Coupled-admissible functions for simple solutions to unsymmetrically laminated shear flexible beams

Abstract

Coupled-admissible functions are derived to obtain simple solutions for unsymmetrically laminated beams. A kinematically admissible variation, as allowed by Rayleigh-Ritz energy method, is assumed for the section rotation. Compatible admissible variations for transverse and axial displacements are derived by making use of equilibrium and boundary conditions. The proposed approach reduces the number of independent unknowns by a factor of three compared to traditional Rayleigh-Ritz method. Expressions for the axial and transverse displacements, section rotation, fundamental frequency and buckling loads for simply-supported, clamped-free and clamped-clamped beams are derived.