chrono::fea::ChBeamSectionRayleighSimple Class Reference

## Description

This works exactly as ChBeamSectionEulerSimple, but adds the effect of Jyy Jzz rotational sectional inertias, whereas the conventional Euler theory would assume the mass to be concentrated in the center of mass, hence Jyy Jzz =0.

For wide sections, Jyy Jzz can become not negligible. In this simple symmetric case with homogeneous density, the values of Jyy Jzz are computed automatically as $$J_{yy} = \rho I_{yy}$$, $$J_{zz} = \rho I_{zz}$$ 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::ChBeamSectionRayleighSimple:
Collaboration diagram for chrono::fea::ChBeamSectionRayleighSimple:

## Public Member Functions

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.

Public Member Functions inherited from chrono::fea::ChBeamSectionEulerSimple
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 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 = alpha*M + beta*K.

double GetRayleighDampingAlpha ()

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

double GetRayleighDampingBeta ()

virtual void SetRayleighDamping (double mbeta, double malpha=0)
Set both beta and alpha coefficients in Rayleigh damping model: R = alpha*M + beta*K. 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< ChBeamSectionShapeGetDrawShape () 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...

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 inherited from chrono::fea::ChBeamSectionEulerSimple
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...

Protected Attributes inherited from chrono::fea::ChBeamSectionEuler
double rdamping_beta

double rdamping_alpha

double JzzJyy_factor

## Member Function Documentation

 void chrono::fea::ChBeamSectionRayleighSimple::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::ChBeamSectionEulerSimple.

## ◆ ComputeInertiaStiffnessMatrix()

 void chrono::fea::ChBeamSectionRayleighSimple::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::ChBeamSectionEulerSimple.

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