两个新型的八结点块体单元-三维离散算子差分法  

Two new eight node brick element three dimension discrete operator difference method

作　　者：田中旭[1] 唐立民[2] 刘正兴[3] 张立志 

机构地区：[1]上海大学上海市机械自动化及机器人重点实验室,200072 [2]大连理工大学工程力学系,116024 [3]上海交通大学工程力学系,200030 [4]吉林油田集团公司,131100

出　　处：《计算力学学报》2002年第2期202-206,共5页Chinese Journal of Computational Mechanics

摘　　要：给出了弹性力学三维问题的离散算子差分法 ,讨论离散算子差分法在三维问题中的特点 ,意在为该方法的进一步发展提供依据 ,为应用弱形式进行数值求解的研究提供参考。本文从弹性力学平衡方程更为一般的弱形式出发 ,给出了含边界参数的弱形式方程。由该方程不仅可以得到有限元法 ,还可得到离散算子差分法。给出了两个八结点块体单元 ,虽然单元中位移函数是非协调的 ,不需特殊处理便可保证离散格式收敛 ,并对单元位移有十分好的反映能力。A discrete operator difference method is established for three-dimension elastic problems. The character of the three-dimension method is investigated in order to provide a basic understanding for its further development and some references for the study of solutions by using weak form equations. A weak form equation containing boundary parameters is given for the three-dimension elastic problems. Both the finite element method and the discrete operator difference method can be pushed forward from each. Two kinds of the eight-node brick elements are deduced by using the discrete operator difference method. Although the displacements are unformed, their discrete schemes are convergent without additional disposal. Furthermore, the method is very simple both in formula's generating and programming, and the computational results are stable with changed meshes.

关 键 词：弱形式 八结点块体单元 离散算子差分法 有限元法 弹性力学 三维问题 位移函数 

分 类 号：O241.82[理学—计算数学] O343.2[理学—数学]