Billion-design-variable-scale topology optimization of vehicle frame structure in multiple-load case

In topology optimization, sufficient resolution and a constraint volume of less than 1% are required to obtain a practical vehicle body structure without solid circular-section frames. To meet the requirement for sufficient resolution, the authors are developing voxel topology optimization software, including a finite element solver that utilizes the building cube method framework available in massively parallel environments. The authors have performed a topology optimization of billions of elements intended for a vehicle frame using 35,000-66,000 processors and measured its parallel performance. In addition, four different methods to treat multiple-load cases required for vehicle performance into single objective functions are examined. As a result, normalizing compliance with the appropriate target energy obtained by the original body-in-white frame balances the optimization performance across cases. In the single-load case, thick solid beams are generated through optimization. In contrast, such solid frames are suppressed in multiple-load cases, resulting in a structure similar to a practical body-in-white frame.