Description

Advanced linear elasticity for a Cosserat section, not assuming homogeneous elasticity.

This is the case where one uses a FEA preprocessor to compute the rigidity of a complex beam made with multi-layered reinforcements with different elasticity - in such a case you could not use ChElasticityCosseratAdvanced because you do not have a single E or G, but you rather have collective values of bending/shear/axial rigidities. This class allows using these values directly, bypassing any knowledge of area, Izz Iyy, E young modulus, etc. 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::ChElasticityCosseratAdvancedGeneric:

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Collaboration diagram for chrono::fea::ChElasticityCosseratAdvancedGeneric:

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Public Member Functions
	ChElasticityCosseratAdvancedGeneric (const double mAx, const double mTxx, const double mByy, const double mBzz, const double mHyy, const double mHzz, const double malpha, const double mCy, const double mCz, const double mbeta, const double mSy, const double mSz)

virtual void	SetAxialRigidity (const double mv)
	Sets the axial rigidity, usually A*E for uniform elasticity, but for nonuniform elasticity here you can put a value ad-hoc from a preprocessor.

virtual void	SetXtorsionRigidity (const double mv)
	Sets the torsion rigidity, for torsion about X axis, at elastic center, usually J*G for uniform elasticity, but for nonuniform elasticity here you can put a value ad-hoc from a preprocessor.

virtual void	SetYbendingRigidity (const double mv)
	Sets the bending rigidity, for bending about Y axis, at elastic center, usually Iyy*E for uniform elasticity, but for nonuniform elasticity here you can put a value ad-hoc from a preprocessor.

virtual void	SetZbendingRigidity (const double mv)
	Sets the bending rigidity, for bending about Z axis, at elastic center, usually Izz*E for uniform elasticity, but for nonuniform elasticity here you can put a value ad-hoc from a preprocessor.

virtual void	SetYshearRigidity (const double mv)
	Sets the shear rigidity, for shear about Y axis, at shear center, usually AG(Timoshenko correction factor) for uniform elasticity, but for nonuniform elasticity here you can put a value ad-hoc from a preprocessor.

virtual void	SetZshearRigidity (const double mv)
	Sets the shear rigidity, for shear about Z axis, at shear center, usually AG(Timoshenko correction factor) for uniform elasticity, but for nonuniform elasticity here you can put a value ad-hoc from a preprocessor.

void	SetSectionRotation (double ma)
	Set the rotation in [rad] of the Y Z axes for which the YbendingRigidity and ZbendingRigidity values are defined.

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)
	Set the rotation in [rad] of the Y Z axes for which the YshearRigidity and ZshearRigidity values are defined.

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...

Additional Inherited Members
Public Attributes inherited from chrono::fea::ChElasticityCosserat
ChBeamSectionCosserat *	section

Constructor & Destructor Documentation

◆ ChElasticityCosseratAdvancedGeneric()

chrono::fea::ChElasticityCosseratAdvancedGeneric::ChElasticityCosseratAdvancedGeneric	(	const double	mAx,
		const double	mTxx,
		const double	mByy,
		const double	mBzz,
		const double	mHyy,
		const double	mHzz,
		const double	malpha,
		const double	mCy,
		const double	mCz,
		const double	mbeta,
		const double	mSy,
		const double	mSz
	)

inline

Parameters

mAx	axial rigidity
mTxx	torsion rigidity
mByy	bending regidity on Y of reference at elastic center
mBzz	bending rigidity on Z of reference at elastic center
mHyy	shear rigidity on Y of reference at shear center
mHzz	shear rigidity on Y of reference at shear center
malpha	rotation of reference at elastic center, for bending effects [rad]
mCy	elastic center y displacement respect to centerline
mCz	elastic center z displacement respect to centerline
mbeta	rotation of reference at shear center, for shear effects [rad]
mSy	shear center y displacement respect to centerline
mSz	shear center z displacement respect to centerline

Member Function Documentation

◆ ComputeStiffnessMatrix()

void chrono::fea::ChElasticityCosseratAdvancedGeneric::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::ChElasticityCosserat.

◆ ComputeStress()

void chrono::fea::ChElasticityCosseratAdvancedGeneric::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

Implements chrono::fea::ChElasticityCosserat.

◆ SetShearCenter()

void chrono::fea::ChElasticityCosseratAdvancedGeneric::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

Additional Inherited Members

Constructor & Destructor Documentation

◆ ChElasticityCosseratAdvancedGeneric()

Member Function Documentation

◆ ComputeStiffnessMatrix()

◆ ComputeStress()

◆ SetShearCenter()