Multi-scale design of composite materials and structures for maximum natural frequencies

This paper introduces a hierarchical concurrent design approach to maximizing the natural frequency of a structure. Multiple material phases are considered in the topology optimization performed on both the macro and micro scales. A general problem for composite structure and material design is formulated that contains the cellular design problem as a special case. The design of the macro structure and material micro structure is coupled. The designed material properties are applied to the analysis of the macro structure, while the macro structure displacement field is considered in the sensitivity analysis on the micro scale. The material edistribution is controlled by an optimality criterion for frequency maximization. Convergent and mesh-independent bi-directional evolutionary structural optimization (BESO) algorithms are employed to obtain the final optimal solution. Several numerical examples of composite structures and materials are presented to demonstrate the capability and effectiveness of the proposed approach. Results include various orthotropic or anisotropic composite materials, as well as vibration-resisting layouts of the macro structure. In-depth discussions are also given on the effects of the base material phases and the assignment of the volume fractions on each scale.