改进的r-收敛和h-收敛自适应有限元方法

吉林大学学报(工学版) ›› 2000, Vol. ›› Issue (3): 56-60.

改进的r-收敛和h-收敛自适应有限元方法

刘寒冰, 龚国庆, 魏媛

吉林工业大学理学院, 吉林长春 130025

收稿日期:1999-12-18 出版日期:2000-07-25
基金资助:
国家自然科学基金资助项目(19872029)

Improved r-and h-adaptive Finite Element Method Based on Perturbation and Element Energy Ratio

LIU Han-bing, GONG Guo-qing, WEI Yuan

College of Sciences, Jilin University of Technology, Changchun 130025, China

Received:1999-12-18 Online:2000-07-25

摘要/Abstract

摘要： 提出了一种基于矩阵摄动理论和单元能量比率的改进的r收敛和h收敛自适应有限元方法。在结构动力分析中,通过r收敛过程,实现网格最优划分;通过对单元能量比率变化量的判断,进行h-收敛自适应有限元过程,实现最优局部网格再加密过程,以尽量少的网格数,得到高精度的有限元解。最后通过大量的算例,说明了该方法的实用性和有效性。

关键词: 迭代摄动, 单元能量比率, r-收敛和h-收敛自适应有限元, 网格优化, 固有频率

Abstract: In this paper,the improved r and h adaptive finite element method based on matrix perturbation theory and element energy ratio is proposed.In structure vibration analysis,through r convergence adaptive finite element process,mesh optimization can be realized.In the light of the judgement on the changes in the magnitude of element energy ratio,a local optimal refinement can be achieved in the process of h convergence adaptive finite element method so that more accurate finite element solutions can be obtained with as least grids as possible.A lot of numerical examples are given and the proposed approach is shown to be feasible and effective.

Key words: iterative perturbation, element energy ratio, r and h adaptive FEM, mesh optimization, natural frequency

中图分类号:

O242.21

刘寒冰, 龚国庆, 魏媛. 改进的r-收敛和h-收敛自适应有限元方法[J]. 吉林大学学报(工学版), 2000, (3): 56-60.

LIU Han-bing, GONG Guo-qing, WEI Yuan. Improved r-and h-adaptive Finite Element Method Based on Perturbation and Element Energy Ratio[J]. 吉林大学学报(工学版), 2000, (3): 56-60.

参考文献

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