Fundamental solutions and integral equations of first-order laminated composite beams

Abstract

Laminated composite materials consist of oriented plies usually bonded together to provide desirable mechanical properties such as high stiffness and strength to weight ratio. The result is a feasible solution for many technological problems, principally in the naval, aerospace, and automotive industries. Laminated composite beams have been represented in many mathematical models since 3D elasticity to laminated beam theories such as discrete-layer approaches and equivalent single-layer models (ESL). In this article, the mathematical steps for deriving the fundamental solutions and integral equations of an ESL model, called first-order laminated composite beam theory (FOBT), under static loading are presented. The direct boundary element method (BEM) solution is properly addressed, incorporating topics such as: (a) explicit forms of influence matrices, (b) load vectors for concentrated loading and (trapezoidal, sinusoidal) distributed loading, and (c) reduction of BEM solution to the classical laminated beam theory. Numerical results are presented for beams under different static load cases, boundary conditions, and domain discontinuity problems associated with stepped beams and continuous beams. The results suggest the correctness and effectiveness of this direct BEM formulation.