Nonlinear stability characteristics of piezoelectric cylindrical shells with flexoelectric effects

Unlike the post-buckling behaviors of classical piezoelectric cylindrical shell, the size-dependent effect of flexoelectric material and high strain gradient in the post-buckling process play an important role in the stability analysis of the micro/nano cylindrical shells. To reveal the impacts on the post-buckling of flexoelectric cylindrical shells, an accurate post-buckling model for the flexoelectric cylindrical shells under axial compression is proposed based on the higher-order shear deformation shell theory and von Karman geometrical nonlinearity. The size-dependent post-buckling equilibrium path with mode-jumping phenomena is obtained by using Galerkin’s method and Newton-Raphson method. The predicted results are in agreement with those reported in the open literature. A detailed parametric study is also carried out to investigate the influence of geometrical parameters, flexoelectric coefficients, and electric voltage on the size-dependent post-buckling behaviors of flexoelectric cylindrical shells.