Thermo-elastic analysis of a finite plate containing multiple elliptical inclusions
Thermo-elastic analysis of a finite plate containing multiple elliptical inclusions
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DOI：
10.1016/j.ijmecsci.2013.07.012
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发表时间：
2013-10-01
影响因子：
7.3
通讯作者：
Sun, Huiyu
中科院分区：
文献类型：
--
作者：
Dai, Ming;Sun, Huiyu
本文提出了一种有限板在稳态温度变化场作用下含多个椭圆形夹杂的热弹性问题的级数解。求解的第一步是将热弹性问题转化为不考虑热影响的一般弹性问题，这样就可以应用穆斯赫利什维利弹性理论。然后，夹杂内部的复势以法贝尔级数的形式给出，而多连通基体中的复势则表示为与椭圆形内边界一致的多个特定级数的叠加。最后，借助傅里叶级数展开和带约束的最小二乘法，将所有复势代入待推导的边界条件中。此外，将本文解得到的热应力与解析解和有限元方法得到的热应力进行了比较，同时还研究了矩形板的界面热应力以及等效热膨胀系数。（C）2013爱思唯尔有限公司。保留所有权利。
This paper presents a series solution to the thermo-elastic problem of a finite plate containing multiple elliptical inclusions subjected to a steady-state temperature variation field. The first step of the solution is to transform the thermo-elastic problem into a general elastic problem without considering thermal influence in which the Muskhelishvili's theory of elasticity can be employed. Then the complex potentials inside the inclusions are presented in the form of Faber series, while those in the multi-connected matrix are expressed as a superposition of multiple specific series consistent with elliptical inner boundaries. Finally, all the complex potentials are substituted into the boundary conditions to be derived in assistance with Fourier series expansions and a least squares method with constraints. Additionally, the thermal stresses obtained by the present solution are compared with those by both an analytical solution and the finite element method, while interfacial thermal stresses as well as equivalent thermal expansion coefficients of a rectangular plate are investigated. (C) 2013 Elsevier Ltd. All rights reserved.