Liwen He

Buckling and Post-Buckling of Symmetric Functionally Graded Microplate Lying on Nonlinear Elastic Foundation Based on Modified Couple Stress Theory

This paper is concerned with the buckling and post-buckling behaviors of a simply supported symmetric functionally graded (FG) microplate lying on a nonlinear elastic foundation. The modified couple stress theory is used to capture the size effects of the FG microplate, and the Mindlin plate theory with von Karman’s geometric nonlinearity taken into account is adopted to describe its deflection behavior. Based on these assumptions and the principle of minimum potential energy, the equilibrium equations of the FG microplate and associated boundary conditions are derived. By applying the Galerkin method to the equilibrium equations, closed-form solutions for the critical buckling load and the load–displacement relation in the post-buckling stage are obtained. Furthermore, the effects of the power law index, the material length scale parameter to thickness ratio, the stiffness of the elastic foundation, and in-plane boundary conditions on the buckling and post-buckling behaviors of the FG microplate are disc...

On the coupling effects of piezoelectricity and flexoelectricity in piezoelectric nanostructures

Flexoelectricity is a novel kind of electromechanical coupling phenomenon that is prevalent in all solid dielectrics and usually of vital importance in nanostructures and soft materials. Although the fundamental theory of flexoelectric solids and related beam or plate theories were extensively studied in recent years, the coupling effect of flexoelectricity and piezoelectricity in piezoelectric nanostructures has not been completely clarified yet. In the present work, a geometrically nonlinear piezoelectric plate model is established with a focus on the coupling effect. The constitutive equations for piezoelectric plates are derived under both the electrically short-circuit and open-circuit conditions. It is found that due to the coupling between flexoelectricity and piezoelectricity, stretching-bending coupling stiffness arises in the homogeneous plate and its specific value relies on the applied electrical boundary conditions. The effects of the flexoelectric-piezoelectric coupling on the effective mech...