Closed-Form Probabilistic Analysis of Lamination Parameters for Composite Structures

Probabilistic analyses allow predicting the stochastic distribution of an output variable (e.g., the buckling load of a structure) based on the stochastic distribution of input parameters (e.g., material and geometric properties). In the probabilistic analysis of composite structures, one important quantity that can be subject to scatter is the ply or fiber orientation of the layers. Laminates with a large number of plies lead to a large number of random variables, which makes the probabilistic analysis very time consuming. Lamination parameters allow describing any ply layup by a maximum of 12 parameters. They have therefore been used for the design optimization of thick laminates. In the current paper, a two-step procedure is considered for using lamination parameters for probabilistic analyses of composite structures with many plies. In the first step, the stochastic distribution of lamination parameters is determined. In the second step, the actual probabilistic analysis is performed. A closed-form solution for the stochastic moment of lamination parameters is presented. Furthermore, the paper discusses under which circumstances lamination parameters are approximately normally distributed, which allows increasing the efficiency of both steps.