Nonlinear Dynamical Instability Characteristics of FG Piezoelectric Microshells Incorporating Nonlocality and Strain Gradient Size Dependencies

In the present exploration, the nonlocal stress and strain gradient microscale effects are adopted on the nonlinear dynamical instability feature of functionally graded (FG) piezoelectric microshells under a combination of axial compression, electric actuation, and temperature. To perform this objective, a unified unconventional shell model based on the nonlocal strain gradient continuum elasticity is established to capture the size effects as well as the influence of the geometrical nonlinearity together with the shear deformation along with the transverse direction on the dynamic stability curves. With the aid of an efficient numerical strategy incorporating the generalized differential quadrature strategy and pseudo arc-length continuation technique, the extracted unconventional nonlinear differential equations in conjunction with the associated edge supports are discretized and solved to trace the dynamic stability paths of FG piezoelectric microshells. It is revealed that the nonlocal stress and strain gradient effects result in, respectively, higher and lower values of the nonlinear frequency ratio in comparison with the conventional one due to the stiffening and softening characters associated with the nonlocality and strain gradient size dependency, respectively. In addition, it is observed that within the prebuckling territory, the softening character of nonlocality is somehow more than the stiffening character of strain gradient microsize dependency, while by switching to the postbuckling domain, this pattern becomes vice versa.