Nonlinear analysis of size-dependent annular sector and rectangular microplates under transverse loading and resting on foundations based on the modified couple stress theory

The nonlinear behavior of annular sector microplates remains poorly understood. In this study, a non-classical model for nonlinear bending analysis of annular sector microplates under transverse mechanical loading is developed based on the modified couple stress theory and the first-order shear deformation theory with von Karman nonlinearity. The model captures the size effect by a material length scale parameter. Using the principle of minimum total potential energy, the equilibrium equations and boundary conditions are obtained. The equilibrium equations are discretized according to the generalized differential quadrature method and are solved using the Newton's technique. By a proper change in the geometric parameters of annular sector plates, the results are extended to nonlinear analysis of square microplates under transverse loading. It is assumed that the microplates are resting on the nonlinear elastic foundations. The present results are verified by comparison with existing results in the literature. The effects of nonlinearity, length scale parameter, foundation parameters and geometric parameters on deflections of annular sector and square microplates subjected to distributed transverse loading are studied.