Reliability Analysis of Composite Laminates Based on Generating Function Approach

The reliability analysis of composite laminates involves multivariable, non-normal, non-linear performance function and failure correlation, etc. Aiming at analysis problems, generating function approach is introduced via constructing special generating functions, which are used to describe probability distribution of load, resistance and resistance sequence, by defining relevant compositional operators. By means of the compositional operation of generating functions, reliability analysis model of composite laminates is established based on first/last ply failure criteria and Tsai-Hill strength theory. This method can be applied to the reliability evaluation of structure systems with many random variables(including non-normal random variables) and the non-linear performance function. Failure correlation between failure paths of laminates due to containing common failure elements and failure correlation within each failure path due to sharing the common random load source are considered by this method. In compositional operations of generating functions, K-means clustering and like terms collecting techniques are used to reduce computational costs and the efficiency is dramatically improved. Specific examples are given based on this approach. Analysis results show that the reliability value of the proposed method is closer to the Monte Carlo simulation results than that of traditional first order reliability methods. The new method can provide a new idea for the strength reliability analysis of composite laminates. © 2019 Journal of Mechanical Engineering.