Multi-scale design of composite material structures for maximizing fundamental natural frequency

Abstract

This study deals with the topology optimization (TO) of linear elastic composite structures considering fundamental natural frequency maximization. The concept of functionally graded structures (FGS) is used for anisotropic composite material structure design to improve the structural dynamic performance. The rational approximation of material properties (RAMP) method was employed as an alternative to the solid isotropic material with penalization (SIMP) method to improve the convergence stability for eigen-frequency problem. In the SIMP method, the occurrence of local eigen-modes at low frequencies in the void region causes ill-convergence, whereas the RAMP method prevents local eigen-modes from occurring. The method of moving asymptotes is used as an optimizer. Numerical verification was performed for three structural types: cantilever beam, double-clamped beam, and four-pinned beam structure. In addition, for cantilever beam design, bi-objective optimization for maximizing fundamental natural frequency as well as minimizing structural compliance was performed using the adaptive weighting method that quantitatively reflects the designer's preference by adjusting the weight for each objective function at each iteration.