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Implicit coupling of heterogeneous and asynchronous time-schemes using a primal approach based on velocity continuity at the subdomain interface

机译:基于子域界面的速度连续性的原始方法隐含异步和异步时间方案的隐含耦合

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摘要

In the field of structural dynamics, it can be particularly interesting to consider a different time integrator and time scale in a different part of a problem (i.e. in the case of multi-physics problems, non smooth contact mechanics, seismic engineering with impacts, soil-structure interaction problems, or multiscale models using macro-element systems with a dynamic internal equilibrium). This paper presents a primal coupling algorithm based on a velocity gluing at the interface between two subdomains in order to be able to take into account both heterogeneous (different time schemes) and asynchronous (different time steps) time integrations (HATI). This algorithm allows for an implicit nonlinear resolution in providing the exact algorithmic tangent operator to maintain quadratic convergence for Newton-Raphson procedures. It is not intrusive in the finite element code as it only requires an interface element. The algorithm is presented in this paper for coupling different time schemes stemming from both Newmark families and Euler+0 integration schemes (which can be very attractive when dealing with hard contact non smooth mechanics using complementarity methods). The proposed primal approach, which is based on imposing velocity continuity at the interface, is a viable alternative to the classical dual approaches since it is highly suitable for multiscale and sub-structuring models relying on subdomains with internal time integration schemes as well as for problems using macro-element families. The stability analysis exhibits a second order accuracy of the proposed approach. A selection of numerical examples under linear and nonlinear assumptions and for multiple degree-of-freedom system is provided; these examples show that no energy is being dissipated at the interface and overlap very closely with reference solutions.
机译:在结构动态领域,在问题的不同部分中考虑不同的时间积分器和时间尺度可以特别有趣(即,在多物理问题的情况下,非平滑接触力学,抗冲击性的地震工程,土壤 - 使用具有动态内部均衡的宏观元件系统的结构交互问题,或多尺度模型)。本文介绍了基于两个子域之间的界面处的速度胶合的原始耦合算法,以便能够考虑异构(不同的时间方案)和异步(不同的时间步骤)时间集成(HATI)。该算法允许隐式非线性分辨率提供精确的算法切线操作员,以维持用于牛顿-Raphson程序的二次收敛。它在有限元代码中并不侵入,因为它只需要接口元素。本文提出了该算法,用于耦合来自纽马克族和欧拉+ 0集成方案的不同时间方案(使用互补方法处理硬接触非平滑机械时可能非常有吸引力)。基于界面处的速度连续性的提出的原始方法是经典双方法的可行替代方法,因为它非常适合多尺度和子结构模型,依赖于具有内部时间集成方案的子域以及问题使用宏元素系列。稳定性分析表现出所提出的方法的二阶精度。提供了线性和非线性假设下的数值实例和多自由度系统的选择;这些示例表明,没有能量在界面处消散并与参考解决方案非常密切地重叠。

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