Description

Advanced linear elasticity for a Cosserat beam.

Uniform stiffness properties E,G are assumed through the section as in ChElasticityCosseratSimple, but here it also supports the advanced case of Iyy and Izz axes rotated respect reference, elastic center with offset from reference, and shear center with offset from reference. This material can be shared between multiple beams. The linear elasticity is uncoupled between shear terms S and axial terms A as to have this stiffness matrix pattern:

 n_x   [A       A A ]   e_x
 n_y   [  S S S     ]   e_y
 n_z = [  S S S     ] * e_z
 m_x   [  S S S     ]   k_x
 m_y   [A       A A ]   k_y
 m_z   [A       A A ]   k_z

#include <ChBeamSectionCosserat.h>

Inheritance diagram for chrono::fea::ChElasticityCosseratAdvanced:

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Collaboration diagram for chrono::fea::ChElasticityCosseratAdvanced:

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Public Member Functions
	ChElasticityCosseratAdvanced (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, const double malpha, const double mCy, const double mCz, const double mbeta, const double mSy, const double mSz)

void	SetSectionRotation (double ma)
	"Elastic reference": set alpha, the rotation of the section for which the Iyy Izz are defined, respect to the reference section coordinate system placed at centerline.

double	GetSectionRotation ()

void	SetCentroid (double my, double mz)
	"Elastic reference": set the displacement of the elastic center (or tension center) respect to the reference section coordinate system placed at centerline.

double	GetCentroidY ()

double	GetCentroidZ ()

void	SetShearRotation (double mb)
	"Shear reference": set beta, the rotation of the section for shear decoupling, respect to the reference section coordinate system placed at centerline.

double	GetShearRotation ()

void	SetShearCenter (double my, double mz)
	"Shear reference": set the displacement of the shear center S respect to the reference beam line placed at centerline. More...

double	GetShearCenterY ()

double	GetShearCenterZ ()

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

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

Public Member Functions inherited from 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)

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	SetGshearModulus (double mG)
	Set G, the shear modulus.

double	GetGshearModulus () const

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

Public Attributes
double	alpha
	Rotation of Izz Iyy respect to reference section, centered on line x.

double	Cy
	Elastic center, respect to reference section (elastic center, tension center)

double	Cz

double	beta
	Rotation of shear reference section, centered on line x.

double	Sy
	Shear center, respect to reference section.

double	Sz

Public Attributes inherited from chrono::fea::ChElasticityCosseratSimple
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

◆ ChElasticityCosseratAdvanced()

chrono::fea::ChElasticityCosseratAdvanced::ChElasticityCosseratAdvanced	(	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,
		const double	malpha,
		const double	mCy,
		const double	mCz,
		const double	mbeta,
		const double	mSy,
		const double	mSz
	)

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
malpha	section rotation for which Iyy Izz are computed
mCy	Cy offset of elastic center about which Iyy Izz are computed
mCz	Cz offset of elastic center about which Iyy Izz are computed
mbeta	section rotation for which Ks_y Ks_z are computed
mSy	Sy offset of shear center
mSz	Sz offset of shear center

Member Function Documentation

◆ ComputeStiffnessMatrix()

void chrono::fea::ChElasticityCosseratAdvanced::ComputeStiffnessMatrix	(	ChMatrixNM< double, 6, 6 > &	K,
		const ChVector<> &	strain_e,
		const ChVector<> &	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::ChElasticityCosseratSimple.

◆ ComputeStress()

void chrono::fea::ChElasticityCosseratAdvanced::ComputeStress	(	ChVector<> &	stress_n,
		ChVector<> &	stress_m,
		const ChVector<> &	strain_e,
		const ChVector<> &	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

Reimplemented from chrono::fea::ChElasticityCosseratSimple.

◆ SetShearCenter()

void chrono::fea::ChElasticityCosseratAdvanced::SetShearCenter	(	double	my,
		double	mz
	)

inline

"Shear reference": set the displacement of the shear center S respect to the reference beam line placed at centerline.

For shapes like rectangles, rotated rectangles, etc., it corresponds to the elastic center C, but for "L" shaped or "U" shaped beams this is not always true, and the shear center accounts for torsion effects when a shear force is applied.

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

◆ ChElasticityCosseratAdvanced()

Member Function Documentation

◆ ComputeStiffnessMatrix()

◆ ComputeStress()

◆ SetShearCenter()