Description

Simple linear elasticity model for a Cosserat beam, using basic material properties (zz and yy moments of inertia, area, Young modulus, etc.).

Uniform stiffness properties E,G are hence assumed through the section. The classical Timoshenko beam theory is encompassed in this model, that can be interpreted as a 3D extension of the Timoshenko beam theory. This can be shared between multiple beams.

#include <ChBeamSectionCosserat.h>

Inheritance diagram for chrono::fea::ChElasticityCosseratSimple:

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Collaboration diagram for chrono::fea::ChElasticityCosseratSimple:

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Public Member Functions
	ChElasticityCosseratSimple (const double mIyy, const double mIzz, const double mJ, const double mG, const double mE, const double mA, const double mKs_y, const double mKs_z)

void	SetArea (double ma)
	Set the A area of the beam.

double	GetArea () const

void	SetIyy (double ma)
	Set the Iyy second moment of area of the beam (for bending about y in xz plane), defined as \( I_y = \int_\Omega z^2 dA \). More...

double	GetIyy () const

void	SetIzz (double ma)
	Set the Izz second moment of area of the beam (for bending about z in xy plane). More...

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

virtual 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. More...

virtual 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. More...

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

double	GetYoungModulus () const

void	SetShearModulus (double mG)
	Set G, the shear modulus.

double	GetShearModulus () const

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

virtual void	ComputeStress (ChVector3d &stress_n, ChVector3d &stress_m, const ChVector3d &strain_e, const ChVector3d &strain_k) override
	Compute the generalized cut force and cut torque. More...

virtual void	ComputeStiffnessMatrix (ChMatrix66d &K, const ChVector3d &strain_e, const ChVector3d &strain_k) override
	Compute the 6x6 tangent material stiffness matrix [Km] = dσ/dε. More...

Public Attributes
double	Iyy

double	Izz

double	J

double	G

double	E

double	A

double	Ks_y

double	Ks_z

Public Attributes inherited from chrono::fea::ChElasticityCosserat
ChBeamSectionCosserat *	section

Constructor & Destructor Documentation

◆ ChElasticityCosseratSimple()

chrono::fea::ChElasticityCosseratSimple::ChElasticityCosseratSimple	(	const double	mIyy,
		const double	mIzz,
		const double	mJ,
		const double	mG,
		const double	mE,
		const double	mA,
		const double	mKs_y,
		const double	mKs_z
	)

inline

Parameters

mIyy	Iyy second moment of area of the beam \( I_y = \int_\Omega z^2 dA \)
mIzz	Izz second moment of area of the beam \( I_z = \int_\Omega y^2 dA \)
mJ	torsion constant (torsion rigidity will be GJ, torsional stiffness = GJ*length)
mG	G shear modulus
mE	E young modulus
mA	A area
mKs_y	Timoshenko shear coefficient Ks for y shear
mKs_z	Timoshenko shear coefficient Ks for z shear

Member Function Documentation

◆ ComputeStiffnessMatrix()

void chrono::fea::ChElasticityCosseratSimple::ComputeStiffnessMatrix	(	ChMatrix66d &	K,
		const ChVector3d &	strain_e,
		const ChVector3d &	strain_k
	)

overridevirtual

Compute the 6x6 tangent material stiffness matrix [Km] = dσ/dε.

Parameters

K	6x6 stiffness matrix
strain_e	local strain (deformation part): x= elongation, y and z are shear
strain_k	local strain (curvature part), x= torsion, y and z are line curvatures

Reimplemented from chrono::fea::ChElasticityCosserat.

Reimplemented in chrono::fea::ChElasticityCosseratAdvanced.

◆ ComputeStress()

void chrono::fea::ChElasticityCosseratSimple::ComputeStress	(	ChVector3d &	stress_n,
		ChVector3d &	stress_m,
		const ChVector3d &	strain_e,
		const ChVector3d &	strain_k
	)

overridevirtual

Compute the generalized cut force and cut torque.

Parameters

stress_n	local stress (generalized force), x component = traction along beam
stress_m	local stress (generalized torque), x component = torsion torque along beam
strain_e	local strain (deformation part): x= elongation, y and z are shear
strain_k	local strain (curvature part), x= torsion, y and z are line curvatures

Implements chrono::fea::ChElasticityCosserat.

Reimplemented in chrono::fea::ChElasticityCosseratAdvanced.

◆ SetAsCircularSection()

void chrono::fea::ChElasticityCosseratSimple::SetAsCircularSection ( double diameter )

virtual

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

You must set E and G anyway.

◆ SetAsRectangularSection()

void chrono::fea::ChElasticityCosseratSimple::SetAsRectangularSection	(	double	width_y,
		double	width_z
	)

virtual

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.

You must set E and G anyway.

◆ SetIyy()

void chrono::fea::ChElasticityCosseratSimple::SetIyy ( double ma )

inline

Set the Iyy second moment of area of the beam (for bending about y in xz plane), defined as \( I_y = \int_\Omega z^2 dA \).

Note: some textbook calls this Iyy as Iy Ex SI units: [m^4]

◆ SetIzz()

void chrono::fea::ChElasticityCosseratSimple::SetIzz ( double ma )

inline

Set the Izz second moment of area of the beam (for bending about z in xy plane).

defined as \( I_z = \int_\Omega y^2 dA \). Note: some textbook calls this Izz as Iz Ex SI units: [m^4]

◆ SetKsy()

void chrono::fea::ChElasticityCosseratSimple::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::ChElasticityCosseratSimple::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/ChBeamSectionCosserat.h
/builds/uwsbel/chrono/src/chrono/fea/ChBeamSectionCosserat.cpp

Description

Public Member Functions

Public Attributes

Constructor & Destructor Documentation

◆ ChElasticityCosseratSimple()

Member Function Documentation

◆ ComputeStiffnessMatrix()

◆ ComputeStress()

◆ SetAsCircularSection()

◆ SetAsRectangularSection()

◆ SetIyy()

◆ SetIzz()

◆ SetKsy()

◆ SetKsz()