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

#include <1s_33_ancf.h>

Inheritance diagram for MBSimFlexibleBody::FiniteElement1s33ANCF:

Public Member Functions
	FiniteElement1s33ANCF (double sl0, double srho, double sE, double sG, double sA, double sI0, double sI1, double sI2, const fmatvec::Vec &sg)
	constructor More...

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	computeJacobianOfMotion (const fmatvec::Vec &qElement, double s)

void	setCurlRadius (double R1, double R2)

void	setMaterialDamping (double depsilons)

void	initM ()
	calculate constant mass matrix

fmatvec::Vec	LocateBalken (const fmatvec::Vec &qElement, double s)
	return the position and Cardan angles at a contour point More...

fmatvec::Vec	StateBalken (const fmatvec::Vec &qElement, const fmatvec::Vec &qpElement, double s)
	return the state including Cardan angles at a contour point 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::Vec3	getTangent (const fmatvec::Vec &qElement, double s)
	returns the tangent More...

fmatvec::Vec3	getNormal (const fmatvec::Vec &qElement, double s)
	returns the normal More...

fmatvec::Vec3	getBinormal (const fmatvec::Vec &qElement, double s)
	returns the binormal 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 Member Functions
	FiniteElement1s33ANCF (const FiniteElement1s33ANCF &)
	copy constructor is declared private

FiniteElement1s33ANCF &	operator= (const FiniteElement1s33ANCF &)
	assignment operator is declared private

Private Attributes
double	l0
	beam element length

double	rho
	density

double	E
	Young's modulus.

double	G
	shear modulus

double	A
	cross-secion area

double	I0
	polar moment of inertia

double	I1
	area moment of inertia

double	I2
	area moment of inertia

double	wss01
	predefined bending curvature

double	wss02
	predefined bending curvature

double	depsilon
	longitudinal damping

fmatvec::Vec	g
	gravitation

fmatvec::SymMat	M
	mass matrix

fmatvec::Vec	h
	right hand side

fmatvec::SqrMat	Damp
	damping matrix

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 spatial beam using Absolute Nodal Coordinate Formulation (ANCF)

cable element with no explicit torsion, i.e. angular velocity and Jacobian of rotation depend only on two bending angles

Author: Thorsten Schindler

Date: 2014-03-20 initial commit

model based on DOMBROWSKI, S.: Analysis of Large Flexible Body Deformation in Multibody Systems Using Absolute Coordinates. Multibody System Dynamics (2002)

Constructor & Destructor Documentation

◆ FiniteElement1s33ANCF()

MBSimFlexibleBody::FiniteElement1s33ANCF::FiniteElement1s33ANCF	(	double	sl0,
		double	srho,
		double	sE,
		double	sG,
		double	sA,
		double	sI0,
		double	sI1,
		double	sI2,
		const fmatvec::Vec &	sg
	)

explicit

constructor

Parameters

undeformed	lenght of element
cross-section	area
density	of beam
Young's	modulus
shear	modulus
polar	moment of inertia
area	moment of inertia
area	moment of inertia
vector	of gravitational acceleration

Member Function Documentation

◆ computedhdz()

void MBSimFlexibleBody::FiniteElement1s33ANCF::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::FiniteElement1s33ANCF::computeElasticEnergy ( const fmatvec::Vec & q )

overridevirtual

compute elastic energy

Parameters

generalised positions

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ computeGravitationalEnergy()

double MBSimFlexibleBody::FiniteElement1s33ANCF::computeGravitationalEnergy ( const fmatvec::Vec & q )

overridevirtual

compute gravitational energy

Parameters

generalised positions

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ computeh()

void MBSimFlexibleBody::FiniteElement1s33ANCF::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::FiniteElement1s33ANCF::computeKineticEnergy	(	const fmatvec::Vec &	q,
		const fmatvec::Vec &	u
	)

overridevirtual

compute kinetic energy

Parameters

generalised	positions
generalised	velocities

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ computeM()

void MBSimFlexibleBody::FiniteElement1s33ANCF::computeM ( const fmatvec::Vec & q )

overridevirtual

compute mass matrix

Parameters

generalised positions

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ getBinormal()

Vec3 MBSimFlexibleBody::FiniteElement1s33ANCF::getBinormal	(	const fmatvec::Vec &	qElement,
		double	s
	)

returns the binormal

Parameters

generalised	coordinates
contour	point

Returns: binormal

◆ getdhdq()

const fmatvec::SqrMat & MBSimFlexibleBody::FiniteElement1s33ANCF::getdhdq ( ) const

inlineoverridevirtual

Returns: Jacobian of implicit integration regarding position

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ getdhdu()

const fmatvec::SqrMat & MBSimFlexibleBody::FiniteElement1s33ANCF::getdhdu ( ) const

inlineoverridevirtual

Returns: Jacobian of implicit integration regarding velocity

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ geth()

const fmatvec::Vec & MBSimFlexibleBody::FiniteElement1s33ANCF::geth ( ) const

inlineoverridevirtual

Returns: smooth right hand side of discretization

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ getM()

const fmatvec::SymMat & MBSimFlexibleBody::FiniteElement1s33ANCF::getM ( ) const

inlineoverridevirtual

Returns: mass matrix of discretization

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ getNormal()

Vec3 MBSimFlexibleBody::FiniteElement1s33ANCF::getNormal	(	const fmatvec::Vec &	qElement,
		double	s
	)

returns the normal

Parameters

generalised	coordinates
contour	point

Returns: normal

◆ getqSize()

int MBSimFlexibleBody::FiniteElement1s33ANCF::getqSize ( ) const

inlineoverridevirtual

Returns: dimension of positions

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ getTangent()

Vec3 MBSimFlexibleBody::FiniteElement1s33ANCF::getTangent	(	const fmatvec::Vec &	qElement,
		double	s
	)

returns the tangent

Parameters

generalised	coordinates
contour	point

Returns: tangent

◆ getuSize()

int MBSimFlexibleBody::FiniteElement1s33ANCF::getuSize ( ) const

inlineoverridevirtual

Returns: dimension of velocities

Implements MBSimFlexibleBody::DiscretizationInterface.

◆ GlobalShapeFunctions()

Mat MBSimFlexibleBody::FiniteElement1s33ANCF::GlobalShapeFunctions ( double s )

return the matrix of global shape functions

Parameters

contour point

Returns: matrix of global shape functions

◆ JGeneralized()

Mat MBSimFlexibleBody::FiniteElement1s33ANCF::JGeneralized	(	const fmatvec::Vec &	qElement,
		double	s
	)

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

Parameters

generalised	coordinates
contour	point

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

◆ LocateBalken()

Vec MBSimFlexibleBody::FiniteElement1s33ANCF::LocateBalken	(	const fmatvec::Vec &	qElement,
		double	s
	)

return the position and Cardan angles at a contour point

Parameters

generalised	coordinates
contour	point

Returns: position and Cardan angles

◆ StateBalken()

Vec MBSimFlexibleBody::FiniteElement1s33ANCF::StateBalken	(	const fmatvec::Vec &	qElement,
		const fmatvec::Vec &	qpElement,
		double	s
	)

return the state including Cardan angles at a contour point

Parameters

generalised	positions
generalised	velocities
contour	point

Returns: state including Cardan angles

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

/mbsim-env/mbsim/modules/mbsimFlexibleBody/mbsimFlexibleBody/flexible_body/fe/1s_33_ancf.h
/mbsim-env/mbsim/modules/mbsimFlexibleBody/mbsimFlexibleBody/flexible_body/fe/1s_33_ancf.cc

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ FiniteElement1s33ANCF()

Member Function Documentation

◆ computedhdz()

◆ computeElasticEnergy()

◆ computeGravitationalEnergy()

◆ computeh()

◆ computeKineticEnergy()

◆ computeM()

◆ getBinormal()

◆ getdhdq()

◆ getdhdu()

◆ geth()

◆ getM()

◆ getNormal()

◆ getqSize()

◆ getTangent()

◆ getuSize()

◆ GlobalShapeFunctions()

◆ JGeneralized()

◆ LocateBalken()

◆ StateBalken()