A unified third-order shear deformation theory for static analysis of laminated composite beams

Abstract

A unified higher-order shear deformation theory for static analysis of laminated composite beams is proposed in this paper. The theory is based on a higher-order shear deformation beam theory in which a general shear function is proposed. The characteristic equations are derived from Lagrange’s equations and then Ritz method is used to determine the stiffness matrix. As for static analysis, the potential kinetic energy in the Lagrange's equation is ignored. The shape functions for Ritz method approximation of displacement variables are selected to satisfy the boundaiy conditions. Numerical results are compared to those from previous works and are used to investigate the effects of fiber orientation, span-to-thickness ratio and boundary conditions on deflection and stresses of laminated composite beams.