Laminate component method for optimal design of hybrid structures for vibration reduction

Abstract

Steel-composite hybrid structures play an important role in vibration reduction in modern ship hulls. The optimal design of a hybrid structure involves simultaneous materials selection and determination of component sizes. It is difficult to establish mathematical optimisation formulations with only continuous variables and a single structural analysis model. The employment of different design variables, such as choice of materials, elastic modulus of materials, topological distribution of materials and thickness of components, may lead to different hybrid structural optimisation models with a mixture of continuous and discrete variables. In this paper, a laminate component method of modelling is proposed for the optimal design of hybrid structures. By introducing the concept of laminated components, hybrid structural design problems are formulated as a size or topology optimisation problem with all materials considered for selection within one structural analysis model. Three kinds of mathematical formulations for optimal design of materials selection in hybrid steel-composite structures are established considering the vibration-level difference, stress and displacement constraints. For ease of implementation, a mapping transformation function approach is presented to convert the mixed variable formulation to the one with only continuous variables. Comparative studies on different formulations for the hybrid steel-composite floating raft vibration reduction design show the effectiveness of the proposed methods.

Keywords:

• hybrid structures
• material selection
• structural optimisation
• vibration reduction
• composite material

Acknowledgement

This work was partially supported by the National Natural Science Foundation of China (grant nos. 10672100, 11072149). This support is gratefully acknowledged by the authors.