有限元分析中的最优离散化

系统的最优离散化具有很大的实用价值和理论意义。采用这种方法可以用最少的自由度得到最精确的数值解。本文给出了两种有代表性的方法,并收集了一些应用实例,其中包括笔者和刘永成、朱建中在Zienkiewicz指导下所作的一些工作。这种方法作为一种重分析方法不仅可用于线性问题,而且也可以用于具有表面非线性的弹性接触问题。 

OPTIMAL DISCRETIZATION IN FINITE ELEMENT ANALYSIS

Optimization of finite element grids based on the minimum potential energy is important both in theory and practice. By means of this method, the most accurate numerical results can be obtained with the least degrees of freedom. In this paper, two kinds of procedures are presented as typical adaptive processes in grid optimization.A series of examples including some research work by Dr. JVC. Zhu, Dr. Y.C.Liu and the author under the guidance of Prof. Zienkiewicz: are given to show the validity and versatility of the procedures.As refinement processes, they can be applied not only in linear problems but also in elastic contact problems, a type of surface nonlinear problems.