Frequency optimization is an important issue in the design of structures subjected to dynamic loading. The response of a structure to dynamic loading depends mainly on the first natural frequency of the structure because the resonance occurs when the frequency of dynamic loading is close to one of the natural frequencies. In order to avoid intensive vibration, it is necessary to shift the first frequency of the structure from the frequency range of the dynamic loading. Many papers have been concerned with frequency optimization problems of linear structures. While there are also a few papers for optimization of structures with geometrical nonlinearity, material nonlinearity has not considered yet. The basic concept of the Evolutionary Structural Optimization (ESO) method is a systematically removing of inefficient ma-terials, while the residual shape of the structure evolves into an optimum design. Some re-searchers proposed new methods such as Bi-directional Evolutionary Structural Optimization (BESO) to improve the ESO procedure. This paper pertains to topology optimization using the BESO method in order to maximize the first eigenfrequency of structures with elasto-plastic bodies. In order to obtain the frequencies of a structure with elasto-plastic bodies, it is necessary to perform a two-step numerical analysis; a nonlinear static analysis and a modal analysis. The advantages of the proposed method are verified by several numerical examples. The optimum results show that it is possible to solve topology optimization problems for the fundamental eigenfrequency maximization of elasto-plastic bodies using the BESO method. Convergent solid-void and bi-material optimal solutions in two states of elastic and elasto-plastic are obtained.

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