Elas2DQ4 Class Reference
[Solid Mechanics]

#include <Elas2DQ4.h>

Inheritance diagram for Elas2DQ4:

Detailed Description

To build element equations for 2-D linearized elasticity using 4-node quadrilaterals.

This class enables building finite element arrays for linearized isotropic elasticity problem in 2-D domains using 4-Node quadrilaterals.
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 Vect< double > &bf, 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 (const Vect< double > &sf, int opt=LOCAL_ARRAY)
	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	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.
	Elas2DQ4 (const Side *side, const Vect< double > &u, const double &time=0.)
	Constructor using side and previous time data.
	Elas2DQ4 (const Element *element, const Vect< double > &u, const double &time=0.)
	Constructor using element and previous time data.
	Elas2DQ4 (const Side *sd)
	Constructor using side data.
	Elas2DQ4 (const Element *el)
	Constructor using element data.
	Elas2DQ4 ()
	Default Constructor Constructs an empty equation.
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)
	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.
virtual void	MassToLHS (double coef=1)
	Add consistent mass contribution to left-hand side.
virtual void	MassToRHS (double coef=1)
	Add consistent mass contribution to right-hand side.
void	PlaneStrain (double E, double nu)
	Set plane strain hypothesis by giving values of Young's modulus and Poisson ratio.
void	PlaneStrain ()
	Set plane strain hypothesis.
void	PlaneStress (double E, double nu)
	Set plane stress hypothesis by giving values of Young's modulus and Poisson ratio.
void	PlaneStress ()
	Set plane stress hypothesis.
T_ *	Prev ()
	Return element matrix as a C-array.
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	SideVector (const Vect< T_ > &b)
	Localize Side Vector.
void	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 (LocalVect< double, 3 > &eps)
	Calculate strains at element barycenter.
void	Stress (LocalVect< double, 3 > &sigma, LocalVect< double, 3 > &s, double &vm)
	Calculate principal stresses and Von-Mises stress at element barycenter.
void	Stress (LocalVect< double, 3 > &s, double &vm)
	Calculate principal stresses and Von-Mises stress at element barycenter.
void	updateBC (const Vect< T_ > &bc)
	Update Right-Hand side by taking into account essential boundary conditions.
	~Elas2DQ4 ()
	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

Elas2DQ4 ( )

Default Constructor Constructs an empty equation.

Elas2DQ4	(	const Element *	element,
		const Vect< double > &	u,
		const double &	time = `0.`
	)

Constructor using element and previous time data.

Parameters:

`[in]`	element	Pointer to element
`[in]`	u	Vect instance containing solution at previous time step
`[in]`	time	Current time value

Elas2DQ4	(	const Side *	side,
		const Vect< double > &	u,
		const double &	time = `0.`
	)

Constructor using side and previous time data.

Parameters:

`[in]`	side	Pointer to side
`[in]`	u	Vect instance containing solution at previous time step
`[in]`	time	Current time value

Member Function Documentation

void BodyRHS	(	const Vect< double > &	bf,
		int	opt = `LOCAL_ARRAY`
	)

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

Parameters:

`[in]`	bf	Vector containing source at element nodes (DOF by DOF).
`[in]`	opt	Vector is local (LOCAL_ARRAY) with size 8 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	(	const Vect< double > &	sf,
		int	opt = `LOCAL_ARRAY`
	)

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

Parameters:

`[in]`	sf	Vector containing source at element nodes (DOF by DOF).
`[in]`	opt	Vector is local (LOCAL_ARRAY) with size 4 or global (GLOBAL_ARRAY) with size = Number of side DOF.

void BoundaryRHS ( UserData< double > & ud )

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

Boundary forces are deduced from UserData instance ud.

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 DilatationToRHS ( double coef = 1. )

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

To use for explicit formulations

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 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().

virtual void MassToLHS ( double coef = 1 ) [virtual, inherited]

Add consistent mass contribution to left-hand side.

Parameters:

[in] coef coefficient to multiply by the matrix before adding [default: 1]

virtual void MassToRHS ( double coef = 1 ) [virtual, inherited]

Add consistent mass contribution to right-hand side.

Parameters:

[in] coef coefficient to multiply by the vector before adding [default: 1]

void PlaneStrain	(	double	E,
		double	nu
	)

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

Parameters:

`[in]`	E	Young's modulus
`[in]`	nu	Poisson ratio

void PlaneStress	(	double	E,
		double	nu
	)

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

Parameters:

`[in]`	E	Young's modulus
`[in]`	nu	Poisson ratio

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().

void Strain ( LocalVect< double, 3 > & eps )

Calculate strains at element barycenter.

Parameters:

[out] eps Vector containing strains in element

void Stress	(	LocalVect< double, 3 > &	sigma,
		LocalVect< double, 3 > &	s,
		double &	vm
	)

Calculate principal stresses and Von-Mises stress at element barycenter.

Parameters:

`[out]`	sigma	Vector containing principal stresses in element
`[out]`	s	Vector containing principal stresses in element
`[out]`	vm	Value of Von-Mises stress in element

void Stress	(	LocalVect< double, 3 > &	s,
		double &	vm
	)

Calculate principal stresses and Von-Mises stress at element barycenter.

Parameters:

`[out]`	s	LocalVect containing principal stresses in element
`[out]`	vm	Value of Von-Mises stress in element

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

Elas2DQ4 Class Reference [Solid Mechanics]

Detailed Description

Public Member Functions

Protected Member Functions

Constructor & Destructor Documentation

Member Function Documentation

Elas2DQ4 Class Reference
[Solid Mechanics]