Nonlinear bending, postbuckling and snap-through of circular size-dependent functionally graded piezoelectric plates

In the present work, the nonlinear thermoelectrical stability of perfect/imperfect circular size-dependent functionally graded piezoelectric plates is studied according to modified couple stress theory. The second, concurrent aim is to address snap-through phenomenon in the thermally preloaded plates due to concentrated/uniform lateral loads. Ritz finite element method is implemented into virtual displacement principle to construct the matrix representation of nonlinear governing equations. Under certain circumstances, bifurcational instability may occur in which case a direct displacement control scheme is utilized. In other cases, the response is unique and stable to which any standard load control strategy seems appropriate and thus Newton-Raphson method is selected. Standard load control strategies, however, fail to trace nonlinear equilibrium paths through limit points and path following methods must be employed in snap-through problems. Being more popular among the existing path following solution methods, cylindrical arc-length method is adopted. Two types of thermal loading as well as two cases of boundary conditions are considered. Moreover, various parametric studies are conducted to assess the influence of involved parameters.