条分法的数值分析
The Numerial Analysis of Strip Partition Method
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摘要: 本文在总结前人研究成果(主要是摩根斯顿—普赖斯方法和潘家铮方法)的基础上,证明了给定滑动面安全系数的极大值定理,建立了模糊约束条件,并与传统的安全系数、最小安全系数的概念相对应,提出了安全系数的模糊解集和最小模糊解集的概念,把条分法的数学模型归结为:在边界条件和模糊约束条件下,寻求基本方程组隐式描述的泛函的最小模糊解集的问题。在构造未知函数空间Rm、滑动面空间Rn及其可行域与广义坐标的基础上,提出一个数值计算稳定、简便而又具有降低未知函数维数作用的FT计算格式,从而建立了数值计算的最优化方法——双层复形法。根据工程计算成果,推荐一个“工程方法”供一般工程计算使用,其求出的最小模糊解集,足以满足规范要求的计算精度。Abstract: In this paper on the basis of summing up the researching results of predecessors, synthesizing their method of advantages (especially Morgenstern-Price's and Pan Jia-zheng's works), it has been proved the theorem of maximum value of safety coefficient of the given slip surface and established the Fuzzy Function and the Fuzzy restricted conditions to suit to the concept of traditional safety coefficient and minimum safety coefficient. It has been put forward the concept of Fuzzy Solution Set of safety coefficient and minimum Fuzzy Solution Set, and defined the mathematical model of Strip Partition Method as the problem of seeking the minimum Fuzzy Solution Set being implicitly described functional in basic equations under the boundary condition and Fuzzy restricted condition. On the basis of establishing unknown function spacs Rm, slip surface space Rn and their feasible region and generalized coordinates, it has been put forward FT calculating form which is stable, convenient and possesses the function of reducing unknown functional dimensions,and thereby an optimized numerical calculation method-double complex method hasbeen established. According to the engineering calculating results, a "Engineering Method" is recommended for the use in engineering. The minimum Fuzzy Solution Set evaluated from it can be satisfied the calculating precision required by the standard sufficiently.