Size-dependent buckling and postbuckling behavior of piezoelectric cylindrical nanoshells subjected to compression and electrical load

•Development an efficient size-dependent shell model including surface free energy effects•Nonlinear postbuckling behavior of piezoelectric nanoshells under combinations of axial compression and electrical field•Prediction the surface effects on the critical buckling load and associated postbuckling path of piezoelectric nanoshell

This paper studies the nonlinear buckling and postbuckling characteristics of piezoelectric cylindrical nanoshells subjected to an axial compressive mechanical load and an electrical load in the presence of surface free energy effects. The electrical field is applied along the transverse direction. A size-dependent shell model is adopted based on the Gurtin–Murdoch elasticity theory and von Karman geometrical nonlinearity. To satisfy the balance conditions on the surfaces of the nanoshell, a linear variation is considered for the normal stress of the bulk through the thickness. A boundary layer theory is employed including surface energy effects in conjunction with the effects of nonlinear prebuckling deformation, large deflections in the postbuckling regime and initial geometrical imperfections. Afterwards, a two-stepped singular perturbation technique is employed to obtain the size-dependent critical buckling load and the associated postbuckling equilibrium path for alternative electric loadings. It is found that the surface free energy and electrical load can cause an increase or decrease on the critical buckling load and the associated postbuckling strength of a nanoshell depending on the sign of surface properties and applied voltage. These anticipations are the same for the both perfect and imperfect piezoelectric nanoshells.

Graphical abstractA piezoelectric nanoshell with surface layers subjected to combination of axial compression and electrical loadFigure optionsDownload full-size imageDownload as PowerPoint slide