Buckling and bending analysis of functional porous plate using shear deformation theory

In this study, the elastic buckling and static bending of a functionally graded porous plate based on shear deformation theory have been investigated. The effect of the type and degree of porosity on the mechanical behavior of the plate using the principle of potential energy is the main goal of this research. The modulus of elasticity and mass density of the porous sheet are graded in terms of thickness according to two different distribution patterns. The system of partial differential equations governing the buckling and bending behavior of the plate is derived from Hamilton's principle. The Ritz method is used to calculate the critical buckling loads and transverse bending curvature. In order to validate the method and the results presented in this research, a comparison was made with the results presented in authoritative references and articles. In addition, the finite element modeling results have been compared with the present analysis. Also, a parametric study has been performed to investigate the effects of porosity coefficient and length to thickness ratio of plate on buckling and flexural properties of porous sheets with simply support boundaries. The effect of different porosity distributions on plate performance is discussed. In this research, by applying different porosity coefficients and changes in length to thickness ratio, buckling load and flexural behavior of a graded porous plate with a specific porosity distribution pattern has been investigated. According to parametric study of porous plate, the buckling load and the maximum transverse displacement on bending increase with increasing the porosity coefficient and the ratio of length to thickness. The results of this study are used to design of porous plate in various designs such as implants.