Assembly-Free Buckling Analysis on Graphics Processing Unit

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.