A microstructure-dependent orthotropic plate model based on a modified couple stress theory

In this paper a modified couple stress model containing only one material length scale parameter is developed for the static analysis of orthotropic micro-plates with arbitrary shape. The proposed model is capable of handling plates with complex geometries and boundary conditions. From a variational procedure the governing equilibrium equation of the micro-plate and the most general boundary conditions are derived, in terms of the deflection, using the principle of minimum potential energy. The resulting boundary value problem is of the fourth order (instead of existing gradient theories which is of the sixth order) and it is solved using the Analog Equation Method (AEM), which is a boundary-type meshless method. Several plates of various shapes, aspect and Poisson’s ratios are analyzed to illustrate the applicability of the developed micro-plate model and to reveal the differences between the current model and the classical plate model. Moreover, useful conclusions are drawn from the micron-scale response of this new orthotropic plate model.