Integration of beam functions

Leung, Andrew Yee Tak

doi:10.1016/0045-7949(88)90332-X

Integration of beam functions

Author(s)

Leung, Andrew Yee Tak

Date Issued

1988

Publisher

Elsevier

Journal

Computers & Structures

Volume

29

Issue

6

Start page

1087

End page

1094

Abstract

The beam functions satisfying d⁴φ/dξ⁴ = β⁴φ with the associated boundary conditions are convenient admissible comparison functions for the approximated solutions of complex structural problems by the well known Rayleigh-Ritz method. Reliable integration formulae for products of various beam functions φ and ψ with an arbitrary function θ are essential. Felgar's recurrence formula for ∫ θφψdξ is found to be in error and is corrected here. The condition when the characteristic values of θ and ψ are identical is also considered. A simple subroutine is given to evaluate ∫ θ(ξ)(dⁿφ/dξⁿ)(d^mψ/dξ^mdξ for all possible sets of boundary conditions. Applications to the free vibration of nonuniform beams and plate systems are demonstrated.

URI

https://repository.sfu.edu.hk/handle/sfu/3279

DOI

10.1016/0045-7949(88)90332-X

SFU Affiliated Publication

No

Availability at SFU Library

No database links found.