Asymptotic Analysis of the Problem of Equilibrium of an Inhomogeneous Body with Hinged Rigid Inclusions of Various Widths
N. P. Lazarev1, V. A. Kovtunenko2,3
1Institute of Mathematics and Information Science, North-Eastern Federal University named after M. K. Ammosov, Yakutsk, Russia
2Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
3Department of Mathematics and Scientific Computing, University of Graz, Graz, Austria
Keywords: variational problem, rigid inclusion, non-penetration condition, elastic matrix, hinged connection
Abstract
Two models are considered, which describe the equilibrium state between an inhomogeneous two-dimensional body with two connected rigid inclusions. The first model corresponds to an elastic body with three-dimensional rigid inclusions located in regions with a constant width (curvilinear rectangle and trapezoid). The second model involves thin inclusions described by curves. In both models, it is assumed that there is a crack described by the same curve on the interface between the elastic matrix and rigid inclusions. The crack boundaries are subjected to a one-sided condition of non-penetration. The dependence of the solutions of equilibrium problems on the width of three-dimensional inclusions is studied. It is shown that the solutions of equilibrium problems in the presence of three-dimensional inclusions in a strong topology are reduced to the solutions of problems for thin inclusions with the width parameter tending to zero.
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