Homogenization of elasticity problems on singular structures
Homogenization of elasticity problems on singular structures
复制标题
奇异结构弹性问题的均质化
DOI：
10.1070/im2002v066n02abeh000380
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
V. Zhikov
中科院分区：
文献类型：
--
作者：
V. Zhikov
我们考虑了周期网络、结点和更一般的奇异对象的均匀化理论。我们证明了均匀化问题具有典型的“非经典”特征。与标量问题相比，这一事实是弹性问题均质化的一个显著特征。研究了各种奇异结构的Sobolev空间性质，证明了一般型奇异周期结构的非经典均匀化原理，并描述了具有两个小几何参数的模型问题的“标度效应”。
We consider homogenization theory on periodic networks, junctions and more general singular objects. We show that the homogenized problem typically has a "non-classical" character. This fact is a distinctive feature of homogenization of elasticity problems in contrast to scalar problems. We investigate the properties of Sobolev spaces for various singular structures, prove a non-classical homogenization principle for singular periodic structures of general type and describe a "scaling effect" for model problems with two small geometrical parameters.