图形处理器上免组装有限元屈曲分析

Assembly-Free Buckling Analysis on Graphics Processing Unit

为了提高大型三维有限元屈曲分析的速度,克服大规模屈曲拓扑优化的计算速度制约,提出了一种基于免组装有限元的线性屈曲分析算法。针对屈曲分析涉及应力刚度矩阵的特殊性,使用了逆迭代法求解特征值问题;利用体素网格的单元一致性,免组装有限元避免了总体刚度矩阵的组装和存储,减少了计算过程中的内存占用,且有利于并行运算;在图形处理器(GPU)上进行稀疏矩阵与向量乘积的运算,利用并行运算进一步加速了有限元的求解速度。算例结果表明,该算法能有效提高大型三维结构屈曲分析的计算速度,与商用软件Ansys、HyperWorks相比,计算时间可减少60%以上,且随着模型自由度的增加,计算速度提高的程度更加显著。

In order to improve the computational efficiency of large-scale 3D finite element analysis for buckling problem, and to overcome the limitation of computation speed for the large- scale buckling topology optimization, this paper presents a linear buckling analysis algorithm based on the assembly-free finite element method. For the particularity that buckling analysis involves stress stiffness matrix, an inverse iteration method is used to solve eigenvalue problems. In the assembly-free method, the structure is discretized by uniform voxels and there is no need to assemble and store the global stiffness matrix. So the memory footprint is reduced, which is beneficial to parallel computation. The sparse matrix-vector multiplication is performed on GPU （graphics processing unit）, so the parallel computation can further accelerate the speed of finite element analysis. Numerical examples demonstrate that this algorithm can improve the speed of large-scale 3D linear buckling analysis. Compared with the commercial software Ansys and HyperWorks, the computing time of this algorithm can be reduced by more than 60%, and the improvement of the computing speed becomes more obvious with the increase of the model＇s degree of freedom.