Analytical study of Timoshenko-like deformation in beams with graded Poisson’s ratio

Behavior of a structure under any loading condition is governed by its associated material/structural properties. Inhomogeneity and/or anisotropy in the material plays a crucial role in determining the response of such structures. In most of the cases, Functionally Graded Materials (FGMs), which are based on the idea of varied Young’s modulus of the material (inhomogeneity), ignore the contribution of Poisson’s ratio while Auxetic materials are solely based on the idea of variation of Poisson’s ratio. The consideration of variation of Poisson’s ratio show the capability to fine-tune the results for such analysis. In this work, Variational Asymptotic Method (VAM) has been adopted to analyze beam-type structure with constant Young’s modulus but varied Poisson’s ratio. The plots for strains have been drawn and compared with the results from FEA tool Abaqus. The plot behavior justifies the need to consider the variation of Poisson’s ratio in such analysis.