弹性力学中无网格和有限元耦合的元胞自动机算法

发布时间：2018-05-09 02:44

本文选题：耦合算法 + 元胞自动机　；参考：《中国机械工程》2017年17期

【摘要】：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。
[Abstract]:Combining the advantages of finite element method and meshless algorithm, a cellular automaton algorithm is proposed to solve two-dimensional elastic problems. The algorithm discretizes the two-dimensional model into a series of nodes, which are divided into finite element group and meshless group. The finite element region is defined near the boundary of the problem, in which the mechanical relations between any node and adjacent points are established by finite element element, and the meshless region is defined far from the boundary of the principle problem. The relationship between nodes is established by the concept of displacement interpolation in finite element method. No matter in the finite element region or in the meshless region, any node is dealt with under the framework of cellular automata, that is, the displacement of nodes is solved by cellular automata. Compared with the finite element method, the proposed cellular automata algorithm does not need to use traditional system solvers such as Gao Si elimination method, but solves the problem by the automatic evolution of cellular automata. According to this algorithm, the finite element method and the meshless method can realize the seamless connection. Numerical examples verify the novelty and correctness of the algorithm.
【作者单位】：西南科技大学制造科学与工程学院;
【基金】：国家自然科学基金资助项目(11472232) 四川省教育厅教改项目(14JGCX07) 制造过程测试技术省部共建实验室基金资助项目(13zxzk05)
【分类号】：O343

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