A novel GPU-accelerated topology optimization method for large-scale steel frame structures under extreme loading conditions

Due to limitations in computational resources, conventional topology optimization in civil engineering primarily focuses on the component level. This approach fails to meet the optimization requirements of large-scale and complex civil structures under multiple complex loading conditions. This study achieves a threefold increase in computational speed and a two-thirds reduction in CPU memory usage by implicitly assembling the node index matrix and computing compliance derivatives within the GPU, combined with a reanalysis strategy of the solution. The proposed method enables large-scale topology optimization with nearly 100 million 3D elements and 300 million degrees of freedom on a standard consumer-grade computer. In the case study of a frame design with 100 million elements, the average iteration time is only 362 s. This open-source, low-cost framework will facilitate the development of other large-scale topology optimization algorithms, such as stress-based and multi-material topology optimization methods for large-scale structures. To address the instability associated with the minimization of maximum compliance under multiple loading conditions, this study introduces an average compliance measure and the KS aggregation function to reformulate the problem. Consequently, for multiple loading conditions, an approach for minimizing maximum compliance based on three-field solid isotropic material with penalization (SIMP) is established. Numerical results demonstrate a stable iterative process and improved results, confirming that large-scale complex structures subjected to extreme loading conditions can be designed on consumer-grade computers.