Uncertainty Quantification of Dynamic Characteristics of Composites - a Fuzzy Approach

The quantification of uncertainty in composite structures has intuitively significant threat to ensure structural reliability. Due to inherent complexities, composite structures are difficult to manufacture accurately according to its exact design specifications resulting in unavoidable uncertainties. Typical uncertainties are inadvertently induced due to intralaminate voids, incomplete curing of resin, excess resin between plies, excess matrix voids, porosity, variations in material properties and fibre parameters. In general, random field models are extensively used to represent a spatially varying function. Different probabilistic approaches (Monte Carlo simulation, perturbation methods, random matrix, and generalized polynomial chaos with Karhunen-Loève expansion) are employed for composites. In a probabilistic setting, uncertainty associated with the system parameters can be modelled as random variables or stochastic processes using the so-called parametric approach. But in real-life situation due to the availability of limited sample data (crisp inputs), it will be more practical or realistic to follow non-probabilistic approach rather than probabilistic approach. In the present study, fuzzy approach is introduced to carry out the uncertainty propagation in natural frequencies of laminated composite plates using Gram-Schmidt Polynomial Chaos (PC). The proposed PC fuzzy model is integrated with finite element to predict the possible two extreme bound of responses for different degree of fuzziness. The fuzzy variable is represented as a set of interval variables via membership function. The most significant input parameters are identified and then fuzzified. Fuzzy analysis of the first three natural frequencies for typical laminate configuration is presented to illustrate the results and its performance