用随机无网格点插值法分析齿轮弯曲疲劳强度的可靠性

用摄动随机无网格点插值法（PSMPIM）分析了齿轮弯曲疲劳强度的可靠性。在无网格点插值法中，所求解问题的域由分布的节点表示；并且利用具有Delta函数性质的多项式进行节点插值，为此，很容易类似有限元法一样处理本质边界条件。同时利用摄动技术，建立了随机结构分析的摄动随机无网格点插值法。并应用随机无网格点插值法分析了齿轮弯曲疲劳强度的可靠性。数值实例表明在随机结构分析与可靠性计算方面随机无网格法具有明显的优势。

The Bending Fatigue Reliability Analysis of Gear Teeth Using Stochastic Meshless Point Interpolation Method

The bending fatigue reliability of gear teeth has been analyzed by perturbation stochastic meshless point interpolation method(PSMPIM).In the meshless point interpolation method the problem domain is represented by properly scattered points.A technique is proposed to construct polynomial interpolants with delta function property based only on a group of arbitrarily distributed points,so the essential boundary conditions can be implemented with ease as the finite element methods.With application of perturbation technique,a perturbation stochastic meshless point interpolation method in probabilistic structural analysis is constructed,and the bending fatigue reliability of gear teeth has been analyzed by stochastic meshless point interpolation method.Numerical example shows that stochastic meshless method has obvious advantages in the probabilistic structure and reliability analysis