EBBeam Class Reference

Class for calculating the analytical solution to the Euler-Bernoulli beam model in fixed-free configuration. More...

#include <EBBeam.hpp>

Public Member Functions
	EBBeam (const double H, const double K, const double L, const double E, const double rho, const double h, const double g2)
	constructor More...
double	operator() (const int i) const
	returns the deformation at x = i * h More...
double	d (const int i) const
	returns the first derivative of the deformation at x = i * h More...

Detailed Description

Class for calculating the analytical solution to the Euler-Bernoulli beam model in fixed-free configuration.

Implementation of the classical analytical solution to the Euler-Bernoulli beam model in fixed-free configuration, for a cuboid beam, i.e.

\[ \eta(x) = \frac{q x^2 (6 L^2 - 4 L x + x^2)}{24 E J} \]

where \( q = g \rho(x) A(x) \), where \( g \) is the gravitational acceleration, \( \rho *\) the mass density and \( A(x) = H * K \) the area for the cross section,

where \( L \) is the length of the object, \( E \) is Young's modulus of elasticity and

where \( J = \frac{K H^3}{12} \) is the second moment of area for the cuboid with the neutral line in the centroid.

Constructor & Destructor Documentation

EBBeam()

EBBeam	(	const double	H,
		const double	K,
		const double	L,
		const double	E,
		const double	rho,
		const double	h,
		const double	g2
	)

constructor

Parameters

H	the thickness in the z-direction
K	the thickness in the y-direction
L	the length of the beam, in the z-direction
E	Young's modulus
rho	the mass density
h	stepsize used in the beam
g2	vertical component of the gravity direction vector

Member Function Documentation

d()

double d

(

const int

i

)

const

returns the first derivative of the deformation at x = i * h

Parameters

i	the index at which to return the deformation

Returns

the first derivative of the deformation

operator()()

double operator()

(

const int

i

)

const

returns the deformation at x = i * h

Parameters

i	the index at which to return the deformation

Returns

the deformation

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

• EBBeam.hpp