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 引用本文: 邓佳东, 程耿东. 基于局部插值的结构动力模型降阶方法[J]. 力学学报, 2012, 44(2): 342-350.
Deng Jiadong, Cheng Gengdong. STRUCTURE DYNAMIC MODEL REDUCTION TECHNIQUE BASED ON LOCAL INTERPOLATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2012, 44(2): 342-350.
 Citation: Deng Jiadong, Cheng Gengdong. STRUCTURE DYNAMIC MODEL REDUCTION TECHNIQUE BASED ON LOCAL INTERPOLATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2012, 44(2): 342-350.

## STRUCTURE DYNAMIC MODEL REDUCTION TECHNIQUE BASED ON LOCAL INTERPOLATION

• 摘要: 提出了一种基于局部插值对大型结构有限元模型的特征值问题进行降阶的方法. 该方法通过局部插值将复杂结构的有限元模型中节点的位移用凝聚点的位移插值来表示, 从而得到用插值函数表示的简化基向量, 实现对结构广义特征值问题的降阶. 为了提高降阶模型的精度, 采用非协调元的插值函数作为局部插值函数来弱化凝聚后的结构刚度, 并且在有限元模型上进行逆迭代, 对得到的降阶后的广义特征值问题的特征值和特征向量进行改善. 为了提高模型降阶的效率, 采用规整网格包围整个结构生成均匀的凝聚点, 高效地确定了有限元模型中节点所依附的凝聚点. 最后, 对 3 个机床部件的模态分析验证了提出的简化方法的高效性和可行性.

Abstract: Based on complex structural finite element model, a new reduction method of structural dynamic model using local interpolation is proposed in this paper. The displacement of a node in the finite element model is obtained through interpolation of the displacements of the condensation nodes it attaches to. Every entry of the dynamic condensation matrix is formed by interpolation functions. To improve accuracy of the reduction method, the shape function of the non-conforming element is adopted as the interpolation function to lower the reduced structural stiffness after condensation, and the eigenvalues and eigenvectors are ameliorated through inverse iteration on the finite element model. To enhance efficiency of the reduced method, regular grids which just encompass the structure are employed to generate the condensation points. Due to the regularity of the grids, we can easily determine the condensation points to which a node in the finite element model attaches. Finally, mode analyses of three machine tool components demonstrate the effectiveness and the feasibility of the reduction method proposed in this article.

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