平面弹性力学中的细胞自动机方法  

Cellular automata for analysis of plane problems in theory of elasticity

作　　者：沈成武[1] 戴诗亮[2] 杨吉新[1] 唐小兵[1] 

机构地区：[1]武汉理工大学船舶与土木工程学院,武汉430063 [2]清华大学工程力学系,北京100084

出　　处：《清华大学学报（自然科学版）》2001年第11期35-38,共4页Journal of Tsinghua University(Science and Technology)

基　　金：国家自然科学基金资助项目 (19772 0 3 8)

摘　　要：用细胞自动机作平面弹性力学分析 ,将结构的静平衡认为是在力和位移边界条件下 ,物体元胞间的自组织过程。探讨了该方法的可行性 ,给出元胞的划分和力学特性 ,编制了相应的程序。由于该方法不必解结构的偏微分方程边值问题 ,或形成有限元的总体刚度矩阵 ,并解大型线代数方程 ,因而计算工作量小。算例表明 ,该方法对结点位移和应力、应变的收敛速度均较快 。Cellular automata was applied to solve plane problems in theory of elasticity. Static equilibrium of structure is regarded as a self organizing process of cells under the condition of force and displacement boundary. The feasibility of the new method is discussed. The characteristic of cell and the way of dividing cell are studied, while a program is presented. The calculation of the new method is simpler because it need not form the global stiffness matrix that is necessary in FEM, and solve the boundary problems of partial differential equations. Numerical computing results show that the new method has not only rapid speed of convergence to nodal displacement, stress and strain of elements, but also good prospects on solving problems in solid mechanics.

关 键 词：细胞自动机 元胞 平面弹性力学 收敛速度 

分 类 号：O343.1[理学—固体力学]