
`[in]`	dof	DOF setting: = 0, All DOFs are taken into account [ default ] != 0, Only DOF No. dof is handled in the sustem The resulting local vector can be accessed by attribute ePrev. This member function is to be used if a constructor with Element was invoked.

References Equation::b(), Side::getDOF(), Node::getDOF(), Side::getNbDOF(), and Node::getNbDOF().

void LMass ( double coef = 1. )

Add element lumped mass contribution to matrix and right-hand side after multiplication by coef.

Parameters:

[in] coef Coefficient to multiply by added term [default=1].

References Elas2DT3::LMassToLHS(), and Elas2DT3::LMassToRHS().

void LMassToLHS ( double coef = 1. ) [virtual]

Add element lumped mass contribution to matrix after multiplication by coef.

Parameters:

[in] coef Coefficient to multiply by added term [default=1].

Reimplemented from Equa_Solid< double, 3, 6, 2, 4 >.

Referenced by Elas2DT3::LMass().

void LMassToRHS ( double coef = 1. ) [virtual]

Add element lumped mass contribution to right-hand side after multiplication by coef.

Parameters:

[in] coef Coefficient to multiply by added term [default=1].

Reimplemented from Equa_Solid< double, 3, 6, 2, 4 >.

Referenced by Elas2DT3::LMass().

void LocalNodeVector ( AbsVect< T_ > * b ) [inherited]

Localize Element Vector from a NodeVect instance.

Parameters:

[in] b Pointer to global vector to be localized. The resulting local vector can be accessed by attribute ePrev. This member function is to be used if a constructor with Element was invoked.

References Node::getLabel(), and Node::getNbDOF().

void Mass ( double coef = 1. )

Add element consistent mass contribution to matrix and right-hand side after multiplication by coef.

Parameters:

[in] coef Coefficient to multiply by added term [default=1].

References Elas2DT3::MassToLHS(), and Elas2DT3::MassToRHS().

void MassToLHS ( double coef = 1. ) [virtual]

Add element consistent mass contribution to matrix after multiplication by coef.

Parameters:

[in] coef Coefficient to multiply by added term [default=1].

Reimplemented from Equa_Solid< double, 3, 6, 2, 4 >.

Referenced by Elas2DT3::Mass().

void MassToRHS ( double coef = 1. ) [virtual]

Add element consistent mass contribution to right-hand side after multiplication by coef.

Parameters:

[in] coef Coefficient to multiply by added term [default=1].

Reimplemented from Equa_Solid< double, 3, 6, 2, 4 >.

Referenced by Elas2DT3::Mass().

void Media	(	double	E,
		double	nu,
		double	rho
	)

Set media properties.

Useful to override material properties deduced from mesh file.

void Periodic ( double coef = 1.e20 )

Add contribution of periodic boundary condition (by a penalty technique).

Boundary nodes where periodic boundary conditions are to be imposed must have codes equal to PERIODIC_A on one side and PERIODIC_B on the opposite side.

Parameters:

[in] coef Value of penalty parameter (default = 1.e20)

void PlaneStrain	(	double	E,
		double	nu
	)

Set plane strain hypothesis by giving values of Young's modulus E and Poisson ratio nu.

void PlaneStress	(	double	E,
		double	nu
	)

Set plane stress hypothesis by giving values of Young's modulus E and Poisson ratio nu.

void Reaction ( SideVect< double > & r )

Calculate reactions.

This function can be invoked in postprocessing.

double setMaterialProperty	(	const string &	exp,
		const string &	prop
	)			`[inherited]`

Define a material property by an algebraic expression.

Parameters:

`[in]`	exp	Algebraic expression
`[in]`	prop	Property name

Return values:

ret

Return value in expression evaluation:

ret=0, Normal evaluation
ret!=0, An error message is displayed.

Referenced by Equa_Therm< double, 4, 4, 3, 3 >::Conduc(), Equa_Solid< double, 4, 8, 2, 4 >::Density(), Equa_Fluid< double, 4, 8, 2, 4 >::Density(), Equa_Electromagnetics< complex< double >, 3, 3, 2, 2 >::ElectricConductivity(), Equa_Electromagnetics< complex< double >, 3, 3, 2, 2 >::ElectricResistivity(), Equa_Electromagnetics< complex< double >, 3, 3, 2, 2 >::MagneticPermeability(), Equa_Solid< double, 4, 8, 2, 4 >::Poisson(), Equa_Therm< double, 4, 4, 3, 3 >::RhoCp(), Equa_Fluid< double, 4, 8, 2, 4 >::ThermalExpansion(), Equa_Fluid< double, 4, 8, 2, 4 >::Viscosity(), and Equa_Solid< double, 4, 8, 2, 4 >::Young().

void SideVector ( const Vect< T_ > & b ) [inherited]

Localize Side Vector.

Parameters:

[in]

b

Global vector to be localized

= NODE_DOF, DOFs are supported by nodes [ default ]
= ELEMENT_DOF, DOFs are supported by elements
= SIDE_DOF, DOFs are supported by sides

The resulting local vector can be accessed by attribute ePrev. This member function is to be used if a constructor with Side was invoked.

References Equation::b(), Node::getDOF(), and Node::getNbDOF().

int SignoriniContact	(	UserData< double > &	ud,
		double	coef = `1.e07`
	)

Penalty Signorini contact contribution to matrix and right-hand side.

Parameters:

`[in]`	ud	UserData instance defining contact data, [default=1.e07]
`[in]`	coef	Value by which the added term is multiplied [Default: 1]

void Strain ( Vect< double > & eps )

Calculate strains in element.

This function can be invoked in postprocessing.

void Stress	(	Vect< double > &	s,
		double &	vm
	)

Calculate principal stresses and Von-Mises stress in element.

Parameters:

`[in]`	s	vector of principal stresses
`[in]`	vm	Von-Mises stress. This function can be invoked in postprocessing.

void updateBC ( const Vect< T_ > & bc ) [inherited]

Update Right-Hand side by taking into account essential boundary conditions.

Init solution.

Parameters:

[in] bc Vector that contains imposed values at all DOFs

Elas2DT3 Class Reference [Solid Mechanics]

Detailed Description

Public Member Functions

Protected Member Functions

Constructor & Destructor Documentation

Member Function Documentation

Elas2DT3 Class Reference
[Solid Mechanics]