稳态传热与接触耦合问题解的唯一性与迭代算法的振荡性

UNIQUENESS AND OSCILLATION PROBLEMS FOR COUPLED ANALYSIS BETWEEN STABLE HEAT TRANSFER AND CONTACT PROCESSES

对稳态条件下热接触两类过程耦合作用分析解的唯一性进行讨论，给出问题不唯一解的实例。进一步地，文中讨论了耦合分析迭代求解的算法可能出现的求解过程的振荡性与不收敛性问题，与传统的稳态热分析的一步法不同，本文建议对这类稳态热传导接触耦合问题采取增量小步长迭代技术求解，文中给出了算例。文中给出了稳态条件下热接触耦合问题的基本控制方程与变分方程，变分方程分为两类，一类是热力学变分泛函，其考虑了接触区域对结构热传导的影响；另一类是二维热弹性接触分析的参数变分原理，可以方便地对接触问题进行求解。作者认为，对本文提出问题的深人研究是很有必要的，本文给出例题可供进一步研究时参考。

The uniqueness problem existing in the solutions of the mathematical model is discussed, and a real example is shown. Furthermore, the possible oscillation and unconvergency problems for the numerical method are studied. To overcome thes difficulty, unlike the one loading step algorithm used for traditional heat transfer problems, the incremental lteration technique is proposed, and a numerical example, where the oscillation phenomena could be found with the one-step method, has ben computed. To solve the problems in numerical way, two kinds of variational principle are put forward,, i.e. respectively for heat transfer and contact analysis, based on the governing equations for coupled analysis between stable heat transfer and contact processes. As the authors' view points, further investigation for the problems declared here is quite necessary, and the examples shown in the paper could be take as the reference for this kind of research.