Elasticity solution for cross-ply composite and sandwich laminates

Abstract

A novel semi-analytical model is presented here for accurate estimation of stresses and displacements in composite and sandwich laminates. Displacements and corresponding transverse stresses are considered as primary variables of interest. Formulation is based on solution of a two-point boundary value problem (BVP) governed by a set of linear first-order ordinary differential equations (ODEs) through the thickness of a laminate. These first-order ODEs are numerically integrated by using fourth-order Runge-Kutta-Gill routine. Present model is free from any simplifying assumptions and also satisfies the continuity requirements of displacements and interlaminar transverse stresses at the laminae interfaces. Solutions for a wide range of composite and sandwich laminates are obtained to validate the present formulation. Results obtained through this technique are seen to compare well with the available three dimensional (3D) elasticity and other two dimensional (2D) analytical and 2D/3D finite element (FE) solutions. Few new benchmark solutions are also presented for future reference.