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This paper presents prediction of static behavior of composite beams with arbitrary anisotropic materials. The procedure is based on decomposing a 3-D nonlinear elasticity problem into a 2-D analysis of cross section and a 1-D analysis across the beam length. This is accomplished by assuming that magnitude of strain is small compared to unity and cross section size is small relative to wave length of deformation, inherent to beam-like structures. In 2-D cross sectional analysis warping functions are calculated in terms of 1-D strain parameters and finally, fully coupled classical stiffness constants are derived which include extension, torsion and bending in two directions. 1-D analysis is modeled by Finite Element Method through calculating beam strain energy. In this article warpings are derived using Rayleigh-Ritz method. The great advantage of using Rayleigh-Ritz is simplifying cross sectional analysis in contrast with the mesh generation in FEM of similar procedures. Different cross section stiffnesses are investigated for ply orientation angle. Calculated results for symmetric and anti-symmetric composite box beams correlate well with 3-D FEM using Abaqus software as well as experimental results. The present solution has more accurate results for anti-symmetric composite box beam. According to costly use of 3-D FEM analysis, the present procedure with high speed and acceptable accuracy, is truly sufficient for preliminary and optimization problems.

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This paper, presents the static analysis of composite beams with transverse shear effects using polynomials based dimensional reduction method. In dimensional reduction method, a three dimensional elasticity problem is split into a two dimensional cross section analysis and a one dimensional beam analysis. FEM is commonly used to analyze beam cross section in the literature. In this study, polynomial functions and Rayleigh-Ritz method are used to present an analytical procedure for two dimensional cross section analysis. Variational Asymptotic Method (VAM) is employed considering shear stiffnesses of composite beam cross section. VAM, asymptotically generates fully coupled cross section stiffness matrix. VAM benefits small parameters, related to characteristic length of cross section, to find stationary values of beam energy functional. By minimizing the energy functional with respect to warpings, in and out of plane warping functions are acquired. In this article, isotropic beams with different cross section geometries and symmetric as well as anti-symmetric composite box beams are investigated. Presented results show appropriate correlation of the present study with theoretical and experimental results, as well as 3D Finite Element analysis. Using dimensional reduction method reduces the computing time and empowers researchers to design and optimize composite beam-like structures.