A consistently linearized spectral stochastic finite element formulation for geometric nonlinear composite shells

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Abstract Material and geometrical properties have a major influence on the structural behavior of geometric nonlinear shell structures. Therefore, uncertain structural parameters have to be considered within the context of stochastic structural analysis. The Monte Carlo simulation (MCS) is a widely used method for estimating statistical properties of the random structural response. Considering the computation time, however, this technique is challenging for complex finite element (FE) models and requires numerical efficient surrogate modelling approaches. An efficient way to propagate parametric uncertainties through complex models is the polynomial chaos expansion (PCE). Within the spectral stochastic finite element method (SFEM), the PCE is integrated into the FE formulation of structural elements. The application of the SFEM to geometrical nonlinear mechanical structures remains comparatively unexplored. In this paper, we present a geometric nonlinear spectral stochastic shell formulation. We use a layerwise formulation of the linear elastic material law to describe the behavior of composite materials. In order to apply Newton’s method during the nonlinear solution procedure, all equations are consistently linearized to achieve a quadratic convergence in the iteration behavior. Two numerical examples show the applicability and efficiency of the presented spectral stochastic FE formulation. The SFEM results show a very good agreement compared to the results of the MCS. Special focus is set on the polynomial basis, which has a significant influence on the quality of the results, but also on the computational effort. We show, that the SFEM calculation provides a surrogate model, that can be used efficiently for further post-processing computations.

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