We propose a model of flexural elastic plates accounting for boundary layer effects due to the most usual boundary conditions or to geometrical defects, constructed via matched asymptotic expansions. In particular, considering a rectangular plate clamped at two opposite edges while the other two are free, we derive the effective boundary conditions or effective transmission conditions that the two first terms of the outer expansion must satisfy. The new boundary value problems thus obtained are studied and compared with the classical Love-Kirchhoff plate model. Two examples of application illustrate the results.

中文翻译：

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由于弯曲弹性板中通常边界条件或几何缺陷引起的边界层效应分析：Love-Kirchhoff 模型的改进

我们提出了一种弯曲弹性板模型，该模型考虑了由于最常见的边界条件或几何缺陷引起的边界层效应，通过匹配的渐近扩展构建。特别地，考虑一个矩形板夹在两个相对的边缘而另外两个是自由的，我们推导出外膨胀的两个第一项必须满足的有效边界条件或有效传输条件。研究了由此获得的新边值问题，并与经典的 Love-Kirchhoff 板模型进行了比较。两个应用示例说明了结果。