finite element for spatial beam using Cosserat model More...

#include <1s_33_cosserat_translation.h>

Inheritance diagram for MBSimFlexibleBody::FiniteElement1s33CosseratTranslation:

Public Member Functions
	FiniteElement1s33CosseratTranslation (double l0_, double rho_, double A_, double E_, double G_, double I1_, double I2_, double I0_, const fmatvec::Vec &g_, CardanPtr ag_)
	constructor More...

	~FiniteElement1s33CosseratTranslation () override
	destructor

const fmatvec::SymMat &	getM () const override

const fmatvec::Vec &	geth () const override

const fmatvec::SqrMat &	getdhdq () const override

const fmatvec::SqrMat &	getdhdu () const override

int	getqSize () const override

int	getuSize () const override

void	computeM (const fmatvec::Vec &qG) override
	compute mass matrix More...

void	computeh (const fmatvec::Vec &qG, const fmatvec::Vec &qGt) override
	compute smooth right hand side More...

void	computedhdz (const fmatvec::Vec &qG, const fmatvec::Vec &qGt) override
	compute Jacobian for implicit integration More...

double	computeKineticEnergy (const fmatvec::Vec &qG, const fmatvec::Vec &qGt) override
	compute kinetic energy More...

double	computeGravitationalEnergy (const fmatvec::Vec &qG) override
	compute gravitational energy More...

double	computeElasticEnergy (const fmatvec::Vec &qG) override
	compute elastic energy More...

virtual fmatvec::Vec3	getPosition (const fmatvec::Vec &qElement, double s)

virtual fmatvec::SqrMat3	getOrientation (const fmatvec::Vec &qElement, double s)

virtual fmatvec::Vec3	getVelocity (const fmatvec::Vec &qElement, const fmatvec::Vec &qpElement, double s)

virtual fmatvec::Vec3	getAngularVelocity (const fmatvec::Vec &qElement, const fmatvec::Vec &qpElement, double s)

virtual fmatvec::Mat	computeJacobianOfMotion (const fmatvec::Vec &qG, double s)

void	setMaterialDamping (double cEps0D_, double cEps1D_, double cEps2D_)

void	setShearCorrectionFactors (double sigma1_, double sigma2_)

double	getl0 () const

const fmatvec::Vec &	computeStateTranslation (const fmatvec::Vec &qG, const fmatvec::Vec &qGt, double s)
	compute state of finite element More...

fmatvec::Mat	computeJXqG (const fmatvec::Vec &qG, double x)
	compute JACOBIAN of contact description in global coordinates More...

void	initM ()
	initialize translational part of mass matrix

Public Member Functions inherited from MBSimFlexibleBody::DiscretizationInterface
	DiscretizationInterface ()=default
	constructor

virtual	~DiscretizationInterface ()=default
	destructor

virtual const fmatvec::SymMat &	getM () const =0

virtual const fmatvec::Vec &	geth () const =0

virtual const fmatvec::SqrMat &	getdhdq () const =0

virtual const fmatvec::SqrMat &	getdhdu () const =0

virtual int	getqSize () const =0

virtual int	getuSize () const =0

virtual void	computeM (const fmatvec::Vec &q)=0
	compute mass matrix More...

virtual void	computeh (const fmatvec::Vec &q, const fmatvec::Vec &u)=0
	compute smooth right hand side More...

virtual void	computedhdz (const fmatvec::Vec &q, const fmatvec::Vec &u)=0
	compute Jacobian for implicit integration More...

virtual double	computeKineticEnergy (const fmatvec::Vec &q, const fmatvec::Vec &u)=0
	compute kinetic energy More...

virtual double	computeGravitationalEnergy (const fmatvec::Vec &q)=0
	compute gravitational energy More...

virtual double	computeElasticEnergy (const fmatvec::Vec &q)=0
	compute elastic energy More...

Private Member Functions
	FiniteElement1s33CosseratTranslation (const FiniteElement1s33CosseratTranslation &)

FiniteElement1s33CosseratTranslation &	operator= (const FiniteElement1s33CosseratTranslation &)

Private Attributes
double	l0
	length of finite element

double	rho
	density

double	A
	cross sectional area

double	E
	Young's modulus.

double	G
	shear modulus

double	I1
	geometrical moment of inertia

double	I2

double	I0

fmatvec::Vec	g
	gravitation

double	cEps0D
	strain damping

double	cEps1D

double	cEps2D

double	sigma1
	shear correction factors

double	sigma2

fmatvec::SymMat	M
	global system description

fmatvec::Vec	h

fmatvec::SqrMat	dhdq
	matrices for implicit integration

fmatvec::SqrMat	dhdu

fmatvec::Vec	X
	state at Lagrangian coordinate

CardanPtr	ag
	Cardan-object.

Detailed Description

finite element for spatial beam using Cosserat model

Author: Thorsten Schindler; Christian Käsbauer; Thomas Cebulla

Date: 2011-09-10 initial commit (Thorsten Schindler) \data 2011-10-08 basics derived and included (Thorsten Schindler); 2011-10-13 strain rhs corrected and added, strain energy calculated (Thorsten Schindler); 2011-10-13 gyroscopic terms added (Christian Kaesbauer, Thorsten Schindler); 2011-10-15 strain dissipation in rhs (Christian Kaesbauer, Thorsten Schindler)

Todo:

contact Jacobian TODO

computeState only in FlexibleBody TODO

implicit integration TODO

Cosserat model based on H. Lang, J. Linn, M. Arnold: Multi-body dynamics simulation of geometrically exact Cosserat rods but with

Kirchhoff assumption (-> less stiff)
Cardan parametrisation (-> less problems with condition and drift for quaternion dae system)
piecewise constant Darboux vector with evaluation according to I. Romero: The interpolation of rotations and its application to finite element models of geometrically exact beams

Constructor & Destructor Documentation

◆ FiniteElement1s33CosseratTranslation()

MBSimFlexibleBody::FiniteElement1s33CosseratTranslation::FiniteElement1s33CosseratTranslation	(	double	l0_,
		double	rho_,
		double	A_,
		double	E_,
		double	G_,
		double	I1_,
		double	I2_,
		double	I0_,
		const fmatvec::Vec &	g_,
		CardanPtr	ag_
	)

constructor

Parameters

length	of finite element
density
cross-sectional	area
Young's	modulus
shear	modulus
first	area moment of inertia
second	area moment of inertia
torsional	moment of inertia
acceleration	of gravity
cardan	object

Member Function Documentation

◆ computedhdz()

void MBSimFlexibleBody::FiniteElement1s33CosseratTranslation::computedhdz	(	const fmatvec::Vec &	q,
		const fmatvec::Vec &	u
	)

overridevirtual

compute Jacobian for implicit integration

Parameters

generalised	positions
generalised	velocities

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ computeElasticEnergy()

double MBSimFlexibleBody::FiniteElement1s33CosseratTranslation::computeElasticEnergy ( const fmatvec::Vec & q )

overridevirtual

compute elastic energy

Parameters

generalised positions

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ computeGravitationalEnergy()

double MBSimFlexibleBody::FiniteElement1s33CosseratTranslation::computeGravitationalEnergy ( const fmatvec::Vec & q )

overridevirtual

compute gravitational energy

Parameters

generalised positions

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ computeh()

void MBSimFlexibleBody::FiniteElement1s33CosseratTranslation::computeh	(	const fmatvec::Vec &	q,
		const fmatvec::Vec &	u
	)

overridevirtual

compute smooth right hand side

Parameters

generalised	positions
generalised	velocities

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ computeJXqG()

Mat MBSimFlexibleBody::FiniteElement1s33CosseratTranslation::computeJXqG	(	const fmatvec::Vec &	qG,
		double	x
	)

compute JACOBIAN of contact description in global coordinates

Parameters

global	coordinates
LAGRANGIAN	parameter

◆ computeKineticEnergy()

double MBSimFlexibleBody::FiniteElement1s33CosseratTranslation::computeKineticEnergy	(	const fmatvec::Vec &	q,
		const fmatvec::Vec &	u
	)

overridevirtual

compute kinetic energy

Parameters

generalised	positions
generalised	velocities

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ computeM()

void MBSimFlexibleBody::FiniteElement1s33CosseratTranslation::computeM ( const fmatvec::Vec & q )

overridevirtual

compute mass matrix

Parameters

generalised positions

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ computeStateTranslation()

const Vec & MBSimFlexibleBody::FiniteElement1s33CosseratTranslation::computeStateTranslation	(	const fmatvec::Vec &	qG,
		const fmatvec::Vec &	qGt,
		double	s
	)

compute state of finite element

Parameters

global	coordinates
global	velocities
LAGRANGIAN	parameter in [0,l0]

◆ getdhdq()

const fmatvec::SqrMat & MBSimFlexibleBody::FiniteElement1s33CosseratTranslation::getdhdq ( ) const

inlineoverridevirtual

Returns: Jacobian of implicit integration regarding position

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ getdhdu()

const fmatvec::SqrMat & MBSimFlexibleBody::FiniteElement1s33CosseratTranslation::getdhdu ( ) const

inlineoverridevirtual

Returns: Jacobian of implicit integration regarding velocity

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ geth()

const fmatvec::Vec & MBSimFlexibleBody::FiniteElement1s33CosseratTranslation::geth ( ) const

inlineoverridevirtual

Returns: smooth right hand side of discretization

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ getM()

const fmatvec::SymMat & MBSimFlexibleBody::FiniteElement1s33CosseratTranslation::getM ( ) const

inlineoverridevirtual

Returns: mass matrix of discretization

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ getqSize()

int MBSimFlexibleBody::FiniteElement1s33CosseratTranslation::getqSize ( ) const

inlineoverridevirtual

Returns: dimension of positions

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ getuSize()

int MBSimFlexibleBody::FiniteElement1s33CosseratTranslation::getuSize ( ) const

inlineoverridevirtual

Returns: dimension of velocities

Implements MBSimFlexibleBody::DiscretizationInterface.

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

/mbsim-env/mbsim/modules/mbsimFlexibleBody/mbsimFlexibleBody/flexible_body/fe/1s_33_cosserat_translation.h
/mbsim-env/mbsim/modules/mbsimFlexibleBody/mbsimFlexibleBody/flexible_body/fe/1s_33_cosserat_translation.cc

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ FiniteElement1s33CosseratTranslation()

Member Function Documentation

◆ computedhdz()

◆ computeElasticEnergy()

◆ computeGravitationalEnergy()

◆ computeh()

◆ computeJXqG()

◆ computeKineticEnergy()

◆ computeM()

◆ computeStateTranslation()

◆ getdhdq()

◆ getdhdu()

◆ geth()

◆ getM()

◆ getqSize()

◆ getuSize()