A normalization strategy for BESO-based structural optimization and its application to frequency response suppression

The bi-directional evolutionary structural optimization (BESO) method has been widely studied and applied due to its efficient iteration and clear boundaries. However, due to the use of the discrete design variable, numerical difficulties are more likely to occur with this method, especially in cases with strong nonlinearity. This limits the application of the BESO method in certain cases, such as the suppression of structural dynamic frequency response under high-frequency excitation. In this work, a normalization strategy is proposed for the BESO-based topology optimization, by which the magnitude of the sensitivities can be efficiently unified to the same order to avoid the possible numerical instabilities caused by the nonlinearity. To validate its merit in applications, the normalization-based BESO (NBESO) method is proposed for minimizing the structural frequency response. By means of the weighted sum method, a normalized weighted sum method is also proposed for multi-frequency involved problems. A series of 2D and 3D numerical examples is presented to illustrate the advantages of the NBESO. The effectiveness of the NBESO for multi-frequency response suppression is also demonstrated, in which the frequency ranges below and above the eigenfrequency are involved, respectively.