General theory for cross-ply laminated beams

We present a general formulation of the elasticity theory of the cross ply composite laminated beam subjected to various loadings such as axial load, bending moment, shear/bending, and torsion. The formulation is based on the integral equation theory, and a direct approach is employed to obtain the boundary integral equations for the analysis of the laminated beam, The integral equations governing the elasticity problem are directly deduced from the reciprocity theorem, by using the singular solutions of the orthotropic elasticity explicitly derived. The numerical solution is achieved by the boundary element method, which gives, once the traction free boundary conditions and the interfacial continuity conditions are enforced, a linear system of algebraic equations. The theoretical approach does not require any a priori assumption, and it is absolutely general with regard to the section properties. The method of analysis provides efficient computation and accurate solutions for many applications. Four-ply, symmetric cross-ply laminates under uniform axial strain and shear/bending loading are examined in detail, Numerical results are presented and compared with existing data.