Corner Singularities and Regularity Results for the Reissner/Mindlin Plate Model
Corner Singularities and Regularity Results for the Reissner/Mindlin Plate Model
复制标题
Reissner/Mindlin 板模型的角点奇点和规律性结果
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
A. Sändig
中科院分区：
文献类型：
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作者：
A. Rössle;A. Sändig
利用一般椭圆型方程组的椭圆边值问题理论，系统地研究了多边形区域上Reissner/Mindlin板模型一类边值问题弱解的角奇异性和正则性.在Sobolev空间Hs（s>1是真实的数）中给出了中平面偏转和纤维垂直于中平面转动的正则性结果。一般来说，数s取决于几何形状、材料参数和边界条件，并且与场在奇异部分和规则部分中的分解有关。计算了一类边界条件（36种组合）的主要奇异项。的结果进行了严格的比较与那些已知的应力电位的方法。
The theory for elliptic boundary value problems for general elliptic systems is used in order to investigate systematically corner singularities and regularity for weak solutions to a broad class of boundary value problems for the Reissner/Mindlin plate model in polygonal domains. The regularity results for the deflection of the midplane and for the rotation of fibers normal to the midplane are formulated in Sobolev spaces Hs, where s>1 is a real number. The number s depends on the geometry, the material parameters and the boundary conditions in general and is related to a decomposition of the fields in a singular and a regular part. The leading singular terms are calculated for a wide class of boundary conditions (36 combinations). The results are critically compared with those known from a stress potential approach.