Asymptotic analysis of Timoshenko-like orthotropic beam with elliptical cross-section

Abstract

Abstract: This work presents the asymptotically exact analysis of homogeneous-orthotropic prismatic beam with elliptic cross-section. Variational Asymptotic Method (VAM) has been used to systematically reduce the 3D elastic problem of beam analysis into 2D cross-sectional analysis and 1D along the length of beam analysis. This reduction simplifies beam analysis to a great extent. The 2D analysis supplies cross-sectional stiffness constants to the 1D beam problem. This analysis provides closed-form expression of cross-sectional stiffness constants, 3D displacement and strain fields in terms of 1D strain measures. Present work does not make any a priori ad-hoc assumptions about the deformation as it uses VAM and ensures asymptotic correctness of the solution. The results are obtained for Classical and Timoshenko-like beam models loaded with most general loads. These results are validated by comparing them with existing results in the literature and Finite Element Analysis (FEA) results. Current results are in close agreement with FEA results.