N. P. Lazarev, V. A. Kovtunenko, “Asymptotic analysis of the problem of equilibrium of an inhomogeneous body with hinged rigid inclusions of various widths”, Prikl. Mekh. Tekh. Fiz., 2023, Volume 64, Issue 5,Pages <nobr>205

This article is cited in 13 papers

Asymptotic analysis of the problem of equilibrium of an inhomogeneous body with hinged rigid inclusions of various widths

N. P. Lazarev^a, V. A. Kovtunenko^bc

^a Research Institute of Mathematics of North-Eastern Federal University named after M. K. Amosov, Yakutsk, Russia
^b Lavrentyev Institute of Hydrodynamics of Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
^c Department of Mathematics and Scientific Computing, University of Graz, Graz, Austria

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.

Keywords: variational problem, rigid inclusion, non-penetration condition, elastic matrix, hinged connection.

UDC: 539.311

Received: 23.03.2023
Revised: 10.04.2023
Accepted: 24.04.2023

DOI: 10.15372/PMTF202315275