Modeling Spatially Varying Uncertainty in Composite Structures Using Lamination Parameters

Abstract

An approach is presented for modeling spatially varying uncertainty in the ply orientations of composite structures. Lamination parameters are used with the aim of reducing the required number of random variables. Karhunen–Loève expansion is employed to decompose the uncertainty in each ply into a sum of random variables and spatially dependent functions. An intrusive polynomial chaos expansion is proposed to approximate the lamination parameters while preserving the separation of the random and spatial dependency. Closed-form expressions are derived for the expansion coefficients in two case studies; an initial example in which uncertainty is modeled using random variables, and a second random field example. The approach is compared against Monte Carlo simulation results for a variety of layups as well as closed-form expressions for the mean and covariance. By summing the polynomial chaos basis functions through the laminate thickness, the separation of the random and spatial dependency may be preserved at a laminate level and the number of random variables reduced for some minimum number of plies. The number of variables increases nonlinearly with the number of Karhunen–Loève expansion terms, and as such, the approach is only beneficial in low-order expansions using relatively few Karhunen–Loève expansion terms.