关键词: 逼近组合法, 病态方程组, 奇异值分解法, 重分析

Abstract: Reanalysis is used for analyzing the modified structure according the initial analysis results instead of solving the equilibrium equations. It can greatly improve calculation efficiency with enough accuracy. This study proposed a modified reanalysis method by integration of singular value decomposition (SVD) and combined approximation (CA) for the singularity problems. The modified reanalysis method can solve the problem of singular stiffness matrix, as well as keep the accuracy of CA method. To validate the feasibility of the modified reanalysis, a cylinder shell example and real vehicle frame stiffness are performed by the proposed method successfully. Test results demonstrated that the modified reanalysis method can solve the singular problems efficiently with accuracy. And, by comparing the results of the two numerical examples, when the stiffness matrix has high singularity, the common method replacing the inverse by the pseudo inverse is not feasible. Therefore, the modified reanalysis method has advantages in solving singular problems.

Key words: Combined approximation, Ill-conditioned system of equations, Reanalysis, Singular value decomposition