Abstract: Aiming at the complex gradient changes of graphene-reinforced composite materials, a finite element method based on 20-node nonlinear gradient element is proposed to satisfy the analysis of the mechanical properties of complex gradient materials. In this paper, the finite element models of U-shaped, X-shaped and O-shaped gradient distribution cantilever plates are established, and the static displacement, stress and mode of the cantilever plates under the three gradient distribution forms are compared and analyzed. The method in this paper is compared and verified with the finite element layered method. The results show that compared with the nonlinear gradient element method, the traditional layered method model will cause the bending stiffness of the X-shaped cantilever plate and the corresponding natural frequencies of each order to be larger than the actual values, while the bending stiffness of the O-shaped cantilever plate and the corresponding natural frequencies of each order are smaller than the actual values. Compared with the U-shaped distribution, the X-shaped gradient distribution can improve the bending stiffness of the cantilever plate, mentioning the natural frequencies of each order of the cantilever plate, while the O-shaped distribution can reduce the bending stiffness of the cantilever plate and reduce the natural frequencies of each order. The nonlinear gradient element method can solve the stress in the thickness direction of the functionally graded plate, which provides a theoretical basis for the fatigue life analysis of the functionally graded plate.

Key words: graphene, nonlinear gradient element, stress, modal, finite element layered method