Baranova S, Mogilevskaya S G
Department of Civil, Environmental and Geo-Engineering, University of Minnesota, 500 Pillsbury Drive S.E., Minneapolis MN, 55455, USA.
Philos Trans A Math Phys Eng Sci. 2022 Sep 5;380(2231):20210420. doi: 10.1098/rsta.2021.0420. Epub 2022 Jul 18.
This paper reviews several leading approaches for asymptotic modelling of thin layers in elastostatics and wave propagation phenomena. The issues related to applications of the so-called 'equivalent' or 'effective' boundary conditions and their interpretations are highlighted. Comparative analysis of asymptotic models is performed for a two-dimensional elastostatic case using a novel complex variables-based modelling tool. Its implementation allows for straightforward derivations of higher order boundary conditions for problems with layers of arbitrary sufficiently smooth curvatures. Explicit expressions for the conditions up to the third order are provided. All models are tested using available benchmark solutions and the solutions for the limiting cases of the layer parameters. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'.
本文综述了弹性静力学和波传播现象中薄层渐近建模的几种主要方法。强调了与所谓“等效”或“有效”边界条件的应用及其解释相关的问题。使用一种基于复变量的新型建模工具，对二维弹性静力学情况进行了渐近模型的比较分析。它的实现使得对于具有任意足够光滑曲率层的问题，能够直接推导高阶边界条件。给出了直至三阶条件的显式表达式。所有模型都使用可用的基准解以及层参数极限情况的解进行了测试。本文是主题为“多尺度复杂介质和结构化超材料中的波产生与传播（第1部分）”的一部分。
