Problems of Thin Inclusions in a Two-Dimensional Viscoelastic Body
Problems of Thin Inclusions in a Two-Dimensional Viscoelastic Body
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二维粘弹性体中的薄夹杂物问题
DOI：
10.1134/s1990478918020114
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发表时间：
2018
影响因子：
--
通讯作者：
T. Popova
中科院分区：
文献类型：
--
作者：
T. Popova
本文研究了含分层薄夹杂的二维粘弹性体在弹性夹杂和刚性夹杂情况下的平衡问题。提出了具有非线性边界条件的问题的变分和微分公式，并证明了其唯一的可解性。对于薄弹性夹杂的情况下，作为一个Bernoulli-Euler梁建模，我们认为通过到极限的夹杂的刚度参数趋于无穷大。在极限情况下，这是一个薄的刚性夹杂的问题。建立了薄刚性夹杂问题与体积刚性夹杂问题之间的联系。在夹杂物无分层的情况下，相应的限值通过是合理的。
Under study are the equilibrium problems for a two-dimensional viscoelastic body with delaminated thin inclusions in the cases of elastic and rigid inclusions. Both variational and differential formulations of the problems with nonlinear boundary conditions are presented; their unique solvability is substantiated. For the case of a thin elastic inclusion modelled as a Bernoulli–Euler beam, we consider the passage to the limit as the rigidity parameter of the inclusion tends to infinity. In the limit it is the problem about a thin rigid inclusion. Relationship is established between the problems about thin rigid inclusions and the previously considered problems about volume rigid inclusions. The corresponding passage to the limit is justified in the case of inclusions without delamination.