Bending analysis of composite and sandwich beams using Ritz method

Abstract

In the present paper, the bending behaviour of laminated composite and sandwich beams subjected to various sets of boundary conditions which are simply supported (SS), clamped-simply supported (CS), clamped-clamped (CC) and clamped-free (CF) are investigated by using the Timoshenko beam theory and the Ritz method. In order to solve the problem, the shape functions for axial, transverse deflections and the rotation of the cross-section are presented in polynomial forms. The validation and convergence studies are performed by solving symmetric and anti-symmetric cross-ply composite beam problems with various boundary conditions and aspect ratios by adding auxiliary functions to the shape functions. The results in terms of mid-span deflections, axial and shear stresses are compared with those from previous studies to validate the accuracy of the present study. The effects of fiber angle, lay-up and aspect ratio on displacements and stresses are studied.