Linear thermo-elasticity equations are derived in this paper for anisotropic, particle-reinforced composite structures at mesoscale. The full set of equations is first derived at microscale where the structure is represented as a three-dimensional body with spherical inclusions of known spatial distribution. Limiting the consideration by infinitesimal strains and assuming that the inclusions are embedded into the body firmly and that there are no any defects at the interface of inclusions, the mesoscale limit of the set of equations is derived as the scale parameter decreases to 0. Convergence of the corresponding solutions is established. Material characteristics at mesoscale are expressed in terms of Dirac distribution corresponding to a structure with point inhomogeneities. It is shown that the effective or macroscale material characteristics evaluated in terms of the mesoscale ones, match the well-known rule of mixtures. A particular case of Ambarcumyan plate with random distribution of spherical inclusions is studied numerically.

本文推导了中尺度各向异性，颗粒增强复合材料结构的线性热弹性方程。首先在微观尺度上推导完整的方程组，其中结构表示为三维物体，具有已知空间分布的球形夹杂物。限制考虑的因素为无穷小应变，并假设夹杂物牢固地嵌入体内，并且在夹杂物的界面处没有任何缺陷，当比例参数减小到0时，得出方程组的中尺度极限。建立相应的解决方案。中尺度的材料特性用狄拉克分布表示，该分布对应于具有点不均匀性的结构。结果表明，根据中尺度材料评估的有效或宏观材料特性符合众所周知的混合物规则。数值研究了一个随机分布的球形夹杂物的Ambarcumyan板的特殊情况。