A Most Probable Point-Based Univariate Method for Reliability Evaluation of Composite Laminates with Random and Interval Parameters

Due to complicated manufacturing processes and inherent dispersions of constituents, uncertainty is unavoidably existing in mechanical properties, including strength, of composite laminates which can be described as random or interval variables. Considering the multivariable and hybrid uncertainty, the hybrid reliability evaluation of composite laminates is quite an important problem. The objective of this paper is to construct a reliability evaluation method to evaluate hybrid reliability of composite laminates accurately and efficiently. The existence of interval variables produced a limit-state strip formed by minimum and maximum limit state function (LSF). Combining first-order reliability method (FORM) and univariate method, the paper developed a strategy to search the most probable point (MPP) of minimum and maximum LSF. In the process of MPP searching, the univariate function of interval variables is constructed by Legendre orthogonal polynomials and the least-square fitting method. Then, the minimum and maximum LSF are constructed at MPP in a similar way with interval variables which can ensure the accuracy of LSF approximation. Furthermore, Monte-Carlo simulation can be utilized to calculate interval of failure probability. Finally, the results of examples verified the accuracy and efficiency of the constructed model.