BeamGeometry Class Reference

Base class for discrete beam geometries. More...

#include <BeamGeometry.hpp>

Inherited by BeamGeometryCuboid.

Public Member Functions
	BeamGeometry (double L, const std::vector< double > &Exvec, const std::vector< double > &vxvec, const std::vector< double > &rhovec, const rw::math::Transform3D<> &wTb, const rw::math::Vector3D<> &G)
	Constructor for the BeamGeometry class. More...
void	setTransform (const rw::math::Transform3D<> &T)
	Sets the homogeneous transform of the beam. More...
rw::math::Transform3D	getTransform (void) const
	Retrieves the world to beam base transform of the beam. More...
void	setG (const rw::math::Vector3D<> &G)
	sets the directional vector of gravity More...
rw::math::Vector3D	getG (void) const
	retrieves the directional vector of gravity More...
Methods for retrieving material parameters
double	Ex (const int i) const
	returns the value of Young's modulus at x = i * h More...
double	vx (const int i) const
	returns the value of Poisson's ratio at x = i * h More...
double	rho (const int i) const
	returns the value of the mass density at x = i * h More...
double	kappa (const int i) const
	returns the kappa coefficient at x = i * h More...
double	g1 (void) const
	returns the x-component of vector of gravity for the current configuration of the beam More...
double	g2 (void) const
	returns the y-component of vector of gravity for the current configuration of the beam More...

Integrals to be evaluate by derived classes
virtual double	b0 (const int i) const =0
	Evaluate the \(b_0\) integral. More...
virtual double	b1 (const int i) const =0
	Evaluate the \(b_1\) integral. More...
virtual double	c2 (const int i) const =0
	Evaluate the \( c_2 \) integral. More...
virtual double	c3 (const int i) const =0
	Evaluate the \( c_3 \) integral. More...
virtual double	c4 (const int i) const =0
	Evaluate the \( c_4 \) integral. More...
virtual double	B0 (const int i) const =0
	evaluate the \( B_0 \) constant More...
double	get_a (void) const
	return left boundary of domain More...
double	get_b (void) const
	return right boundary of domain More...
double	get_h (void) const
	return stepsize More...
double	getL (void) const
	return length of beam More...
int	getM (void) const
	return number of cross sections in beam More...
std::ostream &	operator<< (std::ostream &out, const BeamGeometry &obj)

Detailed Description

Base class for discrete beam geometries.

Constructor & Destructor Documentation

BeamGeometry()

BeamGeometry	(	double	L,
		const std::vector< double > &	Exvec,
		const std::vector< double > &	vxvec,
		const std::vector< double > &	rhovec,
		const rw::math::Transform3D<> &	wTb,
		const rw::math::Vector3D<> &	G
	)

Constructor for the BeamGeometry class.

Note

For a Mod Russel beam in a typical coordinate frame, the vector of gravitiy G should be defined as to make the gravitational potential energy increase for increased values of y, e.g. \( G=(0.0, 9.82, 0.0) \)

Parameters

L	length of object
Exvec	vector of Young's modulus for each cross beam cros section, in MPa
vxvec	vector of Poisson's ratio for each cross beam cros section
rhovec	vector of mass density for each cross beam cros section, in kg/mm^3
wTb	world to base of beam transform
G	vector of gravity, m/s^2

Member Function Documentation

b0()

virtual double b0 ( const int  i ) const

pure virtual

Evaluate the \(b_0\) integral.

Evaluate the \(b_0\) integral, defined as

\[ b_0 = \int \int_{A(x)} \rho (x, y, z) y^0 dz dy \]

at \(x = i h\)

Parameters

i	index at which to evaluate the integral

Returns

the integral value

Implemented in BeamGeometryCuboid.

B0()

virtual double B0 ( const int  i ) const

pure virtual

evaluate the \( B_0 \) constant

\[ B_0(x) = B_0^*(L) - B_0^*(x) \]

with

\[ B_0^*(x) = \int_0^x b_0(s) ds \]

Parameters

i	index at which to evaluate the integral

Returns

the constant value

Implemented in BeamGeometryCuboid.

b1()

virtual double b1 ( const int  i ) const

pure virtual

Evaluate the \(b_1\) integral.

Evaluate the \(b_1\) integral, defined as

\[ b_1 = \int \int_{A(x)} \rho (x, y, z) y^1 dz dy \]

at \(x = i h\)

Parameters

i	index at which to evaluate the integral

Returns

the integral value

Implemented in BeamGeometryCuboid.

c2()

virtual double c2 ( const int  i ) const

pure virtual

Evaluate the \( c_2 \) integral.

Evaluate the \( c_2 \) integral, defined as

\[ c_2 = \int \int_{A(x)} \frac{K(x,y,z)}{8} y^2 dz dy \]

at \( x = i h \)

Parameters

i	index at which to evaluate the integral

Returns

the integral value

Implemented in BeamGeometryCuboid.

c3()

virtual double c3 ( const int  i ) const

pure virtual

Evaluate the \( c_3 \) integral.

Evaluate the \( c_3 \) integral, defined as

\[ c_3 = \int \int_{A(x)} \frac{K(x,y,z)}{8} y^3 dz dy \]

at \( x = i h \)

Parameters

i	index at which to evaluate the integral

Returns

the integral value

Implemented in BeamGeometryCuboid.

c4()

virtual double c4 ( const int  i ) const

pure virtual

Evaluate the \( c_4 \) integral.

Evaluate the \( c_4 \) integral, defined as

\[ c_4 = \int \int_{A(x)} \frac{K(x,y,z)}{8} y^4 dz dy \]

at \( x = i h \)

Parameters

i	index at which to evaluate the integral

Returns

the integral value

Implemented in BeamGeometryCuboid.

Ex()

double Ex

(

const int

i

)

const

returns the value of Young's modulus at x = i * h

Parameters

i	index at which to return the value

Returns

Young's modulus at x = i * h

g1()

double g1

(

void

)

const

returns the x-component of vector of gravity for the current configuration of the beam

Returns

x-component of gravity

g2()

double g2

(

void

)

const

returns the y-component of vector of gravity for the current configuration of the beam

Returns

y-component of gravity

get_a()

double get_a ( void  ) const

inline

return left boundary of domain

Returns

left boundary

get_b()

double get_b ( void  ) const

inline

return right boundary of domain

Returns

right boundary

get_h()

double get_h ( void  ) const

inline

return stepsize

Returns

stepsize

getG()

rw::math::Vector3D getG

(

void

)

const

retrieves the directional vector of gravity

Returns

directional vector of gravity

getL()

double getL ( void  ) const

inline

return length of beam

Returns

double

getM()

int getM ( void  ) const

inline

return number of cross sections in beam

Returns

number of cross sections

getTransform()

rw::math::Transform3D getTransform

(

void

)

const

Retrieves the world to beam base transform of the beam.

Returns

world to beam base transform

kappa()

double kappa

(

const int

i

)

const

returns the kappa coefficient at x = i * h

Kappa is the coefficient relating the i,k = (1,1) coefficients of strain to stress in a plane stress situation, i.e.

\[ \sigma_{11} = \frac{E}{1 - \nu^2} u_{11} \]

with \( \kappa = \frac{E}{1 - \nu^2} \)

Parameters

i	index at which to return the value

Returns

kappa at x = i * h

rho()

double rho

(

const int

i

)

const

returns the value of the mass density at x = i * h

Parameters

i	index at which to return the value

Returns

mass density at x = i * h

setG()

void setG

(

const rw::math::Vector3D<> &

G

)

sets the directional vector of gravity

Parameters

G	directional vector of gravity

setTransform()

void setTransform

(

const rw::math::Transform3D<> &

T

)

Sets the homogeneous transform of the beam.

Parameters

T	world to beam base transform

vx()

double vx

(

const int

i

)

const

returns the value of Poisson's ratio at x = i * h

Parameters

i	index at which to return the value

Returns

Poisson's ratio at x = i * h

Friends And Related Function Documentation

operator<<

std::ostream& operator<< ( std::ostream &  out, const BeamGeometry &  obj  )

friend

outputs the geometry to stream

Parameters

out	the stream
obj	the geometry

Returns

the geometry as a stream

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

• BeamGeometry.hpp