Meshfree approach on buckling and free vibration analysis of porous FGM plate with proposed IHHSDT resting on the foundation

Abstract

In the present work, new inverse hyperbolic higher-order shear deformation theory (IHHSDT) is proposed and implemented for buckling analysis and free vibration analysis of porous Functionally Graded Material (FGM) plate on the foundation. The proposed theory follows the approximately parabolic distribution of the transverse stresses through the plate thickness and satisfies the conditions of continuity and differentiability. Three different types of porosity distribution considered. Governing differential equations (GDEs) of the plate is developed in the framework of proposed theories by Hamilton’s principle. Multiquadrics radial basis function (MQ-RBF) based Meshfree method used for discretizing the GDEs. The result obtained by the present theory is validated with the three-dimensional elastic theory and other available solutions in the literature to ensure the efficacy and accuracy of the proposed theory. Numerical results obtained for buckling and free vibration for porous FGM plate resting on the foundation. Effect of grading index, porosity fraction, porosity distribution, the effect of foundation, and the span to thickness ratio have discussed. The secured results can consider as a benchmark for future studies.

Buckling Response of Functionally Graded Porous Plates Due to a Quasi-3D Refined Theory

“…where λ m = mπ a , µ n = nπ b , m, and n are mode numbers and U, V, W, X, Y, and Z are arbitrary parameters to be determined by substituting Equation (21) into Equation (19). Then, the following analytical solution is obtained:…”

“…A few investigations are focused on the buckling of FG porous plates. Kumar et al [21] used hyperbolic higher-order shear deformation theory to study the buckling and free vibration of FG porous plates resting on an elastic base. In this study, the symmetric center, top, and bottom enhanced porosity distributions were considered.…”

New HSDT for free vibration analysis of elastically supported porous bidirectional functionally graded sandwich plate using collocation method

“…Kumar et al 76 carried out a nonlinear analysis of porous FGM elastically supported plate subjected to various types of loadings and porosity distribution via HSDT based on the MQRBF meshfree method. Kumar et al 77 proposed IHHSDT and used it for free vibration and buckling analysis of porous FGM plates resting on foundation considering three types of porosity distribution and GDEs are discretized via MQRBF approach.…”

Three-Dimensional Buckling Analysis of Functionally Graded Saturated Porous Rectangular Plates under Combined Loading Conditions

“…A refined theory was also proposed by Ebrahimi and Jafari [9] to treat the buckling problem of smart magneto-electro-elastic-FG porous plates, accounting for two different FG distributions. Hyperbolic higher-order shear deformation theory (HSDT) was combined with a mesh-free approach in [10] to investigate the buckling and free vibration behavior of porous FG plates resting on an elastic foundation. Among coupled problems, Cong et al [11] focused on the nonlinear thermomechanical buckling and post-buckling of porous FG plates with two poro/nonlinear symmetric and non-symmetric distributions, by using the Reddy's HSDT and Galerkin method.…”