Bending-extension coupling analysis of shear deformable laminated composite curved beams with non-uniform thickness

Abstract

In this paper, the boundary-based finite element method (BFEM) is developed for the bending-extension coupling analysis of shear deformable laminated composite curved beams with non-uniform thickness. The curved beams are discretized into a series of uniform straight segments. Based upon the first order shear deformation theory and the reciprocal theorem of Betti and Rayleigh, the boundary integral equations (BIEs) associated with each beam segment are derived and expressed in explicit form. The fundamental solutions required in the BIEs are obtained explicitly from the associated Green’s function. Since no singular integrals, numerical integrations and function interpolations are involved in the BIEs, our proposed BFEM provides an exact solution for a straight beam with uniform thickness, and only one single element with two end nodes is required for our analysis. Even only an approximate solution is provided for a curved beam with non-uniform thickness, BFEM converges faster than the conventional finite element method, and the results are in well agreement with those obtained by the commercial finite element software. Through the illustrated numerical examples, its generality is shown by: (1) stacking sequence of laminates: symmetric or unsymmetric; (2) beam geometries: straight, stepped, or curvilinear with uniform or non-uniform thickness; (3) loading types: axial force, transverse force and/or bending moment; distributed or concentrated; and (4) supporting conditions: clamped, simply supported, or free; with or without internal supports.