Beam3DL2 Class Reference

To build element equations for 3-D beam equations using 2-node lines. More...

Inheritance diagram for Beam3DL2:

List of all members.

Public Member Functions
	Beam3DL2 ()
	Default Constructor.
	Beam3DL2 (Element *el, double A, double I1, double I2)
	Constructor using element data.
	Beam3DL2 (Element *el, double A, double I1, double I2, const Vect< double > &u, const double &time=0)
	Constructor for dynamic problems.
	Beam3DL2 (Mesh &ms, const Vect< double > &u, Vect< double > &d)
	Constructor to determine displacements.
	~Beam3DL2 ()
	Destructor.
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 RHS after multiplication by coef.
void	MassToLHS (double coef=1.)
	Add element consistent Mass contribution to matrix after multiplication by coef (not implemented)
void	MassToRHS (double coef=1.)
	Add element consistent Mass contribution to RHS after multiplication by coef (not implemented)
void	Stiffness (double coef=1.)
	Add element stiffness to left hand side.
void	Load (const Vect< double > &f)
	Add contributions for loads.
void	setBending ()
	Set bending contribution to stiffness.
void	setAxial ()
	Set axial contribution to stiffness.
void	setShear ()
	Set shear contribution to stiffness.
void	setTorsion ()
	Set torsion contribution to stiffness.
void	setNoBending ()
	Set no bending contribution.
void	setNoAxial ()
	Set no axial contribution.
void	setNoShear ()
	Set no shear contribution.
void	setNoTorsion ()
	Set no torsion contribution.
void	setReducedIntegration ()
	Set reduced integration.
double	AxialForce () const
	Return axial force in element.
Point< double >	ShearForce () const
	Return shear force in element.
Point< double >	BendingMoment () const
	Return bending moment in element.
double	TwistingMoment () const
	Return twisting moment in element.
void	buildEigen (SkSMatrix< double > &K, Vect< double > &M)
	Build global stiffness and mass matrices for the eigen system.
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.
virtual void	Mass (double coef=1)
	Add consistent mass matrix to left-hand side.
virtual void	LMass (double coef=1)
	Add lumped mass matrix to left-hand side.
virtual void	Deviator (double coef=1)
	Add deviator matrix to left-hand side taking into account time integration scheme.
virtual void	Dilatation (double coef=1)
	Add dilatation matrix to left-hand side taking into account time integration scheme.
virtual void	DilatationToRHS (double coef=1)
	Add dilatation vector to right-hand side taking into account time integration scheme.
virtual void	DeviatorToRHS (double coef=1)
	Add deviator vector to right-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	setDilatation ()
	Add dilatation matrix to left and/or right-hand side taking into account time integration scheme.
void	setDeviator ()
	Add deviator matrix to left and/or right-hand side taking into account time integration scheme.
void	setStiffness ()
	Add convection contribution to left and/or right-hand side taking into account time integration scheme.
void	buildEigen (SkSMatrix< double > &K, SkSMatrix< double > &M)
	Build global stiffness and mass matrices for the eigen system.
void	updateBC (const Vect< T_ > &bc)
	Update Right-Hand side by taking into account essential boundary conditions.
void	DiagBC (int dof_type=NODE_DOF, int dof=0)
	Update element matrix to impose bc by diagonalization technique.
void	LocalNodeVector (Vect< T_ > &b)
	Localize Element Vector from a Vect instance.
void	ElementVector (const Vect< T_ > &b, int dof_type=NODE_FIELD, int flag=0)
	Localize Element Vector.
void	SideVector (const Vect< T_ > &b)
	Localize Side Vector.
void	ElementNodeCoordinates ()
	Localize coordinates of element nodes.
void	SideNodeCoordinates ()
	Localize coordinates of side nodes.
void	ElementAssembly (Matrix< T_ > *A)
	Assemble element matrix into global one.
void	ElementAssembly (SkSMatrix< T_ > &A)
	Assemble element matrix into global one.
void	ElementAssembly (SkMatrix< T_ > &A)
	Assemble element matrix into global one.
void	ElementAssembly (SpMatrix< T_ > &A)
	Assemble element matrix into global one.
void	ElementAssembly (TrMatrix< T_ > &A)
	Assemble element matrix into global one.
void	ElementAssembly (Vect< T_ > &v)
	Assemble element vector into global one.
void	SideAssembly (Matrix< T_ > *A)
	Assemble side (edge or face) matrix into global one.
void	SideAssembly (SkSMatrix< T_ > &A)
	Assemble side (edge or face) matrix into global one.
void	SideAssembly (SkMatrix< T_ > &A)
	Assemble side (edge or face) matrix into global one.
void	SideAssembly (SpMatrix< T_ > &A)
	Assemble side (edge or face) matrix into global one.
void	SideAssembly (Vect< T_ > &v)
	Assemble side (edge or face) vector into global one.
size_t	getNbNodes () const
	Return number of element nodes.
size_t	getNbEq () const
	Return number of element equations.
T_ *	A ()
	Return element matrix as a C-array.
T_ *	sA ()
	Return side matrix as a C-array.
T_ *	b ()
	Return element right-hand side as a C-array.
T_ *	sb ()
	Return side right-hand side as a C-array.
T_ *	Prev ()
	Return element matrix as a C-array.
LocalMatrix< T_, NEE_, NEE_ > &	EA ()
	Return element matrix as a LocalMatrix instance.
LocalMatrix< T_, NSE_, NSE_ > &	SA ()
	Return side matrix as a LocalMatrix instance.
LocalVect< T_, NEE_ > &	Eb ()
	Return element right-hand side as a LocalVect instance.
LocalVect< T_, NEE_ > &	Ep ()
	Return element matrix as a C-array.
void	setInitialSolution (const Vect< T_ > &u)
	Set initial solution (previous time step)
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.
Mesh &	getMesh () const
	Return reference to Mesh instance.
LinearSolver< T_ > &	getLinearSolver ()
	Return reference to linear solver instance.
void	setSolver (int ls, int pc=IDENT_PREC)
	Choose solver for the linear system.
int	solveEigenProblem (int nb_eigv, bool g=false)
	Compute eigenvalues and eigenvectors.
double	getEigenValue (int n) const
	Return the n-th eigenvalue.
void	getEigenVector (int n, Vect< double > &v) const
	Store the eigenvector corresponding to a given eigenvalue.
class Eigen &	getEigenSolver ()
	Return reference to eigenproblem solver.
Protected Member Functions
void	Young (const double &E)
	Set (constant) Young modulus.
void	Young (const char *exp)
	Set Young modulus given by an algebraic expression.
void	Poisson (const double &nu)
	Set (constant) Poisson ratio.
void	Poisson (const char *exp)
	Set Poisson ratio given by an algebraic expression.
void	Density (const double &rho)
	Set (constant) density.
void	Density (const char *exp)
	Set density given by an algebraic expression.
void	setMaterial ()
	Set material properties.
void	Init (const Element *el)
	Set element arrays to zero.
void	Init (const Side *sd)
	Set side arrays to zero.

---

Detailed Description

To build element equations for 3-D beam equations using 2-node lines.

This class enables building finite element arrays for 3-D beam elements using 6 degrees of freedom per node and 2-Node line elements.

---

Constructor & Destructor Documentation

Beam3DL2	(	Element *	el,
		double	A,
		double	I1,
		double	I2
	)

Constructor using element data.

Parameters:

[in]	el	Pointer to Element
[in]	A	Section area of the beam
[in]	I1	first (x) momentum of inertia
[in]	I2	second (y) momentum of inertia

Beam3DL2	(	Element *	el,
		double	A,
		double	I1,
		double	I2,
		const Vect< double > &	u,
		const double &	time = 0
	)

Constructor for dynamic problems.

Parameters:

[in]	el	Pointer to Element
[in]	A	Section area of the beam
[in]	I1	first (x) momentum of inertia
[in]	I2	second (y) momentum of inertia
[in]	u	Vector containing previous solution (at previous time step)
[in]	time	Current time value

Beam3DL2	(	Mesh &	ms,
		const Vect< double > &	u,
		Vect< double > &	d
	)

Constructor to determine displacements.

The unknowns consist in planar and rotational degrees of freedom. This member function construct a 3-D node vector that gives the displacement vector at each node.

Parameters:

[in]	ms	Mesh instance
[in]	u	Vector containing the solution vector
[out]	d	Vector containing three components for each node that are x, y and z displacements.

---

Member Function Documentation

void buildEigen	(	SkSMatrix< double > &	K,
		Vect< double > &	M
	)

Build global stiffness and mass matrices for the eigen system.

Case where the mass matrix is lumped

Parameters:

[in]	K	Stiffness matrix
[in]	M	Vector containing diagonal mass matrix

Reimplemented from Equa_Solid< double, 2, 12, 1, 1 >.

void buildEigen	(	SkSMatrix< double > &	K,
		SkSMatrix< double > &	M
	)		[inherited]

Build global stiffness and mass matrices for the eigen system.

Case where the mass matrix is consistent

Parameters:

[in]	K	Stiffness matrix
[in]	M	Consistent mass matrix

void updateBC

(

const Vect< T_ > &

bc

)

[inherited]

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

Parameters:

[in]

bc

Vector that contains imposed values at all DOFs

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_FIELD, DOFs are supported by nodes [ default ] = ELEMENT_FIELD, DOFs are supported by elements = SIDE_FIELD, 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

void LocalNodeVector

(

Vect< T_ > &

b

)

[inherited]

Localize Element Vector from a Vect 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.

void ElementVector	(	const Vect< T_ > &	b,
		int	dof_type = NODE_FIELD,
		int	flag = 0
	)		[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_FIELD, DOFs are supported by nodes [ default ] = ELEMENT_FIELD, DOFs are supported by elements = SIDE_FIELD, DOFs are supported by sides
[in]	flag	Option to set: = 0, All DOFs are taken into account [ default ] != 0, Only DOF No. dof is handled in the system The resulting local vector can be accessed by attribute ePrev.

Remarks:

This member function is to be used if a constructor with Element was invoked. It uses the Element pointer _theElement

void SideVector

(

const Vect< T_ > &

b

)

[inherited]

Localize Side Vector.

Parameters:

[in]

b

Global vector to be localized = NODE_FIELD, DOFs are supported by nodes [ default ] = ELEMENT_FIELD, DOFs are supported by elements = SIDE_FIELD, DOFs are supported by sides The resulting local vector can be accessed by attribute ePrev.

Remarks:

This member function is to be used if a constructor with Side was invoked. It uses the Side pointer _theSide

void ElementNodeCoordinates

(

)

[inherited]

Localize coordinates of element nodes.

Coordinates are stored in array _x[0], _x[1], ... which are instances of class Point<double>

Remarks:

This member function uses the Side pointer _theSide

void SideNodeCoordinates

(

)

[inherited]

Localize coordinates of side nodes.

Coordinates are stored in array _x[0], _x[1], ... which are instances of class Point<double>

Remarks:

This member function uses the Element pointer _theElement

void ElementAssembly

(

Matrix< T_ > *

A

)

[inherited]

Assemble element matrix into global one.

Parameters:

A	Pointer to global matrix (abstract class: can be any of classes SkSMatrix, SkMatrix, SpMatrix)

Warning:

The element pointer is given by the global variable theElement

void ElementAssembly

(

SkSMatrix< T_ > &

A

)

[inherited]

Assemble element matrix into global one.

Parameters:

A	Global matrix stored as an SkSMatrix instance

Warning:

The element pointer is given by the global variable theElement

void ElementAssembly

(

SkMatrix< T_ > &

A

)

[inherited]

Assemble element matrix into global one.

Parameters:

[in]

A

Global matrix stored as an SkMatrix instance

Warning:

The element pointer is given by the global variable theElement

void ElementAssembly

(

SpMatrix< T_ > &

A

)

[inherited]

Assemble element matrix into global one.

Parameters:

[in]

A

Global matrix stored as an SpMatrix instance

Warning:

The element pointer is given by the global variable theElement

void ElementAssembly

(

TrMatrix< T_ > &

A

)

[inherited]

Assemble element matrix into global one.

Parameters:

[in]

A

Global matrix stored as an TrMatrix instance

Warning:

The element pointer is given by the global variable theElement

void ElementAssembly

(

Vect< T_ > &

v

)

[inherited]

Assemble element vector into global one.

Parameters:

[in]

v

Global vector (Vect instance)

Warning:

The element pointer is given by the global variable theElement

void SideAssembly

(

Matrix< T_ > *

A

)

[inherited]

Assemble side (edge or face) matrix into global one.

Parameters:

A	Pointer to global matrix (abstract class: can be any of classes SkSMatrix, SkMatrix, SpMatrix)

Warning:

The side pointer is given by the global variable theSide

void SideAssembly

(

SkSMatrix< T_ > &

A

)

[inherited]

Assemble side (edge or face) matrix into global one.

Parameters:

[in]

A

Global matrix stored as an SkSMatrix instance

Warning:

The side pointer is given by the global variable theSide

void SideAssembly

(

SkMatrix< T_ > &

A

)

[inherited]

Assemble side (edge or face) matrix into global one.

Parameters:

[in]

A

Global matrix stored as an SkMatrix instance

Warning:

The side pointer is given by the global variable theSide

void SideAssembly

(

SpMatrix< T_ > &

A

)

[inherited]

Assemble side (edge or face) matrix into global one.

Parameters:

[in]

A

Global matrix stored as an SpMatrix instance

Warning:

The side pointer is given by the global variable theSide

void SideAssembly

(

Vect< T_ > &

v

)

[inherited]

Assemble side (edge or face) vector into global one.

Parameters:

[in]

v

Global vector (Vect instance)

Warning:

The side pointer is given by the global variable theSide

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

Returns:

Return value in expression evaluation:

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

Mesh& getMesh

(

)

const [inherited]

Return reference to Mesh instance.

Returns:

Reference to Mesh instance

void setSolver	(	int	ls,
		int	pc = IDENT_PREC
	)		[inherited]

Choose solver for the linear system.

Parameters:

[in]	ls	Solver of the linear system. To choose among the enumerated values: DIRECT_SOLVER, CG_SOLVER, GMRES_SOLVER = DIRECT_SOLVER, Use a facorization solver [default] = CG_SOLVER, Conjugate Gradient iterative solver = CGS_SOLVER, Squared Conjugate Gradient iterative solver = BICG_SOLVER, BiConjugate Gradient iterative solver = BICG_STAB_SOLVER, BiConjugate Gradient Stabilized iterative solver = GMRES_SOLVER, GMRES iterative solver = QMR_SOLVER, QMR iterative solver
[in]	pc	Preconditioner to associate to the iterative solver. if the direct solver was chosen for the first argument this argument is not used. Otherwise choose among the enumerated values: = IDENT_PREC, Identity preconditioner (no preconditioning [ default ] = DIAG_PREC, Diagonal preconditioner = ILU_PREC, Incomplete LU factorization preconditioner

int solveEigenProblem	(	int	nb_eigv,
		bool	g = false
	)		[inherited]

Compute eigenvalues and eigenvectors.

Eigenvalues and vectors are computed using the Bathe's subspace iteration method.

Parameters:

[in]	nb_eigv	Number of eigenvalues to compute
[in]	g	Option to choose whether to solve a generalized eigenvalue problem (true) or a standard one (false). The generalized eigenvalue problem corresponds to the case where a consistent mass matrix (rather than a lumped one) is computed. Default value is false.

double getEigenValue

(

int

n

)

const [inherited]

Return the n-th eigenvalue.

This functions works only if the member function getEigen was called with an argument nb_eigv greater or equal to n. Otherwise it returns 0.

void getEigenVector	(	int	n,
		Vect< double > &	v
	)		const [inherited]

Store the eigenvector corresponding to a given eigenvalue.

Parameters:

[in]	n	Label of the eigenvalue
[out]	v	Vect instance containing the corresponding eigenvector. This vector is resized.