On a comprehensive analysis for mechanical problems of spherical structures

Abstract

This paper applies a semi-analytical polynomial method (SAPM) to solve the mechanical governing equations of nonlinear static and dynamic deformations, free and forced vibrations, and buckling analyses of nano-sized spherical functionally graded structures. Due to the nano-sized structure, the constitutive equations of motion are obtained based on the nonlocal elasticity theory. The governing equations are solved to obtain the deformations, critical buckling loads, and natural frequencies of the analyzed structure. The SAPM is based on polynomial functions (with no boundary conditions), including unknown finite coefficients. The spherical coordinate system is assumed to obtain several geometrical structures: cylindrical, conical, circular, sectorial, and rectangular. The nonlinear strains and the first-order shear deformation theory (FSDT) are employed to model the structure. The research considers the von Kármán assumptions to formulate the nonlinear strain components in the spherical coordinate system. The obtained results are compared with those in other articles to examine the accuracy of the applied solution method. The formulation's generality and simplicity and the appropriate accuracy of the SAPM's results distinguish this solution method for analyzing all mechanical aspects.