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Partitioned formulation of contact-impact problems with stabilized contact constraints and reciprocal mass matrices
International Journal for Numerical Methods in Engineering ( IF 2.9 ) Pub Date : 2021-05-08 , DOI: 10.1002/nme.6739
José A. González 1 , Ján Kopačka 2 , Radek Kolman 2 , Kwang‐Chun Park 3
Affiliation  

This work presents an efficient and accuracy-improved time explicit solution methodology for the simulation of contact-impact problems with finite elements. The proposed solution process combines four different existent techniques. First, the contact constraints are modeled by a bipenalty contact-impact formulation that incorporates stiffness and mass penalties preserving the stability limit of contact-free problems for efficient explicit time integration. Second, a method of localized Lagrange multipliers is employed, which facilitates the partitioned governing equations for each substructure along with the completely localized contact penalty forces pertaining to each free substructure. Third, a method for the direct construction of sparse inverse mass matrices of the free bodies in contact is combined with the localized Lagrange multipliers approach. Finally, an element-by-element mass matrix scaling technique that allows the extension of the time integration step is adopted to improve the overall performance of the algorithm. A judicious synthesis of the four numerical techniques has resulted in an increased stable explicit step-size that boosts the performance of the bipenalty method for contact problems. Classical contact-impact numerical examples are used to demonstrate the effectiveness of the proposed methodology.

中文翻译:

具有稳定接触约束和互易质量矩阵的接触-冲击问题的分区公式化

这项工作提出了一种有效且精度提高的时间显式求解方法,用于模拟有限元接触-冲击问题。建议的求解过程结合了四种不同的现有技术。首先,接触约束由双惩罚接触影响公式建模,该公式结合了刚度和质量惩罚,保留了无接触问题的稳定性限制,以实现有效的显式时间积分。其次,采用局部拉格朗日乘子的方法,这有助于每个子结构的分区控制方程以及与每个自由相关的完全局部接触惩罚力。子结构。第三,一种直接构造接触自由体的稀疏反质量矩阵的方法与局部拉格朗日乘子方法相结合。最后,采用允许扩展时间积分步骤的逐元素质量矩阵缩放技术来提高算法的整体性能。四种数值技术的明智综合导致增加了稳定的显式步长,从而提高了双罚法在接触问题上的性能。经典的接触影响数值例子被用来证明所提出的方法的有效性。
更新日期:2021-05-08
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