Keywords: random field, reliability, stochastic meshless point interpolation method, Neumann expansion Monte Carlo method, artificial immune genetic algorithm.

The structural reliability of gear teeth subjected to bending has been studied by Neumann expansion Monte Carlo stochastic meshless point interpolation method (NMC-SMPIM) and the artificial immune genetic algorithm (AIGA) in this paper. First, a Neumann expansion Monte Carlo stochastic meshless point interpolation method was constructed for solving boundary value problems in linear elasticity that involves random material properties. The material property was modeled as a homogeneous random field. A meshless formulation was developed to predict stochastic structural response. Unlike the finite element method, the meshless method requires no structured mesh, since only a scattered set of nodal points is required in the domain of interest. There is no need for fixed connectivities between nodes. A technique is proposed to construct polynomial interpolants with delta function property, so the essential boundary conditions can be implemented with ease as the finite element method.

In conjunction with the meshless equations, a Neumann expansion Monte Carlo method was derived to predict high moment characteristics of response. Since mesh generation of complex structures can be a far more time-consuming and costly effort than the solution of a discrete set of equations, the meshless method provides an attractive alternative to the finite element method for solving stochastic mechanics problems. Second, reliability of probabilistic structures is analyzed based on the AIGA. The AIGA is a new intelligent optimum algorithm synthesized the artificial immune algorithm with the genetic algorithm, and the proposed algorithm avoids the problem of precocity, low searching efficiency and the ability to maintain satisfactorily the individual diversity.

Finally, the fatigue reliability of gear teeth subjected to bending had been analyzed by those two methods. Numerical examples show that the NMC-SMPIM and the AIGA have obvious advantages in the analysis of probabilistic structures and demonstrate reliability with a large variance coefficient and high accuracy.

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