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

作为非均匀体瞬态热应力问题的分析方法研究，已发表了以下课题的研究论文。1.温度沿厚度方向变化的非均匀板中瞬态热应力的表达式。2.非均匀双连通区域中的瞬态热应力。3.带方孔非均匀方柱的瞬态热应力。4.含圆孔非均匀矩形区域的瞬态热应力。5.多孔非均匀板中的瞬态热应力（待发表）。6.非均匀多连通区域中平面热应力问题的解析解（第一次报告，非均匀空心圆板中的非对称稳态热应力）。7.基于非均质平面热弹性理论的复合材料结构瞬态热应力分析（已提交）.平面热弹性问题（2.- 7)用应力函数法给出了上述非齐次多连通区域中的应力分布。在公式（2。和4.），推导出新的米歇尔条件以确保旋转和位移的单值性。对于任意非均匀材料性质的情况，基本方程组（2.- 5., 7.）用有限差分法数值求解，为了定量地说明热力学非均匀性对温度和热应力分布的影响，对多连通区域内随位置指数变化的导热系数、Yound模量和线膨胀系数进行了数值计算。

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.