Analysis of a Space-Time Discretization for Dynamic Elasticity Problems Based on Mass-Free Surface Elements
Analysis of a Space-Time Discretization for Dynamic Elasticity Problems Based on Mass-Free Surface Elements
复制标题
基于无质量表面单元的动弹性问题时空离散化分析
DOI：
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发表时间：
2009
影响因子：
2.9
通讯作者：
Barbara Wohlmuth
中科院分区：
文献类型：
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作者：
C. Hager;Barbara Wohlmuth
本文提出了一种基于修正质量矩阵的时空离散化方法。与元素的表层相关联的质量被重新分配，使得边界处的惯性被消除。这种方法的动机是观察到标准的时空离散化方案应用于动态接触问题产生伪振荡。对于这些问题的数值模拟，一种广泛使用的方法是基于代表接触应力的拉格朗日乘子。但将代数接触条件与惯性体积项相结合，往往会产生非物理的接触应力，从而失去算法的稳定性。我们修改的矩阵是通过不需要额外计算的非标准正交公式计算的。此外，将原有算法的守恒特性延续到改进方法中，仍然满足标准的最优先验估计。数值算例验证了该方法的最优性及其在接触问题中的镇定效果。
In this paper, a new space-time discretization is proposed which is based on a modified mass matrix. The mass associated with a surface layer of elements is redistributed such that the inertia at the boundary is removed. This approach is motivated by the observation that standard space-time discretization schemes applied to dynamic contact problems yield spurious oscillations. A widely used approach for the numerical simulation of these problems is based on Lagrange multipliers which represent the contact stresses. But the algebraic contact conditions in combination with the inertia volume terms often yield nonphysical results for the contact stresses, and the stability of the algorithm can be lost. Our modified matrix is calculated via nonstandard quadrature formulas that require no extra computational effort. In addition, the conservation properties of the underlying algorithm are carried over to the modified method, and the standard optimal a priori estimates are still satisfied. Numerical examples confirm the optimality of the approach and its stabilization effect applied to contact problems.