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采用有限元法进行结构应力分析时,经常要处理各种边界约束。本文在讨论一些常见约束的基础上,提出了一个处理位移约束的一般方法,并给出相应的通用程序 采用有限元法对结构作应力分析时,经常会遇到各式各样的约束条件。在实际计算中,必须对约束条件的处理给予足够的重视,若处理不当,将不可能获得符合实际的结果,甚至使结构的法方程出现奇性,计算进行不下去。有限元法的重要特点之一就是计算格式统一,无论刚度矩阵与荷载向量的形成,还是方程求解与应力计算,都具有统一的计算法则,便于编写通用计算程序。关于对称稀疏矩阵的紧缩存贮和大型线性方程组的分块求解方法已趋于成熟,但关于约束条件的处理,尽管各类文章针对具体约束的讨论不少,却还没有一种处理任意约束形式的统一方法。本文的目的是对一些常见的约束进行讨论,然后提出一个处理位移约束条件的一般方法,并给出相应的通用程序。
When structural stress analysis is performed using the finite element method, various boundary constraints are often handled. In this paper, based on the discussion of some common constraints, a general method for dealing with displacement constraints is proposed, and a corresponding general program is given. When using the finite element method for stress analysis of structures, various constraints are often encountered. In the actual calculation, we must pay enough attention to the processing of the constraint conditions. If it is handled improperly, it will be impossible to obtain the actual results, even the singularity of the structure of the equations, the calculation can not continue. One of the important features of the finite element method is the unification of the calculation format. Both the formation of the stiffness matrix and the load vector, the solution of the equation and the calculation of the stress, all have a unified calculation rule, which is convenient for the preparation of a general calculation program. The squeezing storage of symmetric sparse matrices and the block solution method of large-scale linear equations have matured. However, regarding the handling of constraint conditions, although various articles have discussed a lot of specific constraints, they have not yet dealt with arbitrary constraints. The unified method of form. The purpose of this paper is to discuss some common constraints, and then propose a general approach to deal with displacement constraints, and give the corresponding general program.