Exact solutions for static analysis of laminated, box and sandwich beams by refined layer-wise theory

In the present work, a close-form solution based on a unified one-dimensional model is proposed and then applied to static response analyses of cross-ply laminated and sandwich beams subjected to simply supported boundary conditions. The hierarchical beam model is derived within the framework of the Carrera Unified Formulation (CUF), which makes use of Lagrange polynomials to express the three-dimensional (3D) displacement field via arbitrary order approximation of pure displacement variables at each layer over the cross section, in a Layer-Wise (LW) sense. The governing equations are derived via the principle of virtual work and a Navier-type close-form solution is employed to solve the resulting boundary value problem. Four benchmark numerical examples are carried out to demonstrate the efficiency of this novel method, including compact multi-layered cross-ply laminated beams, a thin-walled composite box beam and a composite sandwich-box beam. The results show that accurate displacement and stress components can be obtained as the order of the expansion increases, accompanied by a significant reduction in computational costs in comparison with the 3D finite element solutions. Besides, numerical cases in this research may be taken as benchmarks for future assessments in this field.