Governing Equations of Micro-scale Plate in terms of Displacement Potential Functions

The behavior of solids can be represented by variety of continuum theories. The deformation behavior of materials in the micron scale has been experimentally shown to be size dependent. Therefore, a number of theories containing material length scale parameters and extra freedoms have been presented to solve this defect. For example, Cosseratelastisity allows the points in the continuum to rotate as well as translate, another proposed theory is Couple stress theorywhich is utilized in this paper. In this study, by using the classical form of Lekhnitskii-Hu-Nowacki displacement potential functions, the governingequations of couple stress theory for isotropic micro or nano materials are obtained. These equations include three Partial Differential Equations of sixth order. Solution of the governing equations have shown that the effect of lenghth paremeter is ommited. Due to this defect, the Lekhnitskii-Hu-Nowacki displacement potential functions are modified for micro or nano scale and new potential function is presented. Based on modified displacement potential functions, governing equations are solve for simply supported rectangular plate for micro or nano scale. Comparison of obtained results using proposed method in this research with other works shows good agreement between results

Keywords:

Couple stress , micro-scale , microrotation , governing equations , length scale parameter