Diverse discrete material optimization for multi-patch laminates under vibration environment

In practical engineering, the design scheme is generally a compromise solution that meets various requirements. In most cases, the traditional optimization method provides a single optimized solution, which may be prone to fail during the subsequent design stage because some unpredictable requirements may be not considered in the preliminary optimization process. For example, maximizing fundamental frequency is generally regarded as the optimization objective for aerospace structures under the vibration environment in the preliminary design stage. However, the optimized solution may fail for strength, buckling, or other requirements during the subsequent detailed design stage. Therefore, it is crucial to provide multiple alternative solutions for insurance. In this paper, a diverse discrete material optimization (DDMO) framework is proposed for multi-patch laminates. It can optimize the material topology layout and fiber orientations of composite structures simultaneously and provide multiple alternative solutions that have diversity in design space and different potential performance. In this paper, a diversity index for discrete variables is proposed and the discrete material optimization (DMO) method with the diversity index constraint is employed to perform the DDMO. Two illustrative examples are used to verify the effectiveness of the proposed optimization framework, including a simple example of a composite plate and a complex engineering example of an S-shaped curved shell. Results indicate that, the proposed method can provide multiple diverse alternative solutions with similar performance in the optimization objective, which are verified to have better potential performance than the single solution by the traditional single design method. Moreover, multiple design options by the diverse optimization method can contribute to reducing the probability of redesign and shortening the design cycle.