finite element for planar beam using Redundant Coordinate Method (RCM) More...

#include <1s_21_rcm.h>

Inheritance diagram for MBSimFlexibleBody::FiniteElement1s21RCM:

Public Member Functions
	FiniteElement1s21RCM (double l0_, double Arho_, double EA_, double EI_, const fmatvec::Vec &g_)
	constructor More...

	~FiniteElement1s21RCM () override=default

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 &qElement) override
	compute mass matrix More...

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

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

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

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

virtual double	computePhysicalStrain (const fmatvec::Vec &qElement)

double	computeElasticEnergy (const fmatvec::Vec &qElement) 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	getJacobianOfMotion (const fmatvec::Vec &qElement, double s)

fmatvec::Vec	computeAdditionalElementData (const fmatvec::Vec &qElement, const fmatvec::Vec &qpElement)

void	setCurlRadius (double R)

void	setMaterialDamping (double depsilons)

void	setLehrDamping (double D)

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

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

fmatvec::Mat	JGeneralizedInternal (const fmatvec::Vec &qElement, double s)
	return the JACOBIAN of translation and rotation with respect to generalised internal coordinates More...

fmatvec::Mat	JGeneralized (const fmatvec::Vec &qElement, double s)
	return the JACOBIAN of translation and rotation with respect to generalised global coordinates More...

fmatvec::Mat	JpGeneralized (const fmatvec::Vec &qElement, const fmatvec::Vec &qpElement, double s, double sp)
	return the derivative of the JACOBIAN of translation and rotation with respect to generalised global coordinates More...

fmatvec::Vec	ElementData (fmatvec::Vec qElement, fmatvec::Vec qpElement)
	return some additional element data More...

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...

Protected Attributes
double	l0
	length, line-density, longitudinal and bending stiffness

double	Arho

double	EA

double	EI

double	wss0
	predefined bending curvature

double	depsilon
	longitudinal damping

fmatvec::Vec	g
	gravitation

fmatvec::SymMat	M
	mass matrix

fmatvec::Vec	h
	right hand side

fmatvec::SqrMat	Dhq
	derivative of right hand side with respect to positions and velocities

fmatvec::SqrMat	Dhqp

fmatvec::SqrMat	Damp
	damping matrix

fmatvec::Vec	qLocal
	internal position and velocities as well as smooth right hand side

fmatvec::Vec	qpLocal

fmatvec::Vec	hIntermediate

fmatvec::SymMat	MLocal
	local mass matrix

fmatvec::SqrMat	Jeg
	transformation global -> internal coordinates coordinates and its derivative

fmatvec::SqrMat	Jegp

fmatvec::Vec	qElement_Old
	global and local state of the last time step

fmatvec::Vec	qpElement_Old

double	tol_comp
	tolerance for comparison of state with old state

Private Member Functions
void	BuildqLocal (const fmatvec::Vec &qGlobal, fmatvec::Vec &qLocal)
	calculates the local beam coordinates More...

void	BuildJacobi (const fmatvec::Vec &qLocal, fmatvec::SqrMat &Jeg)
	calculates the JACOBIAN of transformation More...

void	BuildJacobi (const fmatvec::Vec &qLocal, const fmatvec::Vec &qpIntern, fmatvec::SqrMat &Jeg, fmatvec::SqrMat &Jegp)
	calculates the JACOBIAN of transformation and its time derivative More...

fmatvec::Vec3	evalLocalPositions (const fmatvec::Vec &qLocal, double s)
	calculates Cartesian position More...

fmatvec::Vec3	evalLocalVelocities (const fmatvec::Vec &qLocal, const fmatvec::Vec &qpLocal, double s)
	calculates Cartesian velocity More...

fmatvec::Mat	hFullJacobi (const fmatvec::Vec &qElement, const fmatvec::Vec &qpElement, const fmatvec::Vec &qLocal, const fmatvec::Vec &qpLocal, const fmatvec::SqrMat &Jeg, const fmatvec::SqrMat &Jegp, const fmatvec::SymMat &MLocal, const fmatvec::Vec &hIntermediate)
	calculates JACOBIAN of implicit integration More...

	FiniteElement1s21RCM ()=default
	constructor is declared private

Private Attributes
double	l0h2
	powers of the beam length

double	l0h3

double	l0h4

double	l0h5

double	l0h7

double	l0h8

Detailed Description

finite element for planar beam using Redundant Coordinate Method (RCM)

Author: Roland Zander; Thorsten Schindler

Date: 2009-03-23 initial for kernel_dev; 2009-07-27 implicit integration (Thorsten Schindler); 2010-03-07 renamed ElementData to computeAdditionalElementData and wired to class (Roland Zander)

Todo:

transform computeState to Position / Velocity / Orientation / AngularVelocity

JacobianMinimalRepresentation

model based on Zander, R.; Ulbrich, H.: Reference-free mixed FE-MBS approach for beam structures with constraints, Journal of Nonlinear Dynamics, Kluwer Academic Publishers, 2005 Zander, R.; Ulbrich, H.: Impacts on beam structures: Interaction of wave propagationand global dynamics, IUTAM Symposium on Multiscale Problems in Multibody System Contacts Stuttgart, Germany, 2006 Zander, R.; Ulbrich, H.: Free plain motion of flexible beams in MBS - A comparison of models, III European Conference on Computational Mechanics Lisbon, Portugal, 2006

Constructor & Destructor Documentation

◆ FiniteElement1s21RCM()

MBSimFlexibleBody::FiniteElement1s21RCM::FiniteElement1s21RCM	(	double	l0_,
		double	Arho_,
		double	EA_,
		double	EI_,
		const fmatvec::Vec &	g_
	)

constructor

Parameters

undeformed	lenght of element
line-density	of beam
longitudinal	stiffness
bending	stiffness
vector	of gravitational acceleration

◆ ~FiniteElement1s21RCM()

MBSimFlexibleBody::FiniteElement1s21RCM::~FiniteElement1s21RCM ( )

overridedefault

\destructor

Member Function Documentation

◆ BuildJacobi() [1/2]

void MBSimFlexibleBody::FiniteElement1s21RCM::BuildJacobi	(	const fmatvec::Vec &	qLocal,
		const fmatvec::Vec &	qpIntern,
		fmatvec::SqrMat &	Jeg,
		fmatvec::SqrMat &	Jegp
	)

private

calculates the JACOBIAN of transformation and its time derivative

Parameters

local	beam positions
local	beam velocities
JACOBIAN	of transformation
time	derivative of JACOBIAN of transformation

◆ BuildJacobi() [2/2]

void MBSimFlexibleBody::FiniteElement1s21RCM::BuildJacobi	(	const fmatvec::Vec &	qLocal,
		fmatvec::SqrMat &	Jeg
	)

private

calculates the JACOBIAN of transformation

Parameters

local	beam coordinates
JACOBIAN	ot transformation

◆ BuildqLocal()

void MBSimFlexibleBody::FiniteElement1s21RCM::BuildqLocal	(	const fmatvec::Vec &	qGlobal,
		fmatvec::Vec &	qLocal
	)

private

calculates the local beam coordinates

Parameters

global	coordinates
local	coordinates

◆ computeAdditionalElementData()

Vec MBSimFlexibleBody::FiniteElement1s21RCM::computeAdditionalElementData	(	const fmatvec::Vec &	qElement,
		const fmatvec::Vec &	qpElement
	)

compute additional informations for element

◆ computedhdz()

void MBSimFlexibleBody::FiniteElement1s21RCM::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::FiniteElement1s21RCM::computeElasticEnergy ( const fmatvec::Vec & q )

overridevirtual

compute elastic energy

Parameters

generalised positions

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ computeGravitationalEnergy()

double MBSimFlexibleBody::FiniteElement1s21RCM::computeGravitationalEnergy ( const fmatvec::Vec & q )

overridevirtual

compute gravitational energy

Parameters

generalised positions

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ computeh()

void MBSimFlexibleBody::FiniteElement1s21RCM::computeh	(	const fmatvec::Vec &	q,
		const fmatvec::Vec &	u
	)

overridevirtual

compute smooth right hand side

Parameters

generalised	positions
generalised	velocities

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ computeKineticEnergy()

double MBSimFlexibleBody::FiniteElement1s21RCM::computeKineticEnergy	(	const fmatvec::Vec &	q,
		const fmatvec::Vec &	u
	)

overridevirtual

compute kinetic energy

Parameters

generalised	positions
generalised	velocities

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ computeM()

void MBSimFlexibleBody::FiniteElement1s21RCM::computeM ( const fmatvec::Vec & q )

overridevirtual

compute mass matrix

Parameters

generalised positions

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ ElementData()

fmatvec::Vec MBSimFlexibleBody::FiniteElement1s21RCM::ElementData	(	fmatvec::Vec	qElement,
		fmatvec::Vec	qpElement
	)

return some additional element data

Parameters

global	positions
global	velocities

Returns: elongation, elongational velocity, cog position, cog velocity, bending angle sum, bending velocity sum

◆ evalLocalPositions()

Vec3 MBSimFlexibleBody::FiniteElement1s21RCM::evalLocalPositions	(	const fmatvec::Vec &	qLocal,
		double	s
	)

private

calculates Cartesian position

Parameters

local	positions
contour	point

Returns: Cartesian position

◆ evalLocalVelocities()

Vec3 MBSimFlexibleBody::FiniteElement1s21RCM::evalLocalVelocities	(	const fmatvec::Vec &	qLocal,
		const fmatvec::Vec &	qpLocal,
		double	s
	)

private

calculates Cartesian velocity

Parameters

local	positions
local	velocities
contour	point

Returns: Cartesian velocity

◆ getdhdq()

const fmatvec::SqrMat & MBSimFlexibleBody::FiniteElement1s21RCM::getdhdq ( ) const

inlineoverridevirtual

Returns: Jacobian of implicit integration regarding position

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ getdhdu()

const fmatvec::SqrMat & MBSimFlexibleBody::FiniteElement1s21RCM::getdhdu ( ) const

inlineoverridevirtual

Returns: Jacobian of implicit integration regarding velocity

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ geth()

const fmatvec::Vec & MBSimFlexibleBody::FiniteElement1s21RCM::geth ( ) const

inlineoverridevirtual

Returns: smooth right hand side of discretization

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ getM()

const fmatvec::SymMat & MBSimFlexibleBody::FiniteElement1s21RCM::getM ( ) const

inlineoverridevirtual

Returns: mass matrix of discretization

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ getqSize()

int MBSimFlexibleBody::FiniteElement1s21RCM::getqSize ( ) const

inlineoverridevirtual

Returns: dimension of positions

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ getuSize()

int MBSimFlexibleBody::FiniteElement1s21RCM::getuSize ( ) const

inlineoverridevirtual

Returns: dimension of velocities

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ hFullJacobi()

Mat MBSimFlexibleBody::FiniteElement1s21RCM::hFullJacobi	(	const fmatvec::Vec &	qElement,
		const fmatvec::Vec &	qpElement,
		const fmatvec::Vec &	qLocal,
		const fmatvec::Vec &	qpLocal,
		const fmatvec::SqrMat &	Jeg,
		const fmatvec::SqrMat &	Jegp,
		const fmatvec::SymMat &	MLocal,
		const fmatvec::Vec &	hIntermediate
	)

private

calculates JACOBIAN of implicit integration

Parameters

global	positions
global	velocities
local	positions
local	velocities
JACOBIAN	of transformation
derivative	of JACOBIAN of transformation
local	mass matrix
local	right hand side

Returns: JACOBIAN for implicit integration

◆ JGeneralized()

Mat MBSimFlexibleBody::FiniteElement1s21RCM::JGeneralized	(	const fmatvec::Vec &	qElement,
		double	s
	)

return the JACOBIAN of translation and rotation with respect to generalised global coordinates

Parameters

generalised	coordinates
contour	point

Returns: JACOBIAN of translation and rotation with respect to generalised global coordinates

◆ JGeneralizedInternal()

Mat MBSimFlexibleBody::FiniteElement1s21RCM::JGeneralizedInternal	(	const fmatvec::Vec &	qElement,
		double	s
	)

return the JACOBIAN of translation and rotation with respect to generalised internal coordinates

Parameters

generalised	coordinates
contour	point

Returns: JACOBIAN of translation and rotation with respect to generalised internal coordinates

◆ JpGeneralized()

Mat MBSimFlexibleBody::FiniteElement1s21RCM::JpGeneralized	(	const fmatvec::Vec &	qElement,
		const fmatvec::Vec &	qpElement,
		double	s,
		double	sp
	)

return the derivative of the JACOBIAN of translation and rotation with respect to generalised global coordinates

Parameters

generalised	coordinates
generalised	velocities
contour	point
contour	point derivative

Returns: derivative of JACOBIAN of translation and rotation with respect to generalised global coordinates

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

/mbsim-env/mbsim/modules/mbsimFlexibleBody/mbsimFlexibleBody/flexible_body/fe/1s_21_rcm.h
/mbsim-env/mbsim/modules/mbsimFlexibleBody/mbsimFlexibleBody/flexible_body/fe/1s_21_rcm.cc

Public Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ FiniteElement1s21RCM()

◆ ~FiniteElement1s21RCM()

Member Function Documentation

◆ BuildJacobi() [1/2]

◆ BuildJacobi() [2/2]

◆ BuildqLocal()

◆ computeAdditionalElementData()

◆ computedhdz()

◆ computeElasticEnergy()

◆ computeGravitationalEnergy()

◆ computeh()

◆ computeKineticEnergy()

◆ computeM()

◆ ElementData()

◆ evalLocalPositions()

◆ evalLocalVelocities()

◆ getdhdq()

◆ getdhdu()

◆ geth()

◆ getM()

◆ getqSize()

◆ getuSize()

◆ hFullJacobi()

◆ JGeneralized()

◆ JGeneralizedInternal()

◆ JpGeneralized()