Robust inverse identification of the effective three-dimensional elastic behaviour of a piezoceramic patch bonded to a multilayer unidirectional fibre composite

The effective three-dimensional elastic behaviour of a rectangular piezoceramic patch centrally surface-bonded to a free multilayer unidirectional carbon-fibre reinforced plastic composite plate is inversely identified from three potential ones: orthotropic, quasi transversely isotropic (QTI) or transversely isotropic. This is reached through minimizing the finite element-experimental frequency relative deviations of the first eight short-circuit modes of the smart composite structure using a robust multi-objective evolutionary optimization procedure. The latter combines full factorial design of experiments (DoE)-based surface response meta-modelling of the frequency dependence on the patch’s elastic engineering constants and a non-sorting genetic algorithm of second generation. The inverse identification robustness comes from considering large uncertainties (±20%) of the design parameters nominal (initial) values. DoE-based sensitivities of the considered frequencies to the investigated piezoceramic patch’s elastic behaviour engineering constants are analyzed in order to identify the most influent design parameters. The latter are used for reducing the DoE plans and corresponding finite element computations. It is found that the bonded patch’s effective elastic behaviour is QTI (or orthotropic) when all (or the most influent) engineering constants are optimized.