Elas2DQ4 Class Reference

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

#include <Elas2DQ4.h>

Inheritance diagram for Elas2DQ4:

Public Member Functions
	Elas2DQ4 ()
	Default Constructor.
	Elas2DQ4 (Mesh &ms)
	Constructor using Mesh instance.
	Elas2DQ4 (Mesh &ms, Vect< real_t > &u)
	Constructor using Mesh instance and solution vector.
	~Elas2DQ4 ()
	Destructor.
void	PlaneStrain ()
	Set plane strain hypothesis.
void	PlaneStrain (real_t E, real_t nu)
	Set plane strain hypothesis by giving values of Young's modulus and Poisson ratio.
void	PlaneStress ()
	Set plane stress hypothesis.
void	PlaneStress (real_t E, real_t nu)
	Set plane stress hypothesis by giving values of Young's modulus and Poisson ratio.
void	LMass (real_t coef=1.)
	Add element lumped mass contribution to element matrix after multiplication by coef [Default: 1].
void	Mass (real_t coef=1.)
	Add element consistent mass contribution to matrix and right-hand side after multiplication by coef [Default: 1].
void	Deviator (real_t coef=1.)
	Add element deviatoric matrix to element matrix after multiplication by coef [Default: 1].
void	Dilatation (real_t coef=1.)
	Add element dilatational contribution to element matrix after multiplication by coef [Default: 1].
void	BodyRHS (const Vect< real_t > &f)
	Add body right-hand side term to right hand side.
void	BodyRHS ()
	Add body right-hand side term to right hand side.
void	BoundaryRHS (const Vect< real_t > &f)
	Add boundary right-hand side term to right hand side.
void	BoundaryRHS ()
	Add boundary right-hand side term to right hand side.
void	Strain (Vect< real_t > &eps)
	Calculate strains at element barycenters.
void	Stress (Vect< real_t > &st, Vect< real_t > &vm)
	Calculate principal stresses and Von-Mises stress at element barycenter.
void	Stress (Vect< real_t > &sigma, Vect< real_t > &s, Vect< real_t > &st)
	Calculate principal stresses and Von-Mises stress at element barycenter.
Public Member Functions inherited from Equa_Solid< 4, 8, 2, 4 >
	Equa_Solid ()
	Default constructor.
virtual	~Equa_Solid ()
	Destructor.
virtual void	Stiffness (real_t coef=1)
	Add stiffness matrix to left-hand side taking into account time integration scheme, after multiplication by coef [Default: 1].
void	setInput (EType opt, Vect< real_t > &u)
	Set specific input data to solid mechanics.
Public Member Functions inherited from Equation< NEN_, NEE_, NSN_, NSE_ >
	Equation ()
	Equation (Mesh &mesh)
	Constructor with mesh instance.
	Equation (Mesh &mesh, Vect< real_t > &u)
	Constructor with mesh instance and solution vector.
	Equation (Mesh &mesh, Vect< real_t > &u, real_t &init_time, real_t &final_time, real_t &time_step)
	Constructor with mesh instance, matrix and right-hand side.
	~Equation ()
	Destructor.
void	updateBC (const Element &el, const Vect< real_t > &bc)
	Update Right-Hand side by taking into account essential boundary conditions.
void	DiagBC (DOFSupport dof_type=NODE_DOF, int dof=0)
	Update element matrix to impose bc by diagonalization technique.
void	LocalNodeVector (Vect< real_t > &b)
	Localize element vector from a Vect instance.
void	ElementNodeVector (const Vect< real_t > &b, LocalVect< real_t, NEE_ > &be)
	Localize element vector from a Vect instance.
void	SideNodeVector (const Vect< real_t > &b, LocalVect< real_t, NSE_ > &bs)
	Localize side vector from a Vect instance.
void	SideSideVector (const Vect< real_t > &b, vector< real_t > &bs)
	Localize side vector from a Vect instance.
void	ElementNodeVectorSingleDOF (const Vect< real_t > &b, LocalVect< real_t, NEN_ > &be)
	Localize Element Vector from a Vect instance.
void	ElementNodeVector (const Vect< real_t > &b, LocalVect< real_t, NEN_ > &be, int dof)
	Localize Element Vector from a Vect instance.
void	ElementSideVector (const Vect< real_t > &b, LocalVect< real_t, NSE_ > &be)
	Localize Element Vector from a Vect instance.
void	ElementVector (const Vect< real_t > &b, DOFSupport dof_type=NODE_DOF, int flag=0)
	Localize element vector.
void	SideVector (const Vect< real_t > &b, vector< real_t > &sb)
	Localize side vector.
void	ElementNodeCoordinates ()
	Localize coordinates of element nodes.
void	SideNodeCoordinates ()
	Localize coordinates of side nodes.
void	ElementAssembly (Matrix< real_t > *A)
	Assemble element matrix into global one.
void	ElementAssembly (BMatrix< real_t > &A)
	Assemble element matrix into global one.
void	ElementAssembly (SkSMatrix< real_t > &A)
	Assemble element matrix into global one.
void	ElementAssembly (SkMatrix< real_t > &A)
	Assemble element matrix into global one.
void	ElementAssembly (SpMatrix< real_t > &A)
	Assemble element matrix into global one.
void	ElementAssembly (TrMatrix< real_t > &A)
	Assemble element matrix into global one.
void	DGElementAssembly (Matrix< real_t > *A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation.
void	DGElementAssembly (SkSMatrix< real_t > &A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation.
void	DGElementAssembly (SkMatrix< real_t > &A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation.
void	DGElementAssembly (SpMatrix< real_t > &A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation.
void	DGElementAssembly (TrMatrix< real_t > &A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation.
void	SideAssembly (Matrix< real_t > *A)
	Assemble side (edge or face) matrix into global one.
void	SideAssembly (SkSMatrix< real_t > &A)
	Assemble side (edge or face) matrix into global one.
void	SideAssembly (SkMatrix< real_t > &A)
	Assemble side (edge or face) matrix into global one.
void	SideAssembly (SpMatrix< real_t > &A)
	Assemble side (edge or face) matrix into global one.
void	ElementAssembly (Vect< real_t > &v)
	Assemble element vector into global one.
void	SideAssembly (Vect< real_t > &v)
	Assemble side (edge or face) vector into global one.
void	AxbAssembly (const Element &el, const Vect< real_t > &x, Vect< real_t > &b)
	Assemble product of element matrix by element vector into global vector.
void	AxbAssembly (const Side &sd, const Vect< real_t > &x, Vect< real_t > &b)
	Assemble product of side matrix by side vector into global vector.
size_t	getNbNodes () const
	Return number of element nodes.
size_t	getNbEq () const
	Return number of element equations.
real_t	setMaterialProperty (const string &exp, const string &prop)
	Define a material property by an algebraic expression.
Public Member Functions inherited from Equa
	Equa ()
	Default constructor.
virtual	~Equa ()
	Destructor.
void	setMesh (Mesh &m)
	Define mesh and renumber DOFs after removing imposed ones.
Mesh &	getMesh () const
	Return reference to Mesh instance.
LinearSolver &	getLinearSolver ()
	Return reference to linear solver instance.
Matrix< real_t > *	getMatrix () const
	Return pointer to matrix.
void	setSolver (Iteration ls, Preconditioner pc=IDENT_PREC)
	Choose solver for the linear system.
void	setMatrixType (int t)
	Choose type of matrix.
int	solveLinearSystem (Matrix< real_t > *A, Vect< real_t > &b, Vect< real_t > &x)
	Solve the linear system with given matrix and right-hand side.
int	solveLinearSystem (Vect< real_t > &b, Vect< real_t > &x)
	Solve the linear system with given right-hand side.
void	LinearSystemInfo ()
	Print info on linear system solver.

Additional Inherited Members
Protected Member Functions inherited from Equa_Solid< 4, 8, 2, 4 >
void	Young (const real_t &E)
	Set (constant) Young modulus.
void	Young (const string &exp)
	Set Young modulus given by an algebraic expression.
void	Poisson (const real_t &nu)
	Set (constant) Poisson ratio.
void	Poisson (const string &exp)
	Set Poisson ratio given by an algebraic expression.
void	Density (const real_t &rho)
	Set (constant) density.
void	Density (const string &exp)
	Set density given by an algebraic expression.
void	setMaterial ()
	Set material properties.

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 real coef that is multiplied by the contribution of the current element. This makes possible testing different algorithms.

Constructor & Destructor Documentation

Elas2DQ4() [1/3]

Elas2DQ4

(

)

Default Constructor.

Constructs an empty equation.

Elas2DQ4() [2/3]

Elas2DQ4

(

Mesh &

ms

)

Constructor using Mesh instance.

Parameters

[in]

ms

Reference to Mesh instance

Elas2DQ4() [3/3]

Elas2DQ4	(	Mesh &	ms,
		Vect< real_t > &	u
	)

Constructor using Mesh instance and solution vector.

Parameters

[in]	ms	Reference to Mesh instance
[in,out]	u	Solution vector

Member Function Documentation

BodyRHS()

void BodyRHS

(

const Vect< real_t > &

f

)

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

Parameters

[in]

f

Vector containing source at nodes (DOF by DOF).

BoundaryRHS()

void BoundaryRHS

(

const Vect< real_t > &

f

)

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

Parameters

[in]

f

Vector containing source at nodes (DOF by DOF).

PlaneStrain()

void PlaneStrain	(	real_t	E,
		real_t	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

PlaneStress()

void PlaneStress	(	real_t	E,
		real_t	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

Strain()

void Strain

(

Vect< real_t > &

eps

)

Calculate strains at element barycenters.

Parameters

[out]

eps

Vector containing strains in elements

Remarks

The instance of Elas2DQ4 must have been constructed using the constructor with Mesh instance and solution vector

Stress() [1/2]

void Stress	(	Vect< real_t > &	sigma,
		Vect< real_t > &	s,
		Vect< real_t > &	st
	)

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

Parameters

[out]	sigma	Vector containing principal stresses in elements
[out]	s	Vector containing principal stresses in elements
[out]	st	Value of Von-Mises stress in elements

Remarks

The instance of Elas2DQ4 must have been constructed using the constructor with Mesh instance and solution vector

Stress() [2/2]

void Stress	(	Vect< real_t > &	st,
		Vect< real_t > &	vm
	)

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

Parameters

[out]	st	Vector containing principal stresses in elements
[out]	vm	Vector containing Von-Mises stresses in elements

Remarks

The instance of Elas2DQ4 must have been constructed using the constructor with Mesh instance and solution vector