The derivation of the boundary conditions is the most challenging part of the asymptotic techniques underlying low-dimensional models for thin elastic structures. At the moment, these techniques do not take into consideration the effect of the environment, e.g., a Winkler foundation, when tackling boundary conditions, and have to be amended. In this paper as an example we consider an antiplane problem for a thin elastic strip contacting with a relatively compliant Winkler foundation. Refined boundary conditions at an edge loaded by prescribed stresses are established using a properly adjusted Saint-Venant’s principle. They appear to be useful for advanced structure modelling including analysis of the static equilibrium under self-equilibrated loading.

中文翻译：

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在对平面剪切变形作用下由 Winkler 型地基支撑的细弹性条边缘的精细边界条件上


边界条件的推导是薄弹性结构的低维模型基础的渐近技术中最具挑战性的部分。目前，这些技术在处理边界条件时没有考虑环境的影响，例如 Winkler 基金会，因此必须进行修改。在本文中，我们以此为例，考虑了与相对柔顺的 Winkler 基础接触的薄弹性条的对平面问题。由指定应力加载的边缘处的精细边界条件是使用适当调整的 Saint-Venant 原理建立的。它们似乎可用于高级结构建模，包括自平衡载荷下的静态平衡分析。