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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. • Incorporate with bending-extensional coupling and transverse shear deformations. • Develop BFEM for composite laminated curved beams with non-uniform thickness. • Solve all involved integrals and construct element stiffness matrices explicitly. • Derive explicit-form analytical solutions for straight uniform laminated beams. • Provide more efficient and accurate results than conventional finite element method. [ABSTRACT FROM AUTHOR]

Consider the coupling of stretching-bending deformation induced by the arbitrarily laminated composites, and the transverse shear deformation caused by the thick beams. A mathematical model based upon Timoshenko beam theory is established for the general laminated composite beams, and a proper replacement of stiffness is suggested for narrow or wide beam. By using the state-space approach, a general solution is expressed in terms of matrix exponential, which is applicable for any possible loading and boundary conditions. Expand the matrix exponential through Taylor series, an explicit analytical solution is obtained for the arbitrarily laminated composite beams under general loading conditions. With the obtained general solutions, several analytical solutions are derived explicitly such as the Green's functions for an infinite laminated composite thick beam, and the solutions for some typical beam problems. For example, a cantilever beam, a simply supported beam, or a fixed-end beam, subjected to uniformly distributed load, concentrated force/moment, or sinusoidal load, etc. To cover more complicated beam structures, we develop the boundary element method by using the obtained Green's functions. Three numerical examples are implemented to investigate the influences of stacking sequences and beam geometry, and to validate the applicability of boundary element method. [Display omitted] • Derive analytical solutions for arbitrarily laminated composite thick beams. • Incorporate with coupled stretching-bending and transverse shear deformations. • Provide explicit-form solutions for various loading and supported conditions. • Derive Green's function to develop BEM for curved beams with non-uniform thickness. • Discuss the effects of lamination, thickness, width, and non-uniformity. [ABSTRACT FROM AUTHOR]