Finite Element Method And Its Implement Based On Cellular Automata

The mechanical problems in the engineering programs were mostly solved by numerical methods, such as finite element method, boundary method, distinct element method, and so on. Every method has its own field of application. And the finite element method, because of its flexibility and commonality, was widely used. From a new point, this dissertation introduced cellular automata into finite element method. A model of cellular automata for analysis of finite element method was built. The lattice was constituted by node cells and polygon cells. The state of cellular automata is displacements of the node cell and forces of the node cell. Three cellular neighbors were defined in this dissertation. Based on the stiffness matrix, mechanical analysis was made for node cell and its neighbor cell. Then the evolvement rule was built. The evolvement procedure of the node cell was introduced and the evolvement criterion was given. The procedure of FEM based on cellular automata was introduced and compared with FEM.Based on the OOP, the cell class was pick-up; Node cell class and Triangle cell class were built. The flow chart of calculation was given. In the environment of VC++6.0, CA-FEM was developed, which is a visual and message-driven software. In this platform, two examples were calculated to check the theory of CA-FEM. We found, the displacement can converge very well, and the result of displacement is almost similar to the result of FEM.