An Proposal of Analytical Methods to Transient Thermal Stress Problems in Nonhomogeneous Bodies and its Application to Thermal Stress Problem in FRM

作为非均质体中瞬时热应力问题的分析方法研究，发表了以下课题的研究论文。1.温度随厚度变化的非均质板中瞬时热应力的表达式。2.非均匀双连通区的瞬时热应力。3.带方孔的非均匀方柱的瞬时热应力。4.带圆孔的非均匀矩形区域的瞬时热应力。5.穿孔非均质板中的瞬时热应力(待发表)。6.非均匀多连通区域平面热应力问题的解析解(第一篇报告，非均匀中空圆板的非对称稳态热应力)。7.基于非均匀平面热弹性的复合材料结构的瞬时热应力分析(待定)用应力函数法建立了上述非均匀多连通区的平面热弹性问题(2.-7)。在公式(2.和4.)中，导出了新的米歇尔条件以保证转动和位移的单值性。为任意非均匀材料性质的情况所建立的基本方程组(2.-5.，7.)用有限差分法进行了数值求解，并定量地了解了热和力学非均匀性质对温度和热应力分布的影响，数值计算了在多连通区域内随位置呈指数变化的导热系数、Yound模数和线性热膨胀系数。

The research papers of the following subjects have been published as the research of analytical methods to the transient thermal stress problems in nonhomogeneous bodies. 1. An expression for transient thermal stress in a nonhomogeneous plate with temperature variation through thickness. 2. Transient thermal stresses in a nonhomogeneous doubly-connected region. 3. Transient thermal stresses in a nonhomogeneous square cylinder with a square hole. 4. Transient thermal stresses in a Nonhomogeneous rectangular region with a circular hole. 5. Transient thermal stresses in a perforated nonhomogeneous plate ( to be published ). 6. An analytical solution for a plane thermal stress problem in nonhomogeneous multiply-connected regions ( 1st Report, Asymmetric steady-state thermal stresses in a nonhomogeneous hollow circular plate ). 7. An analysis of transient thermal stresses in composite structrues based on nonhomogeneous plane-thermoelasticity ( in submit ).The plane thermoelastic problems( 2.-7) in the nonhomogeneous multiply-connected regions mentioned above have been formulated by the stress function method. In the formulation( 2. and 4. ), new michell's conditions have been derived to assure a single-valuedness of rotation and displacements. The system of fundamental equations formulated for the case of arbitrary nonhomogeneous material properties ( 2.-5., 7.) has been solved numerically by the use of the finite difference method, and to make clear quantitatively the effects of thermal and mechanical nonhomogeneous properties on temperature and thermal stress distributions, numerical calculations have been carried out for the thermal conductivity, Yound's modulus and coefficient of linear thermal expansion which vary exponentially with the position in the multiply-connected regions.