弹性力学中无网格和有限元耦合的元胞自动机算法

摘要

A CA was developed to combine the advantages of FEM and meshless method which was used to analyze 2-dimensional elastic problems.By the CA,a 2-dimensional domain was dis-cretized into a grid of nodes.These nodes were distributed randomly in the domain and they were di-vided into the FEM group and the meshless group.In the FEM zone which was mostly defined near the boundaries of the domain,FEM elements were used to establish the relationship between one node and other adjacent nodes.In the meshless zone which was normally away from the boundaries,the ad-jacent nodes were related by employing the concept of displacement interpolation used in FEM.However, each nodes,wherever they were in the FEM zone or meshless zone,were dealt with under the CA frame,that is,the unknown displacements of each nodes were evaluated by CA algorithm.Unlike FEM,the proposed CA solver worked out the results through automatic evolution,instead of Gaussian elimination or other conven-tional methods.Based on the current CA algorithm,FEM and meshless may be merged seamlessly.The nov-elty and the correctness of the current approach were proven by numerical examples.%结合有限元和无网格算法的优势,提出了一种元胞自动机算法用以求解二维弹性力学问题.该算法将二维模型离散成一系列节点,这些节点被分成有限元群和无网格群.有限元区域被定义在问题的边界附近,其中的任一节点和其周围相邻点的力学关系通过有限元单元建立;无网格区域定义在远离原理问题边界处,其中的节点之间的关系借用有限元中的位移插值概念建立.无论处于有限元区域还是无网格区域,任何一个节点都被置于元胞自动机的框架下进行处理,即节点的位移通过元胞自动机进行求解.与有限元方法相比,所提出的元胞自动机算法无需采用高斯消去法等传统系统求解器,而是通过元胞自动机的自动演化解决问题.依据该算法,有限元和无网格方法可以实现无缝连接.数值算例验证了该算法的新颖性和正确性.