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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R~m、滑动面空间R~n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。
Based on the previous research results (mainly the Morganston-Pules method and the Pan Jiaxuan method), this paper proves the maximal value theorem for a given sliding surface safety factor, establishes the fuzzy constraint condition, and compares it with the traditional one. The concepts of safety factor and minimum safety factor correspond to each other. The concepts of fuzzy solution set and minimum fuzzy solution set of safety factor are proposed. The mathematical model of the score method is attributed to: seeking basic equations under boundary conditions and fuzzy constraints. The problem of the set of minimal fuzzy solutions to functionals that are implicitly described. Based on constructing unknown function space R~m, sliding surface space R~n, and its feasible region and generalized coordinates, a FT calculation format which is stable, simple and has the function of reducing the dimension of unknown function is proposed. Numerical calculation optimization method - double layer complex method. According to the engineering calculation results, an “engineering method” is recommended for general engineering calculations. The minimum set of fuzzy solutions obtained by it is sufficient to meet the calculation accuracy required by the specification.