A Nonclassical Finite Element Approach for the Nonlinear Analysis of Micropolar Plates

Abstract

Based on the micropolar elasticity theory, a size-dependent rectangular element is proposed in this article to investigate the nonlinear mechanical behavior of plates. To this end, a novel three-dimensional formulation for the micropolar theory with the capability of being used easily in the finite element approach is developed first. Afterward, in order to study the micropolar plates, the obtained general formulation is reduced to that based on the Mindlin plate theory. Accordingly, a rectangular plate element is developed in which the displacements and microrotations are estimated by quadratic shape functions. To show the efficiency of the developed element, it is utilized to address the nonlinear bending problem of micropolar plates with different types of boundary conditions. It is revealed that the present finite element formulation can be efficiently employed for the nonlinear modeling of small-scale plates by considering the micropolar effects.