A non-classical theory of elastic dielectrics incorporating couple stress and quadrupole effects: part II - variational formulations and applications in plates

A new Mindlin plate model is developed incorporating the couple stress, quadrupole, and curvature-based flexoelectric effects using a non-classical elastic dielectric theory. The general governing equations and complete boundary conditions are derived simultaneously through a variational approach. The new general plate model includes the model for centrosymmetric materials as a special case. As direct applications of the new plate and to illustrate the flexoelectric effect, the static bending and free vibration problems of a simply supported rectangular plate are analytically solved by directly applying the new centrosymmetric model. The numerical results reveal that the flexoelectric effect is present in centrosymmetric materials and is important when the plate thickness is very thin. The dispersion relations for flexure and fundamental shear modes are obtained. We find electrostatic wave also propagates with the flexure or fundamental shear waves by flexoelectric coupling. The present work can be seen as an extension of mechanical analysis of plate structures with couple stress effects and may be useful to the devices design of micro- or nano-sized objects.