Surface Stress Effect on Nonlinear Instability of Imperfect Piezoelectric Nanoshells under Combination of Hydrostatic Pressure and Lateral Electric Field

Abstract

In this paper, the nonlinear instability of piezoelectric cylindrical nanoshells under the combined radial compression and electrical load including the effects of surface free energy is studied. To consider the surface effects, the Gurtin-Murdoch elasticity theory is utilized along with the classical shell theory to develop an efficient size-dependent shell model. To satisfy the balance conditions on the surfaces of nanoshells, a linear variation of normal stress is assumed through the thickness of the bulk. Electrical field is also exerted along the transverse direction. Based on the virtual work principle, the size-dependent nonlinear governing differential equations are derived in which transverse displacement and Airy stress function are considered as independent variables. After that, a boundary layer theory is used incorporating the surface free energy effects in conjunction with the nonlinear prebuckling deformation, the large deflections in the postbuckling regime, and the initial geometrical imperfection. Finally, a two-stepped singular perturbation technique is employed to obtain the size-dependent critical buckling pressure and the associated postbuckling equilibrium path for alternative electrical loadings. It is revealed that the electrical load increases or decreases the critical buckling pressure and critical end-shortening of nanoshell which depends on the sign of applied voltage. Moreover, it is found that by taking surface free energy effects into account, the influence of electrical load on the postbuckling behavior of nanoshell increases.