A fast calculation method for dynamic topology optimization based on hybrid spectral element method

In this study, a Hybrid Spectral Element Method (HSEM) integrated with Equivalent Static Load (ESL) in the frequency domain is suggested. This integration aims to enhance the computational efficiency of dynamic topology optimization. In comparison with existing techniques, the proposed HSEM transforms the governing equation of dynamic analysis into a spectral element equation within the frequency domain by utilizing the Fast Fourier Transform (FFT) algorithm. This approach enables the representation of both structural displacements and external loads in spectral forms, potentially leading to a reduction in the number of dimensions compared to traditional time-interval-based methods. By using spectral representation, a low-dimensional ESL set can be constructed in the frequency domain for model reduction. To validate the effectiveness of the suggested proposed method, extensive analyses and comparisons using various two-dimensional (2D) and three-dimensional (3D) examples are carried out. The obtained results demonstrate a substantial improvement in computational efficiency, both during the dynamic analysis phase and the quasi-static topology optimization phase, while maintaining high levels of accuracy. Moreover, even as the scale of the model increases, our method maintains its advantage in computational efficiency. In the test examples, a maximum speedup ratio of up to 6.54 times was observed, indicating the significant potential of the proposed HSEM-ESL approach in enhancing the performance of dynamic topology optimization tasks.