摘要
为了避免因网格畸变带来误差,本研究基于元胞自动机的思想发展了一种无网格计算方法。该方法将二维弹性问题的区域离散成随机分布的点,借用有限元方法中的差值概念建立区域中任意一点和其邻域内的其它点之间的位移与力的关系,以此为局部规则,构建了适用于求解二维弹性力学问题的元胞自动机。依据边界条件,元胞自动机自行演化,直至各离散点的位移收敛进而求得弹性问题的解。数值算例表明,该算法简单、正确,可以方便地和有限元结合,增加数值模拟的灵活性,同时,它在并行计算领域具备很大的潜力。
To avoid errors caused by distorted mesh, a new meshless algorithm based on cellular automaton （CA） is proposed in this study. By this algorithm, the domain of a 2-dimensional elastic problem is discretized into a grid of nodes distributed randomly. The mechanical relationship between an arbitrary node and its neighbouring nodes in the 2-dimentional continuum is established by employing the concept of interpolation used infinite element method （FEM）. Further, such mechanical relationship is defined as the local rule based on which a CA/s constructed. Taking the boundary conditions into account, the CA evolves automatically and the original elastic problem can be solved when the displacements at all the random nodes converge. Numerical examples show that the proposed method is simple and promising. It can be incorporated with FEM easily to make numerical simulation more convenient. Moreover, the present meshless algorithm has great potential in parallel processing.
出处
《机械设计与制造》
北大核心
2015年第3期101-103,共3页
Machinery Design & Manufacture
基金
制造过程测试技术省部共建教育部重点实验室资助课题(13ZXZK05)
西南科技大学博士基金(12ZX7105)
西南科技大学研究生创新基金(14ycxjj0124)
作者简介
王积硕，（1987-），男，山东人，硕士研究生，主要研究方向：计算固体力学；
袁卫锋，（1970-），男，河南人，博士，研究员，主要研究方向：计算力学、智能结构与纳米复合材料以及复杂系统数值模拟
