Abstract:Sheet forming is a very important design and manufacturing technology in the modern automotive industry. At present, the element most commonly used for sheet forming calculations is the quadrilateral dynamic nonlinear shell element. Such shell elements are computationally fast, but they also present common problems with mainstream quadrilateral elements when dealing with dynamic large deformations. Compared with the quadrilateral element, the triangular element has a better automatic mesh generation algorithm, which can well approximate the complex geometric surface. The element used in this paper is the Edged-based smoothed triangular shell element (EST) proposed by co-author Cui. The element is a constant strain element and can be obtained high calculation accuracy without adding additional degrees of freedom and parameters. Applying the EST unit to the sheet forming simulation calculation can simplify the simulation process and improve the calculation efficiency. However, for an explicit finite element algorithm with stable conditions, it still represents a huge amount of calculation for larger stampings. Therefore, we use GPU to improve simulation efficiency. Implementation details with computer unified device architecture (CUDA) are considered in this work. In this paper, all the array variables in the calculation process are stored in the global memory. Before copying the data to GPU, we split the multidimensional array into multiple one-dimensional arrays, which can effectively reduce the jump between non-aligned memory accesses between threads. Besides, to avoid the impact of excessive data transfer between the host and the device, all the array variables are transmitted to the device at the beginning of the program. Furthermore, asynchronous data transmission strategy and novel dependency relationship link based method for efficiently solving parallel explicit shell element equations are used to improve the utilization ratio of GPU. Finally, the paper also tries to use the mixed precision algorithm to further improve the computational efficiency. We found that the parallel calculation of sheet metal forming by GPU can ensure the calculation accuracy and obtain the calculation result consistent with the CPU. The speedup of GPU computation increases as the number of elements increases. At the same time, it can also be found that when the speedup is increased to a certain extent, it will not increase and tend to be stable, because the hardware resources for one concurrent execution in the GPU are limited. However, the computational speedup can be further improved by optimizing the way resources are allocated in the program and using GPU hardware with more CUDA cores. Furthermore, if a mixed precision algorithm is used, there will be a small increase in computational efficiency. Of course, the calculation accuracy will be reduced when using the mixed precision calculation, but we believe that it still meets the needs of engineering calculations.Keywords: Sheet metal forming, GPU, Explicit finite element, Parallel computing, Mixed precision