Robust topological design of laminated composite plate under interval random hybrid uncertainties

The laminated composite plate is widely used in contemporary industrial applications. In this work, a robust topology optimisation method is studied to overcome the possible uncertainties existed in the laminated composite plate. Based on the first-order shear deformation theory (FSDT), the laminated composite plate is modelled. A hybrid interval random model is employed to describe the imprecise probability of uncertain material properties and ply orientations in the laminated composite plate, which considers the measurement accuracy and cost in actual engineering. By using the first-order Taylor series expansion twice, the imprecise probabilistic parameters can be exactly expressed by interval values. A hybrid perturbation technique (HPT) is proposed to efficiently estimate the 'worst-case' of the laminated composite under uncertainties. The sensitivity of the structural mean compliance in the 'worst-case' with respect to design variables is further derived. The bi-directional evolutionary structural optimisation (BESO) method is employed to find the robust distribution of the material. Several numerical examples including both static and dynamic situations of the CCCC plate are presented, and the effectiveness of the proposed method is demonstrated clearly.