Simulation of a Gaussian random field over a 3D surface for the uncertainty quantification in the composite structures

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This paper presents a numerical method to simulate a Gaussian random field over a 3D surface whereas the existing methods in the literature are limited to simple 2D surfaces. This new approach is summarized in the following. First, a covariance function is proposed based on the shortest path between two points on the 3D surface. Second, the Karhunen–Loeve expansion is discretized using a coupling between two methods: the Galerkin method with the fast marching method (for computing the covariance function with the shortest path). The proposed numerical method is illustrated with an application to a composite structure representing a chair. The fiber volume fraction, the ratio between fibers and resin volumes, is considered to be uncertain. This uncertain parameter is directly linked to the mechanical parameters of the material. The structural integrity of this structure is represented by the maximal deflection and the maximal Tsai–Wu criterion. Monte Carlo simulations are used to carry out the uncertainty quantification of these responses with respect to the uncertain parameter.