finite element for planar beam using Absolute Nodal Coordinate Formulation (ANCF) More...

#include <1s_21_ancf.h>

Inheritance diagram for MBSimFlexibleBody::FiniteElement1s21ANCF:

Public Member Functions
	FiniteElement1s21ANCF (double sl0, double sArho, double sEA, double sEI, const fmatvec::Vec &sg, bool sEuler=false, double sv0=0.)
	constructor More...

	~FiniteElement1s21ANCF () override

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...

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)

void	setCurlRadius (double R)

void	setMaterialDamping (double depsilon_, double dkappa_)

void	initM ()
	calculate constant mass matrix

fmatvec::Vec	LocateBalken (const fmatvec::Vec &qElement, double s)
	return the planar position and angle at a contour point (Lagrange/Euler) More...

fmatvec::Vec	StateBalken (const fmatvec::Vec &qElement, const fmatvec::Vec &qpElement, double s)
	return the planar state at a contour point (Lagrange/Euler) More...

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

fmatvec::Mat	GlobalShapeFunctions (double s)
	return the matrix of global shape functions More...

fmatvec::Mat	GlobalShapeFunctions_1stDerivative (double s)
	return 1st derivative of the matrix of global shape functions More...

fmatvec::Vec3	getTangent (const fmatvec::Vec &qElement, double s)
	returns the tangent 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...

Private Attributes
double	l0
	beam element length

double	Arho
	line-density

double	EA
	longitudinal stiffness

double	EI
	bending stiffness

bool	Euler
	Euler perspective: true if set.

double	v0
	Euler perspective: constant longitudinal velocity.

double	wss0
	predefined bending curvature

double	depsilon
	longitudinal damping

double	dkappa
	curvature 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

fmatvec::SqrMat	Dhqp
	derivative of right hand side with respect to velocities

Detailed Description

finite element for planar beam using Absolute Nodal Coordinate Formulation (ANCF)

Author: Roland Zander; Thorsten Schindler

Date: 2014-02-27 basic revision; 2014-03-23 damping added; 2014-05-09 Euler perspective added as an option

model based on SHABANA, A. A.: Computer Implementation of the Absolute Nodal Coordinate Formulation for Flexible Multibody Dynamics. In: Nonlinear Dynamics 16 (1998), S. 293-306 SHABANA, A. A.: Definition of the Slopes and the Finite Element Absolute Nodal Coordinate Formulation. In: Nonlinear Dynamics 1 (1997), S. 339-348 SHABANE, A. A.: Dynamics of Multibody Systems. Cambridge University Press (2005)

Constructor & Destructor Documentation

◆ FiniteElement1s21ANCF()

MBSimFlexibleBody::FiniteElement1s21ANCF::FiniteElement1s21ANCF	(	double	sl0,
		double	sArho,
		double	sEA,
		double	sEI,
		const fmatvec::Vec &	sg,
		bool	sEuler = `false`,
		double	sv0 = `0.`
	)

explicit

constructor

Parameters

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

◆ ~FiniteElement1s21ANCF()

MBSimFlexibleBody::FiniteElement1s21ANCF::~FiniteElement1s21ANCF ( )

overridedefault

\destructor

Member Function Documentation

◆ computedhdz()

void MBSimFlexibleBody::FiniteElement1s21ANCF::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::FiniteElement1s21ANCF::computeElasticEnergy ( const fmatvec::Vec & q )

overridevirtual

compute elastic energy

Parameters

generalised positions

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ computeGravitationalEnergy()

double MBSimFlexibleBody::FiniteElement1s21ANCF::computeGravitationalEnergy ( const fmatvec::Vec & q )

overridevirtual

compute gravitational energy

Parameters

generalised positions

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ computeh()

void MBSimFlexibleBody::FiniteElement1s21ANCF::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::FiniteElement1s21ANCF::computeKineticEnergy	(	const fmatvec::Vec &	q,
		const fmatvec::Vec &	u
	)

overridevirtual

compute kinetic energy

Parameters

generalised	positions
generalised	velocities

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ computeM()

void MBSimFlexibleBody::FiniteElement1s21ANCF::computeM ( const fmatvec::Vec & q )

overridevirtual

compute mass matrix

Parameters

generalised positions

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ getdhdq()

const fmatvec::SqrMat & MBSimFlexibleBody::FiniteElement1s21ANCF::getdhdq ( ) const

inlineoverridevirtual

Returns: Jacobian of implicit integration regarding position

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ getdhdu()

const fmatvec::SqrMat & MBSimFlexibleBody::FiniteElement1s21ANCF::getdhdu ( ) const

inlineoverridevirtual

Returns: Jacobian of implicit integration regarding velocity

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ geth()

const fmatvec::Vec & MBSimFlexibleBody::FiniteElement1s21ANCF::geth ( ) const

inlineoverridevirtual

Returns: smooth right hand side of discretization

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ getM()

const fmatvec::SymMat & MBSimFlexibleBody::FiniteElement1s21ANCF::getM ( ) const

inlineoverridevirtual

Returns: mass matrix of discretization

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ getqSize()

int MBSimFlexibleBody::FiniteElement1s21ANCF::getqSize ( ) const

inlineoverridevirtual

Returns: dimension of positions

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ getTangent()

Vec3 MBSimFlexibleBody::FiniteElement1s21ANCF::getTangent	(	const fmatvec::Vec &	qElement,
		double	s
	)

returns the tangent

Parameters

generalised	coordinates
contour	point (Lagrange/Euler)

Returns: tangent

◆ getuSize()

int MBSimFlexibleBody::FiniteElement1s21ANCF::getuSize ( ) const

inlineoverridevirtual

Returns: dimension of velocities

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ GlobalShapeFunctions()

Mat MBSimFlexibleBody::FiniteElement1s21ANCF::GlobalShapeFunctions ( double s )

return the matrix of global shape functions

Parameters

contour point (Lagrange/Euler)

Returns: matrix of global shape functions

◆ GlobalShapeFunctions_1stDerivative()

Mat MBSimFlexibleBody::FiniteElement1s21ANCF::GlobalShapeFunctions_1stDerivative ( double s )

return 1st derivative of the matrix of global shape functions

Parameters

contour point (Lagrange/Euler)

Returns: 1st derivative of the matrix of global shape functions

◆ JGeneralized()

Mat MBSimFlexibleBody::FiniteElement1s21ANCF::JGeneralized	(	const fmatvec::Vec &	qElement,
		double	s
	)

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

Parameters

generalised	coordinates
contour	point (Lagrange/Euler)

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

◆ LocateBalken()

Vec MBSimFlexibleBody::FiniteElement1s21ANCF::LocateBalken	(	const fmatvec::Vec &	qElement,
		double	s
	)

return the planar position and angle at a contour point (Lagrange/Euler)

Parameters

generalised	coordinates
contour	point (Lagrange/Euler)

Returns: planar position and angle

◆ StateBalken()

Vec MBSimFlexibleBody::FiniteElement1s21ANCF::StateBalken	(	const fmatvec::Vec &	qElement,
		const fmatvec::Vec &	qpElement,
		double	s
	)

return the planar state at a contour point (Lagrange/Euler)

Parameters

generalised	positions
generalised	velocities
contour	point (Lagrange/Euler)

Returns: planar state

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

/mbsim-env/mbsim/modules/mbsimFlexibleBody/mbsimFlexibleBody/flexible_body/fe/1s_21_ancf.h
/mbsim-env/mbsim/modules/mbsimFlexibleBody/mbsimFlexibleBody/flexible_body/fe/1s_21_ancf.cc

Public Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ FiniteElement1s21ANCF()

◆ ~FiniteElement1s21ANCF()

Member Function Documentation

◆ computedhdz()

◆ computeElasticEnergy()

◆ computeGravitationalEnergy()

◆ computeh()

◆ computeKineticEnergy()

◆ computeM()

◆ getdhdq()

◆ getdhdu()

◆ geth()

◆ getM()

◆ getqSize()

◆ getTangent()

◆ getuSize()

◆ GlobalShapeFunctions()

◆ GlobalShapeFunctions_1stDerivative()

◆ JGeneralized()

◆ LocateBalken()

◆ StateBalken()