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

#include <Beam3DL2.h>

Inheritance diagram for Beam3DL2:

Public Member Functions
	Beam3DL2 ()
	Default Constructor.

	Beam3DL2 (Mesh &ms, real_t A, real_t I1, real_t I2)
	Constructor using mesh and constant beam properties.

	Beam3DL2 (Mesh &ms)
	Constructor using a Mesh instance.

	Beam3DL2 (Mesh &ms, Vect< real_t > &u)
	Constructor using a Mesh instance and solution vector.

	~Beam3DL2 ()
	Destructor.

void	set (real_t A, real_t I1, real_t I2)
	Set constant beam properties.

void	set (const Vect< real_t > &A, const Vect< real_t > &I1, const Vect< real_t > &I2)
	Set nonconstant beam properties.

void	getDisp (Vect< real_t > &d)
	Get vector of displacements at nodes.

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 RHS after multiplication by `coef` (not implemented)

void	Stiffness (real_t coef=1.)
	Add element stiffness to element matrix.

void	Load (const Vect< real_t > &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.

void	AxialForce (Vect< real_t > &f)
	Return axial force in element.

void	ShearForce (Vect< real_t > &sh)
	Return shear force in element.

void	BendingMoment (Vect< real_t > &m)
	Return bending moment in element.

void	TwistingMoment (Vect< real_t > &m)
	Return twisting moments.

void	build ()
	Build the linear system of equations.

void	buildEigen (SkSMatrix< real_t > &K, Vect< real_t > &M)
	Build global stiffness and mass matrices for the eigen system.

Public Member Functions inherited from Equa_Solid< 2, 12, 1, 6 >
	Equa_Solid ()
	Default constructor.

virtual	~Equa_Solid ()
	Destructor.

virtual void	Deviator (real_t coef=1)
	Add deviator matrix to left-hand side taking into account time integration scheme, after multiplication by `coef` [Default: `1`].

virtual void	Dilatation (real_t coef=1)
	Add dilatation 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< 2, 12, 1, 6 >
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 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() [1/3]

Beam3DL2	(	Mesh &	ms,
		real_t	A,
		real_t	I1,
		real_t	I2 )

Constructor using mesh and constant beam properties.

Parameters

[in]	ms	Mesh instance
[in]	A	Section area of the beam
[in]	I1	first (x) momentum of inertia
[in]	I2	second (y) momentum of inertia

◆ Beam3DL2() [2/3]

Beam3DL2 ( Mesh & ms )

Constructor using a Mesh instance.

Parameters

[in] ms Reference to Mesh instance

◆ Beam3DL2() [3/3]

Beam3DL2	(	Mesh &	ms,
		Vect< real_t > &	u )

Constructor using a Mesh instance and solution vector.

Parameters

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

Member Function Documentation

◆ AxialForce()

void AxialForce ( Vect< real_t > & f )

Return axial force in element.

Parameters

[out] f Vector containing axial force in each element. This vector is resized in the function

◆ BendingMoment()

void BendingMoment ( Vect< real_t > & m )

Return bending moment in element.

Parameters

[out] m Vector containing bending moments (2 components) in each element. This vector is resized in the function

◆ buildEigen()

void buildEigen	(	SkSMatrix< real_t > &	K,
		Vect< real_t > &	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

◆ getDisp()

void getDisp ( Vect< real_t > & d )

Get vector of displacements at nodes.

Parameters

[out] d Vector containing three components for each node that are x, y and z displacements.

◆ set() [1/2]

void set	(	const Vect< real_t > &	A,
		const Vect< real_t > &	I1,
		const Vect< real_t > &	I2 )

Set nonconstant beam properties.

Parameters

[in]	A	Vector containing section areas of the beam (for each element)
[in]	I1	Vector containing first (x) momentum of inertia (for each element)
[in]	I2	Vector containing second (y) momentum of inertia (for each element)

◆ set() [2/2]

void set	(	real_t	A,
		real_t	I1,
		real_t	I2 )

Set constant beam properties.

Parameters

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

◆ ShearForce()

void ShearForce ( Vect< real_t > & sh )

Return shear force in element.

Parameters

[out] sh Vector containing shear forces (2 components) in each element. This vector is resized in the function

◆ TwistingMoment()

void TwistingMoment ( Vect< real_t > & m )

Return twisting moments.

Parameters

[out] m Vector containing twisting moment in each element. This vector is resized in the function

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Beam3DL2() [1/3]

◆ Beam3DL2() [2/3]

◆ Beam3DL2() [3/3]

Member Function Documentation

◆ AxialForce()

◆ BendingMoment()

◆ buildEigen()

◆ getDisp()

◆ set() [1/2]

◆ set() [2/2]

◆ ShearForce()

◆ TwistingMoment()