Couple stress-based nonlinear buckling analysis of hydrostatic pressurized functionally graded composite conical microshells

Abstract

The present study deals with the size-dependent nonlinear buckling characteristics of conical microshells made of functionally graded (FG) composite materials under uniform hydrostatic pressure based upon the modified couple stress theory of elasticity. Accordingly, a modified couple stress-based shell model within the framework of the higher-order shear deformation shell theory and von Karman geometrical nonlinearity is constructed. Using the virtual work's principle in conjunction with the adjacent equilibrium criterion, the non-classical governing differential equations are established. The material properties of FG composite conical microshells are estimated on the basis of different homogenization schemes. To solve the size-dependent nonlinear problem, the generalized differential quadrature discretization pattern together with the Galerkin technique is employed. It is seen that among various types of homogenization scheme, the Voigt and Reuss models represent, respectively, the overestimated and underestimated critical buckling pressures. Also, it is found that for a FG composite conical microshell with higher semi-vertex angle, the influence of the material property gradient index on the nonlinear critical buckling pressure diminishes. In addition, it is observed that the couple stress size dependency plays more important role in the nonlinear buckling behavior of FG composite conical microshells with lower ratio of R1/h. These patterns are the same for all types of boundary conditions.