【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。更多还原

【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.更多还原