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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >The Nitsche method applied to a class of mixed-dimensional coupling problems
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The Nitsche method applied to a class of mixed-dimensional coupling problems

机译：Nitsche方法应用于一类混合维耦合问题

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摘要

A computational approach for the mixed-dimensional modeling of time-harmonic waves in elastic structures is proposed. A two-dimensional (2D) structure is considered, that includes a part which is assumed to behave in a one-dimensional (1D) way. The 2D and 1D structural regions are discretized using 2D and 1D finite element formulations. The coupling of the 2D and 1D regions is performed weakly, by using the Nitsche method. The advantage of using the Nitsche method to impose boundary and interface conditions has been demonstrated by various authors; here this advantage is shown in the context of mixed-dimensional coupling. The computational aspects of the method are discussed, and it is compared to the slightly simpler penalty method, both theoretically and numerically. Numerical examples are presented in various configurations: where the 1D model is either confined laterally or laterally free, and where the 2D part is either simply connected or doubly connected. The performance is investigated for various wave numbers and various extents of the 1D region. Varying material properties and distributed loads in the 1D and 2D parts are also considered. It is concluded that the Nitsche method is a viable technique for mixed-dimensional coupling of elliptic problems of this type.
机译：提出了一种弹性结构中时谐波混合模型的计算方法。考虑了二维（2D）结构，该结构包括假定以一维（1D）方式工作的部分。使用2D和1D有限元公式离散化2D和1D结构区域。通过使用Nitsche方法，很难对2D和1D区域进行耦合。许多作者已经证明了使用Nitsche方法施加边界和界面条件的优势。在此，在混合尺寸耦合的情况下显示了该优点。讨论了该方法的计算方面，并在理论上和数值上将其与较简单的惩罚方法进行了比较。数值示例以各种配置呈现：其中一维模型在横向或横向自由约束，而二维零件在简单连接或双向连接中。对于各种波数和一维区域的各种范围，研究了性能。一维和二维零件中的材料特性和分布载荷也要考虑变化。结论是，尼采方法是解决这类椭圆问题的多维混合的可行技术。

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