Stochastic Methods for the Analysis of Uncertain Composites

B N Singh, Neeraj Grover

Abstract


The involvement of various processes/parameters in the manufacturing and fabrication of laminated composites and the lack of control over these constituent processes cause the uncertainty in the system parameters. Therefore, the consideration of these random parameters in the analysis of composite structures is essential. The objective of the present study is to present state-of-the-art on the stochastic modeling of composite structures. The various techniques available for the uncertainty characterization and their propagation in the deterministic solver are discussed. The significance of various approaches is presented and their applicability to quantify various uncertainties is concluded. The essential requirements to accurately model the multilayered structures are discussed by presenting the classification of available theories. The incorporation of the uncertainty quantification techniques with the deterministic structural mechanics solvers leads to the stochastic techniques such as stochastic finite element analysis. The wide range of applicability and the accuracy of finite element analysis in deterministic environment are both—an added advantage and a priori requirement of an accurate stochastic solver. The finite element method in the stochastic framework is presented to determine the governing equations for the structural behavior of laminated composite and sandwich plates. The stochastic finite element method is then presented in the context of Monte Carlo simulation and perturbation technique. Further, the influence of various uncertain parameters such as material properties, loading conditions etc. on the structural behavior of laminated composite structures is discussed by presenting the observations made in the available literature on such analyses. It is hoped that the present work could facilitate the research community involved in stochastic or deterministic analysis of laminated composites.

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