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

#include <Elas2DT3.h>

Inheritance diagram for Elas2DT3:

Public Member Functions
	Elas2DT3 ()
	Default Constructor.

	Elas2DT3 (Mesh &ms)
	Constructor using Mesh data.

	Elas2DT3 (Mesh &ms, Vect< real_t > &u)
	Constructor using Mesh data and solution vector.

	~Elas2DT3 ()
	Destructor.

void	Media (real_t E, real_t nu, real_t rho)
	Set media properties.

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 `E` and Poisson ratio `nu`

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 `E` and Poisson ratio `nu`

void	LMass (real_t coef=1.)
	Add element lumped mass contribution to element matrix after multiplication by `coef`

void	Mass (real_t coef=1.)
	Add element consistent mass contribution to element matrix after multiplication by `coef`

void	Deviator (real_t coef=1.)
	Add element deviatoric matrix to element matrix after multiplication by `coef`

void	Dilatation (real_t coef=1.)
	Add element dilatational contribution to element matrix after multiplication by `coef`

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.

int	Contact (real_t coef=1.e07)
	Penalty Signorini contact side contribution to matrix and right-hand side.

void	Reaction (Vect< real_t > &r)
	Calculate reactions.

void	ContactPressure (const Vect< real_t > &f, real_t penal, Point< real_t > &p)
	Calculate contact pressure.

void	Strain (Vect< real_t > &eps)
	Calculate strains in element.

void	Stress (Vect< real_t > &s, Vect< real_t > &vm)
	Calculate principal stresses and Von-Mises stress in element.

void	Periodic (real_t coef=1.e20)
	Add contribution of periodic boundary condition (by a penalty technique).

Public Member Functions inherited from Equa_Solid< 3, 6, 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< 3, 6, 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 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 real coef that is multiplied by the contribution of the current element. This makes possible testing different algorithms.

Constructor & Destructor Documentation

◆ Elas2DT3() [1/3]

Elas2DT3 ( )

Default Constructor.

Constructs an empty equation.

◆ Elas2DT3() [2/3]

Elas2DT3 ( Mesh & ms )

Constructor using Mesh data.

Parameters

[in] ms Mesh instance

◆ Elas2DT3() [3/3]

Elas2DT3	(	Mesh &	ms,
		Vect< real_t > &	u )

Constructor using Mesh data and solution vector.

Parameters

[in]	ms	Mesh instance
[in,out]	u	Reference to 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 Vect instance that contains constant traction to impose to side.

◆ Contact()

int Contact ( real_t coef = 1.e07 )

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

Parameters

[in] coef Penalty value by which the added term is multiplied [Default: 1.e07]

Returns: = 0 if no contact is achieved on this side, 1 otherwise

◆ ContactPressure()

void ContactPressure	(	const Vect< real_t > &	f,
		real_t	penal,
		Point< real_t > &	p )

Calculate contact pressure.

This function can be invoked in postprocessing

Parameters

[in]	f
[in]	penal	Penalty parameter that was used to impose contact condition
[out]	p	Contact pressure

◆ Deviator()

void Deviator ( real_t coef = 1. )

virtual

Add element deviatoric matrix to element matrix after multiplication by coef

Parameters

[in] coef Coefficient to multiply by added term [Default: 1].

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

◆ Dilatation()

void Dilatation ( real_t coef = 1. )

virtual

Add element dilatational contribution to element matrix after multiplication by coef

Parameters

[in] coef Coefficient to multiply by added term [Default: 1].

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

◆ LMass()

void LMass ( real_t coef = 1. )

virtual

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

Parameters

[in] coef Coefficient to multiply by added term [Default: 1].

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

◆ Mass()

void Mass ( real_t coef = 1. )

virtual

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

Parameters

[in] coef Coefficient to multiply by added term [Default: 1].

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

◆ Media()

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

Set media properties.

Useful to override material properties deduced from mesh file.

◆ Periodic()

void Periodic ( real_t 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]

◆ Reaction()

void Reaction ( Vect< real_t > & r )

Calculate reactions.

This function can be invoked in postprocessing

Parameters

[in] r Reaction on the side

◆ Strain()

void Strain ( Vect< real_t > & eps )

Calculate strains in element.

This function can be invoked in postprocessing.

Parameters

[out] eps vector of strains in elements

◆ Stress()

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

Calculate principal stresses and Von-Mises stress in element.

Parameters

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

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Elas2DT3() [1/3]

◆ Elas2DT3() [2/3]

◆ Elas2DT3() [3/3]

Member Function Documentation

◆ BodyRHS()

◆ BoundaryRHS()

◆ Contact()

◆ ContactPressure()

◆ Deviator()

◆ Dilatation()

◆ LMass()

◆ Mass()

◆ Media()

◆ Periodic()

◆ Reaction()

◆ Strain()

◆ Stress()