二维等幅加载下疲劳可靠性分析P-S_a-S_m-N曲面族

本文由等幅疲劳三参数P－S－N曲线族方程和等寿命曲线方程，建立了便于工程应用的等幅疲劳P-Sa-Sm-N曲面族方程，并且十分明确地给出了其成立的力学及概率统计前提；根据Weibull对个体S-N曲线所做的单调降和不相交两大假设，用测度论证明户在P-Sa-Sm-N曲面族上，等幅疲劳寿命（N|（Sa，Sm），N|（R，Sa），N（R，Sm））与等幅疲劳强度（Sa|（N．Sm），Sm|（N，Sa））所构成的慨率空间族存在保测同构映射性质，即同一个体在不同的等幅疲劳寿命与等幅疲劳强度概率分布中具有同一百分值；并且对个体的．母体的以及样本的P-Sa-Sm-N曲面施给予了明确区分。

Fatigue reliablity analysis and P-S_a-S_m-N Surface family under two-dimensional Constant amplitude cyclic loading

In this paper, functions of the P-Sa-Sm-N surface family under constant amplitude cyclic loading are established by combining the P-S-N curve family and constant life diagrams,which is fcasible in engineering application. Meanwhile, the preconditions of mechanics and probability-statistics are clearly presented. According to Weibull's assumptions i. e. monotone decreasing and nonintersecting about individual S-N curvers, the relation of isostructural measure preserving transformation (IMPT) between the probability spaces of constant amplitude fatigue life and constant amplitude fatigue strength is proved based on measure theory. Therefore. an individual specimen possesses the same percentile value in different probability spaces of fatigue life and fatigue strength under constant amplitude loading. The P-Sa-Sm-N surfaces of individual,population and sample are also distinguished.