Description

Basic section of an Euler-Bernoulli beam in 3D, for a homogeneous density and homogeneous elasticity, given basic material properties (Izz and Iyy moments of inertia, area, Young modulus, etc.).

This is a simple section model that assumes the elastic center, the shear center and the mass center to be all in the centerline of the beam (section origin); this is the case of symmetric sections for example. To be used with ChElementBeamEuler. This material can be shared between multiple beams.

#include <ChBeamSectionEuler.h>

Inheritance diagram for chrono::fea::ChBeamSectionEulerSimple:

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Collaboration diagram for chrono::fea::ChBeamSectionEulerSimple:

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Public Member Functions
void	SetArea (const double ma)
	Set the cross sectional area A of the beam (m^2)

double	GetArea () const

void	SetIyy (double ma)
	Set the Iyy moment of inertia of the beam (for flexion about y axis) Note: some textbook calls this Iyy as Iz.

double	GetIyy () const

void	SetIzz (double ma)
	Set the Izz moment of inertia of the beam (for flexion about z axis) Note: some textbook calls this Izz as Iy.

double	GetIzz () const

void	SetJ (double ma)
	Set the J torsion constant of the beam (for torsion about x axis)

double	GetJ () const

void	SetKsy (double ma)
	Set the Timoshenko shear coefficient Ks for y shear, usually about 0.8, (for elements that use this, ex. More...

double	GetKsy () const

void	SetKsz (double ma)
	Set the Timoshenko shear coefficient Ks for z shear, usually about 0.8, (for elements that use this, ex. More...

double	GetKsz () const

void	SetAsRectangularSection (double width_y, double width_z)
	Shortcut: set Area, Ixx, Iyy, Ksy, Ksz and J torsion constant at once, given the y and z widths of the beam assumed with rectangular shape.

void	SetAsCircularSection (double diameter)
	Shortcut: set Area, Ixx, Iyy, Ksy, Ksz and J torsion constant at once, given the diameter of the beam assumed with circular shape.

void	SetDensity (double md)
	Set the density of the beam (kg/m^3)

double	GetDensity () const

void	SetYoungModulus (double mE)
	Set E, the Young elastic modulus (N/m^2)

double	GetYoungModulus () const

void	SetShearModulus (double mG)
	Set the shear modulus, used for computing the torsion rigidity = J*G.

double	GetShearModulus () const

void	SetShearModulusFromPoisson (double mpoisson)
	Set the shear modulus, given current Young modulus and the specified Poisson ratio.

virtual double	GetAxialRigidity () const override
	Gets the axial rigidity, usually A*E.

virtual double	GetTorsionRigidityX () const override
	Gets the torsion rigidity, for torsion about X axis at elastic center, usually J*G.

virtual double	GetBendingRigidityY () const override
	Gets the bending rigidity, for bending about Y axis at elastic center, usually Iyy*E.

virtual double	GetBendingRigidityZ () const override
	Gets the bending rigidity, for bending about Z axis at elastic center, usually Izz*E.

virtual double	GetSectionRotation () const override
	Set the rotation of the Y Z section axes for which the YbendingRigidity and ZbendingRigidity are defined.

virtual double	GetCentroidY () const override
	Gets the Y position of the elastic center respect to centerline.

virtual double	GetCentroidZ () const override
	Gets the Z position of the elastic center respect to centerline.

virtual double	GetShearCenterY () const override
	Gets the Y position of the shear center respect to centerline.

virtual double	GetShearCenterZ () const override
	Gets the Z position of the shear center respect to centerline.

virtual void	ComputeInertiaMatrix (ChMatrix66d &M) override
	Compute the 6x6 sectional inertia matrix, as in {x_momentum,w_momentum}=[Mm]{xvel,wvel}.

virtual void	ComputeInertiaDampingMatrix (ChMatrix66d &Ri, const ChVector3d &mW) override
	Compute the 6x6 sectional inertia damping matrix [Ri] (gyroscopic matrix damping) More...

virtual void	ComputeInertiaStiffnessMatrix (ChMatrix66d &Ki, const ChVector3d &mWvel, const ChVector3d &mWacc, const ChVector3d &mXacc) override
	Compute the 6x6 sectional inertia stiffness matrix [Ki^]. More...

virtual void	ComputeQuadraticTerms (ChVector3d &mF, ChVector3d &mT, const ChVector3d &mW) override
	Compute the centrifugal term and gyroscopic term.

virtual double	GetMassPerUnitLength () const override
	Get mass per unit length, ex.SI units [kg/m].

virtual double	GetInertiaJxxPerUnitLength () const override
	Get the Jxx component of the inertia per unit length (polar inertia) in the Y Z unrotated reference frame of the section at centerline. More...

Public Member Functions inherited from chrono::fea::ChBeamSectionEuler
virtual void	ComputeInertialForce (ChVector3d &mFi, ChVector3d &mTi, const ChVector3d &mWvel, const ChVector3d &mWacc, const ChVector3d &mXacc)
	Compute the total inertial forces (per unit length). More...

void	SetArtificialJyyJzzFactor (double mf)
	The Euler beam model has no rotational inertia per each section, assuming mass is concentrated on the centerline. More...

double	GetArtificialJyyJzzFactor ()

virtual void	SetRayleighDampingAlpha (double malpha)
	Set the "alpha" Rayleigh damping ratio, the mass-proportional structural damping in: R = alphaM + betaK.

double	GetRayleighDampingAlpha ()

virtual void	SetRayleighDampingBeta (double mbeta)
	Set the "beta" Rayleigh damping ratio, the stiffness-proportional structural damping in: R = alphaM + betaK.

double	GetRayleighDampingBeta ()

virtual void	SetRayleighDamping (double mbeta, double malpha=0)
	Set both beta and alpha coefficients in Rayleigh damping model: R = alphaM + betaK. More...

Public Member Functions inherited from chrono::fea::ChBeamSection
void	SetDrawShape (std::shared_ptr< ChBeamSectionShape > mshape)
	Set the graphical representation for this section. More...

std::shared_ptr< ChBeamSectionShape >	GetDrawShape () const
	Get the drawing shape of this section (i.e.a 2D profile used for drawing 3D tesselation and visualization) By default a thin square section, use SetDrawShape() to change it.

void	SetDrawThickness (double thickness_y, double thickness_z)
	Shortcut: adds a ChBeamSectionShapeRectangular for visualization as a centered rectangular beam, and sets its width/height. More...

void	SetDrawCircularRadius (double draw_rad)
	Shortcut: adds a ChBeamSectionShapeCircular for visualization as a centered circular beam, and sets its radius. More...

void	SetCircular (bool ic)
	OBSOLETE only for backward compability.

Public Attributes
double	Area

double	Iyy

double	Izz

double	J

double	G

double	E

double	density

double	Ks_y

double	Ks_z

Public Attributes inherited from chrono::fea::ChBeamSectionEuler
bool	compute_inertia_damping_matrix = true
	Flag that turns on/off the computation of the [Ri] 'gyroscopic' inertial damping matrix. More...

bool	compute_inertia_stiffness_matrix = true
	Flag that turns on/off the computation of the [Ki] inertial stiffness matrix. More...

bool	compute_Ri_Ki_by_num_diff = false
	Flag for computing the Ri and Ki matrices via numerical differentiation even if an analytical expression is provided. More...

Additional Inherited Members
Protected Attributes inherited from chrono::fea::ChBeamSectionEuler
double	rdamping_beta

double	rdamping_alpha

double	JzzJyy_factor

Member Function Documentation

◆ ComputeInertiaDampingMatrix()

void chrono::fea::ChBeamSectionEulerSimple::ComputeInertiaDampingMatrix	(	ChMatrix66d &	Ri,
		const ChVector3d &	mW
	)

overridevirtual

Compute the 6x6 sectional inertia damping matrix [Ri] (gyroscopic matrix damping)

Parameters

Ri	6x6 sectional inertial-damping (gyroscopic damping) matrix values here
mW	current angular velocity of section, in material frame

Reimplemented from chrono::fea::ChBeamSectionEuler.

Reimplemented in chrono::fea::ChBeamSectionRayleighSimple.

◆ ComputeInertiaStiffnessMatrix()

void chrono::fea::ChBeamSectionEulerSimple::ComputeInertiaStiffnessMatrix	(	ChMatrix66d &	Ki,
		const ChVector3d &	mWvel,
		const ChVector3d &	mWacc,
		const ChVector3d &	mXacc
	)

overridevirtual

Compute the 6x6 sectional inertia stiffness matrix [Ki^].

Parameters

Ki	6x6 sectional inertial-stiffness matrix [Ki^] values here
mWvel	current angular velocity of section, in material frame
mWacc	current angular acceleration of section, in material frame
mXacc	current acceleration of section, in material frame (not absolute!)

Reimplemented from chrono::fea::ChBeamSectionEuler.

Reimplemented in chrono::fea::ChBeamSectionRayleighSimple.

◆ GetInertiaJxxPerUnitLength()

virtual double chrono::fea::ChBeamSectionEulerSimple::GetInertiaJxxPerUnitLength ( ) const

inlineoverridevirtual

Get the Jxx component of the inertia per unit length (polar inertia) in the Y Z unrotated reference frame of the section at centerline.

Note: it automatically follows Jxx=Jyy+Jzz for the polar theorem. Also, Jxx=density*Ixx if constant density.

Implements chrono::fea::ChBeamSectionEuler.

◆ SetKsy()

void chrono::fea::ChBeamSectionEulerSimple::SetKsy ( double ma )

inline

Set the Timoshenko shear coefficient Ks for y shear, usually about 0.8, (for elements that use this, ex.

the Timoshenko beams, or Reddy's beams)

◆ SetKsz()

void chrono::fea::ChBeamSectionEulerSimple::SetKsz ( double ma )

inline

Set the Timoshenko shear coefficient Ks for z shear, usually about 0.8, (for elements that use this, ex.

the Timoshenko beams, or Reddy's beams)

The documentation for this class was generated from the following files:

/builds/uwsbel/chrono/src/chrono/fea/ChBeamSectionEuler.h
/builds/uwsbel/chrono/src/chrono/fea/ChBeamSectionEuler.cpp