Identification of elastic properties of composite plates using non-destructive two stages derivative based method and meta-heuristic hybrid optimization method / Tam Jun Hui - Tam, Jun Hui (2018)
Researchers have been investing much time and efforts in investigating non-destructive vibrational methods. Accuracy, repeatability, convergence and robustness are the important aspects determining the reliability of a non-destructive method. Evaluating the reliability of a method on the basis of these aspects is subjective because this depends on the compared methods and the applications. In this research, a derivative-based method is developed to identify the elastic properties of composite plates under various boundary conditions. The novelty consists in its composition, where it is constructed adopting the Fourier method, a weighted least squares method and the mode shape error function. The displacement function of the plate structure is defined in terms of two-dimensional Fourier cosine series which is supplemented with several one-dimensional additional terms to accommodate various boundary conditions. The derivatives of mode shape with respect to stiffness rigidity are derived and computed from the model‟s displacement function. A two-stage identification approach is proposed, in which stage 1 uses natural frequencies while stage 2 utilises mode shapes. The use of mode shapes in stage 2 is proven vital in improving the identifiability of the in-plane shear modulus and Poisson‟s ratio. However, the effectiveness of this method is dependent on the initial values. Therefore, a meta-heuristic hybrid optimisation method is proposed to enhance the exploratory and exploitative search processes. In early iterations, the two-point standard mutation is utilised collaboratively with the concept of the ACO unrepeated tour to evade local entrapments, while the one-point refined mutation is used in later iterations to supplement the exploitative search process, which is mainly contributed by the PSO. The proposed method is validated using test functions and well-known engineering design problems. It exhibits an excellent global search capability in the presence of constraints. Furthermore, the applicability of the proposed method in material identification is investigated and compared with those of the conventional methods, namely, ACO, GA and PSO. It is proven to be relatively better than the conventional methods in various aspects. Instead of adopting the conventional natural frequency error function, the FRF error function is used to improve specifically the identifiability of the in-plane shear modulus and Poisson‟s ratio. The effectiveness of the FRF error function in material identification consists in the trade-off range between those of the natural frequency error function and mode shape error function. Comparing the two-stage derivative-based method with the meta-heuristic hybrid optimisation method, the latter is better in terms of accuracy and robustness, while the former exhibits superiority in the aspects of repeatability and convergence.