Fuzzy uncertainty propagation in composites using Gram-Schmidt polynomial chaos expansion

Dey, S., Mukhopadhyay, T., Khodaparast, H. Haddad and Adhikari, S. (2016) Fuzzy uncertainty propagation in composites using Gram-Schmidt polynomial chaos expansion. Applied Mathematical Modelling, 40 (7-8), 4412-4428. (doi:10.1016/j.apm.2015.11.038).

Abstract

The propagation of uncertainty in composite structures possesses significant computational challenges. Moreover, probabilistic descriptions of uncertain model parameters are not always available due to lack of data. This paper investigates on the uncertainty propagation in dynamic characteristics (such as natural frequencies, frequency response function and mode shapes) of laminated composite plates by using fuzzy approach. In the proposed methodology, non-intrusive Gram-Schmidt polynomial chaos expansion (GPCE) method is adopted in uncertainty propagation of structural uncertainty to dynamic analysis of composite structures, when the parameter uncertainties represented by fuzzy membership functions. A domain in the space of input data at zero-level of membership functions is mapped to a zone of output data with the parameters determined by D-optimal design. The obtained meta-model (GPCE) can also be used for higher α-levels of fuzzy membership function. The most significant input parameters such as ply orientation angle, elastic modulus, mass density and shear modulus are identified and then fuzzified. The proposed fuzzy approach is applied to the problem of fuzzy modal analysis for frequency response function of a simplified composite cantilever plates. The fuzzy mode shapes are also depicted for a typical laminate configuration. Fuzzy analysis of the first three natural frequencies is presented to illustrate the results and its performance. The proposed approach is found more efficient compared to the conventional global optimization approach in terms of computational time and cost.

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