Rudoy Evgeny M, Sazhenkov Sergey A
Lavrentyev Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences, Pr. Acad. Lavrentyeva 15, Novosibirsk 630090, Russia.
Laboratory for Mathematical and Computer Modeling in Natural and Industrial Systems, Altai State University, Pr. Lenina 61, Barnaul 656049, Russia.
Philos Trans A Math Phys Eng Sci. 2024 Aug 23;382(2277):20230304. doi: 10.1098/rsta.2023.0304. Epub 2024 Jul 15.
The dynamical problem of linear thermoelasticity for a body with incorporated thin rectilinear inclusions is studied. It is assumed that the inclusions (i.e. filaments and threads) are parallel to each other and the problem contains a small parameter [Formula: see text], which characterizes the distance between two neighbouring inclusions. Using the two-scale convergence approach, we find the limiting problem as [Formula: see text]. As a result, we get a well-posed homogenized model of an anisotropic inhomogeneous body with effective characteristics inheriting thermomechanical properties of inclusions.This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'.
研究了包含细直线状夹杂的物体的线性热弹性动力学问题。假设夹杂（即细丝和线）相互平行，且该问题包含一个小参数[公式：见原文]，它表征相邻两个夹杂之间的距离。利用两尺度收敛方法，我们找到了当[公式：见原文]时的极限问题。结果，我们得到了一个具有有效特性的各向异性非均匀体的适定均匀化模型，该有效特性继承了夹杂的热机械性能。本文是主题为“力学中的非光滑变分问题及其应用”的一部分。
