Pre-buckling and buckling analyses of functionally graded microshells under axial and radial loads based on the modified couple stress theory

In the present paper, the pre-buckling and buckling behaviors of a simply supported functionally graded (FG) microshell under a combined action of axial and radial loads are investigated. The size effects in the mechanical behavior of the microshell are captured by using the modified couple stress theory. The first order shear deformable shell theory together with the von Karman's geometric nonlinearity is adopted to describe its deformation behavior. Based on these assumptions and the Hamilton's principle, the equilibrium equations and associated boundary conditions for the microshell are derived. By applying the Galerkin method to the equilibrium equations, the pre-buckling deformation is obtained. The critical buckling load is then derived with the effect of the pre-buckling deformation taken into consideration. Furthermore, the effects of the material length scale parameter to thickness ratio, the power law index and the radial load to axial load ratio on the pre-buckling and buckling behaviors of the FG microshell are discussed in detail.