Static Analysis of Reddy-Bickford Composite and Sandwich Beams via Ritz Method

This paper is dedicated to present static behaviour of Reddy-Bickford 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) by using Ritz method. An analytical solution based on polynomial series including auixiliary functions which are used to satisfy the boundary conditions is developed to solve the studied problem. The polynomial shape functions for axial, transverse deflections and the rotation of the cross-section are presented. 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. The numerical results in terms of mid-span deflections, axial and shear stresses are obtained to make comparison with previous studies and to investigate the accuracy of the present study. The effects of fiber angle, lay-up and aspect ratio on displacements and stresses are studied. The static response of the various laminated composite sandwich structures which have symmetric lay-up based on the various boundary conditions, fiber angles and thickness ratios is also studied. It is found that the polynomial series with auxiliary functions can be used for the static analysis of the composite and sandwich beams via Ritz method.