Two-dimensional cross-sectional analysis of composite beams using Rayleigh-Ritz-based dimensional reduction method

In this paper, cross-sectional analysis of composite beams using a Rayleigh-Ritz-based dimensional reduction method is presented. In dimensional reduction method, the three-dimensional (3D) elasticity problem is reduced to a two-dimensional (2D) cross-sectional analysis which yields cross-sectional stiffness constants. Then a one-dimensional (1D) beam problem, with fidelity to 3D deformation effects, is attained. Using Rayleigh-Ritz method, the cumbersome procedure of mesh generation on beam section is eliminated in contrast to finite element-based cross-sectional analysis. Shear deformation effects and B-spline basis functions in Rayleigh-Ritz-based cross-sectional analysis are considered in this study. Different isotropic and composite beams are examined. Moreover, the effects of considering transverse shear deformation, coupling stiffness constants and honeycomb core for composite thin-walled beams are investigated. Using the present method, a fast and precise tool for analysis of composite beams with arbitrary cross-section geometry and material anisotropy is available for design of composite beam-like structures.