A new method for concurrent multi-scale design optimization of fiber-reinforced composite frames with fundamental frequency constraints

This paper proposes an efficient methodology for concurrent multi-scale design optimization of composite frames considering specific design constraints to obtain the minimum structure cost when the fundamental frequency is considered as a constraint. To overcome the challenge posed by the strongly singular optimum and the weakness of the conventional polynomial material interpolation (PLMP) scheme, a new area/moment of inertia-density interpolation scheme, which is labeled as adapted PLMP (APLMP) is proposed. The APLMP scheme and discrete material optimization approach are employed to optimize the macroscopic topology of a frame structure and microscopic composite material selection concurrently. The corresponding optimization formulation and solution procedures are also developed and validated through numerical examples. Numerical examples show that the proposed APLMP scheme can effectively solve the singular optimum problem in the multi-scale design optimization of composite frames with fundamental frequency constraints. The proposed multi-scale optimization model for obtaining the minimum cost of structures with a fundamental frequency constraint is expected to provide a new choice for the design of composite frames in engineering applications.