On boundary layer in the Mindlin plate model: Levy plates
On boundary layer in the Mindlin plate model: Levy plates
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Mindlin 板块模型中的边界层：Levy 板块
DOI：
10.1016/j.tws.2007.11.003
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发表时间：
2008
影响因子：
6.4
通讯作者：
B. Brank
中科院分区：
文献类型：
--
作者：
B. Brank
本文研究的是厚矩形利维板的弯曲问题。得到Mindlin（厚）板模型的级数解，并将其表示为Kirchhoff（薄）板模型解、“剪切项”和“边界层项”的和。考虑了软、硬简支、软、硬夹紧和自由边界条件。为了检测Kirchhoff模型足够好的板块区域，以及需要使用Mindlin模型的板块区域，引入了模型误差指标。给出了几个例子，说明了Mindlin和Kirchhoff结果之间的差异，不同边界条件下边界层的强度，几种可能的模型误差指标的准确性以及结果与板厚的依赖关系。
This work is related to the bending problem of thick rectangular Levy plates. Series solution for the Mindlin (thick) plate model is obtained and represented as a sum of the Kirchhoff (thin) plate model solution, the “shear terms” and the “boundary layer terms”. Hard- and soft-simple supported, hard- and soft-clamped and free boundary conditions are considered. In order to detect plate regions where Kirchhoff model is good enough, and plate regions where Mindlin model should be used, a model error indicator is introduced. Several examples are presented, illustrating the difference between the Mindlin and the Kirchhoff results, the strengths of boundary layers for different boundary conditions, accuracy of several possible model error indicators and dependence of results on plate thickness.