Nonlinear Static and Dynamic Buckling Analysis of Imperfect Stiffened Double-Layer FGP Shallow Spherical Shells Embedded Within Elastic Foundations

Abstract

In this work, an analytical method is presented to analyze the nonlinear static and dynamic buckling of imperfect stiffened double-layer functionally graded porous (FGP) shallow shells subjected to external pressure. The shallow spherical shell consists of two layers, where upper layer of shell is nonporous functionally graded (FG) material and the lower layer of shell is FG porous. This spherical shell is resting on elastic foundations, which consist of two-term Winkler–Pasternak’s model. Two FG porous distributions types consisting of symmetric porosity distribution (SPD) and nonsymmetric porosity distribution (NSPD) are investigated. The porous materials are assumed to vary through the thickness direction based on the assumption of a common mechanical feature of the open-cell foam. Utilizing the classical theory of shells considering geometrical nonlinearity based on von Kármán–Donnell relations and Hooke’s law, the governing equations of stiffened double-layer FG porous spherical shells are extracted. To discretize the partial differential equation of shell and obtaining the system equations of motion, the Galerkin method is applied. Regarding the discretized equation of motion, the explicit expressions for dynamic and static critical buckling load are determined. To investigate the dynamic behavior, the equation of motion is solved via a numerical method named Runge–Kutta approach, and then a presented approach by Budiansky–Roth is employed to obtain a critical load for the nonlinear dynamic buckling. The influence of various porosity distributions and coefficients of the shallow shell, elastic foundations, and geometrical characteristics on the nonlinear static and dynamic buckling analysis of imperfect stiffened double-layer FG porous shallow shells is examined.