Surface effects on the buckling behaviors of piezoelectric cylindrical nanoshells using nonlocal continuum model

Abstract

• Nonlocal elasticity theory and surface effects are considered. • Accurate bucking solutions are derived through method of separation of variables. • Buckling results can be classified into two categories under the nonlocal effects. • Critical stresses decline rapidly while nonlocal effect reaches a certain level. • The surface effects and induced electric field can improve stability of nanoshells. The focus of this paper is on the analytical buckling solutions of piezoelectric cylindrical nanoshells under the combined compressive loads and external voltages. To capture the small-scale characteristics of the nanostructures, the constitutive equations with the coupled nonlocal and surface effects are adopted within the framework of Reddy's higher-order shell theory. The governing equations involving the displacements and induced piezoelectric field are solved by employing the separation of variables. The derived accurate solutions conclude that bucking critical stresses should go down rapidly while the nonlocal effects reach a certain level. With the enhancing surface effects, the stability of piezoelectric cylindrical nanoshells can be improved significantly. Meanwhile, the induced electric field also plays an important role in elevating the buckling critical stresses. For the nanoshells with remarkable nonlocal effects, boundary conditions, shell length and radius have little influence on the buckling solutions. The detailed effects of the boundary conditions, geometric parameters, material properties and applied voltages are discussed.