A proposal of mathematical analysis method for a coupled hygrothermoelastic problem in nonhomogeneous bodies and its application to material tailoring of functionally graded material with a function of humidity regulation

本研究的目的是推导出湿热环境下非均质板和非均质空心圆柱体中温度和湿度耦合扩散问题及其相关的湿热弹性问题的解析解，并将这些解析解应用于具有湿度调节功能的梯度材料的材料裁剪。湿度变化对热量扩散的耦合效应（Dufour效应）远小于温度变化对湿度扩散的耦合效应（Soret效应）。因此，本文给出了仅随厚度变化而具有任意非均匀性和温度变化的功能梯度材料板的非耦合瞬态温度场的解析解。通过求解具有分段线性非均匀导热系数，且各层比热和密度均不相同的多层板的非均匀导热问题，确定了瞬态温度解。功能梯度材料板中不耦合的湿度场与温度场具有相同的扩散方程。Soret效应是温度随时间变化对湿度扩散的影响，针对温度随时间变化较大的脉冲加热情况，采用特征化方法求解功能梯度材料板的动态热应力问题。此外，给出了由n块不同分段线性非均匀性的功能梯度材料板组成的板表面突然加热引起的瞬态温度和相关热应力的解析解。采用遗传算法对PSZ和SUS304组成的功能梯度材料板进行了以拉伸热应力最小为目标的材料成分优化。

The purpose of this research is to derive analytical solutions for the coupled diffusion problems of temperature and humidity and the associated hygrothermoelastic problem in nonhomogeneous plate and nonhomogeneous hollow circular cylinder under hygrothermal environment and is to apply these analytical solutions to material tailoring of functionally graded material with a function of humidity regulation.The coupling effect (Dufour effect) of change in humidity on diffusion of heat is much smaller than the coupling effect (Soret effect) of change in temperature on diffusion of humidity. So an analytical solution is presented to the uncoupled transient temperature field in the functionally graded material plate which has arbitrary nonhomogeneities of thermal properties and temperature variation only through the thickness. The transient temperature solution is determined by solving the nonhomogeneous heat conduction problem in a multilayred plate with piecewise-linear nonhomogeneous thermal conductivity, and different, homogeneous specific heat and density in each layr. The uncoupled humidity field in the functionally graded material plate has the same diffusion equation as the temperature field.As Soret effect is the effect of temperature change with time on the diffusion of humidity, dynamic thermal stress problem in a functionally graded material plate is solved by the characteristic method for the case of impulsive heating with large temperature change with time.Furthermore, an analytical solution is presented for a transient temperature and the associated thermal stress due to an abrupt heating on the plate surface in a functionally graded material plate which is composed of n plates with dissimilar piecewise-linear nonhomogeneities. The optimization of material composition taking the minimization of tensile thermal stress into account is carried out for functionally graded material plate composed of PSZ and SUS304 by using genetic algorithm.