Nonlinear instability of hydrostatic pressurized hybrid FGM exponential shear deformable nanoshells based on nonlocal continuum elasticity

The size-dependent radial buckling and postbuckling behavior of functionally graded cylindrical shells at nanoscale integrated with piezoelectric nanolayers is studied in this paper on the basis of nonlocal elasticity theory within the framework of exponential shear deformation shell theory to capture the influence of transverse shear deformation in a refined form. By introducing a new reference surface, the stretching-bending coupling terms due to unsymmetrical material characteristics related to the functionally graded substrate of nanoshell are removed. After that, with the aid of boundary layer of shell buckling, the non-classical partial nonlinear differential equations are constructed to describe the nonlocal instability of nanoscaled shells. Finally, a perturbation-based solution methodology is utilized to propose explicit expressions for the nonlocal equilibrium paths associated with the both prebuckling and postbuckling domains of hybrid functionally graded nanoshells subjected to the combination of hydrostatic pressure and lateral electric field. It is seen that the nonlocality size effect causes to reduce the critical hydrostatic pressure, but it leads to increase the associated shortening of the movable ends of hybrid functionally graded nanoshells.