Postbuckling of multi-direction anisotropic constrained functionally graded material beams

Abstract

In recent years, significant research efforts have been dedicated to the development and application of functionally graded materials (FGMs) in the control and manipulation of engineered materials and structures. This study proposes an analytical investigation of the postbuckling behavior of a multi-direction anisotropic FGMs beam subjected to bilateral constraints. The FGMs beam consists of two isotopic layers and is assumed to be graded in the x, y and z directions. Theoretical models are developed to examine the force-displacement relations and the postbuckling shape configurations of the FGMs. Two elastic moduli (i.e., following polynomial and trigonometric functions) are considered to obtain the desired stored potential energy under static axial compressive loading. Here, the FGMs beam’s behavior is represented by a fourth order nonlinear partial differential equation, while the energy minimization technique is employed to solve the governing equation of the mathematical model. Furthermore, the Nelder-mead algorithm and parallel Kernel configuration are used to determine the minimum energy paths of the deformed elastic beam, along with the corresponding snap through events. We compared the proposed model to existing studies in literature, and satisfactory agreements were obtained. Moreover, parametric studies are carried out to assess the influence of varying the material properties (i.e., volume fraction) on the tunable FGMs beam. The results revealed that the material distribution function has a significant effect on the postbuckling response of FGMs beam. Also, the results showed that optimizing material functions lead to better controllability over the FGM beams. The approach presented in this study provides a promising strategy to exploit the performance of FGMs, predicting and maneuvering the postbuckling response for advanced technological devices.