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Multi-Scale Uncertainty Quantification of Fiber Reinforced Composites Using Polynomial Chaos Decomposition

MISHAL THAPA, SAMEER B. MULANI and ROBERT WALTERS

Abstract


A new non-intrusive polynomial chaos (PC) method is applied to quantify the uncertainties that exists at different scales of a fiber reinforced (FRP) composite to obtain the stochastic effective material properties as well as the responses: stresses and displacements of a composite structure. The inherent uncertainties in matrix and fiber properties at micro-level and the uncertainties in geometric properties-ply orientation and ply thickness- at component/macro level are used to obtain random responses. To account for the propagation of the uncertainties, a new approach known as “Polynomial Chaos Decomposition with Differentiation (PCDD)â€, which is based upon the differentiation of basis orthogonal polynomials as well as sensitivity calculation of the response is implemented that requires 50 % samples of the wellestablished PC methods. The sensitivities in PCDD are also calculated using a new technique known as ‘ModFFD’, which is a higher order finite difference. The multiscale modeling presented here consists of two stages. In the first stage, the PCDD is implemented to obtain the stochastic model of effective material properties of a graphite-fiber/epoxy-matrix FRP composite using Halpin Tsai micromechanics model. In the second stage, the stochastic model of effective material properties is used along with the uncertain geometric properties to determine the response behavior of a laminate. The responses of a composite plate are generated by commercial finite element analysis software for PCDD analysis. The results are then compared with the 50,000 LHS samples, which illustrates the computational advantage of implementing this new method for UQ in multi-scale modeling of a FRP laminate.

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