The coupling of three-dimensional (3D) and plane (2D) finite element (FE) models to form a single hybrid 3D–2D model is considered for linear elastodynamic problems. The 2D model is used to represent a large thin 3D computational domain where the solution behaves approximately in a 2D (plane-elasticity) way. Problems where the normal displacement is important in the thin region (bending) are excluded. The hybrid model, if designed properly, is a more efficient way to solve the full 3D model over the entire problem. This paper focuses on the way the 3D–2D coupling is performed, and on the coupling error generated. The Panasenko technique is used to couple the 3D and 2D models. This method has been used previously for mixed-dimensional coupling in steady-state problems, as well as for 2D–1D coupling of acoustic waves. Here it is being used for the first time for the 3D–2D coupling of time-dependent elastic problems. The hybrid formulation is derived, and is shown to be well-posed. It is shown that the Panasenko method is extremely simple to implement in the framework of FE analysis, yet the resulting coupling yields a rather small error level, provided the 3D–2D interface is sensibly placed. The numerical accuracy and efficiency of the method are explored for a couple of example problems. In particular, it is shown that spurious reflections from the interface back into the 3D region are negligible.

对于线性弹性动力学问题，考虑耦合三维 (3D) 和平面 (2D) 有限元 (FE) 模型以形成单个混合 3D-2D 模型。2D 模型用于表示大型薄 3D 计算域，其中解决方案的行为近似为 2D（平面弹性）方式。排除了在薄区域（弯曲）中法向位移很重要的问题。如果设计得当，混合模型是解决整个问题的完整 3D 模型的更有效方法。本文重点介绍 3D-2D 耦合的执行方式，以及产生的耦合误差。Panasenko 技术用于耦合 3D 和 2D 模型。该方法以前已用于稳态问题中的混合维耦合，以及声波的 2D-1D 耦合。在这里，它首次用于时间相关弹性问题的 3D-2D 耦合。混合公式被推导出来，并且被证明是适定的。结果表明，Panasenko 方法在有限元分析框架中实现起来非常简单，但如果合理放置 3D-2D 接口，则由此产生的耦合会产生相当小的误差水平。针对几个示例问题探讨了该方法的数值准确性和效率。特别是，从界面返回到 3D 区域的杂散反射可以忽略不计。然而，只要合理放置 3D-2D 界面，由此产生的耦合会产生相当小的误差水平。针对几个示例问题探讨了该方法的数值准确性和效率。特别是，从界面返回到 3D 区域的杂散反射可以忽略不计。然而，只要合理放置 3D-2D 界面，由此产生的耦合会产生相当小的误差水平。针对几个示例问题探讨了该方法的数值准确性和效率。特别是，从界面返回到 3D 区域的杂散反射可以忽略不计。