ASYMPTOTIC ANALYSIS OF THE PROBLEM OF EQUILIBRIUM OF AN INHOMOGENEOUS BODY WITH HINGED RIGID INCLUSIONS OF VARIOUS WIDTHS

• Published in: Journal of applied mechanics and technical physics Vol. 64; no. 5; pp. 911 - 920
• Main Authors: Lazarev, N. P., Kovtunenko, V. A.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.10.2023; Springer Nature B.V
• Subjects: Applications of Mathematics; Boundary conditions; Classical and Continuum Physics; Classical Mechanics; Composite materials; Elastic bodies; Equilibrium; Fluid- and Aerodynamics; Inclusions; Inequality; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mechanical Engineering; Physics; Physics and Astronomy; Topology; Two dimensional bodies; elastic matrix; variational problem; rigid inclusion; non-penetration condition; hinged connection
• ISSN: 0021-8944; 1573-8620
• DOI: 10.1134/S0021894423050206

Two models are considered, which describe the equilibrium state of an inhomogeneous two-dimensional body with two connected rigid inclusions. The first model corresponds to an elastic body with two-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 two-dimensional inclusions is studied. It is shown that the solutions of equilibrium problems in the presence of two-dimensional inclusions in a strong topology are reduced to the solutions of problems for thin inclusions with the width parameter tending to zero.