传热与接触两类问题耦合作用的有限元分析

考虑传热接触耦合作用的热力学分析问题大量存在于工程中，分析的难点是必须考虑热与可移动接触边界间的耦合作用。针对这类问题的求解，该文给出了接触边界上热交换与温度边界条件，并在此基础上建立了两类变分方程，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。文中给出有限元分析的离散公式，并进一步给出两类问题耦合分析的迭代算法，其中接触分析的惩罚因子是可以消除的，数值结果验证了该文的理论与算法。

THE FINITE ELEMENT ANALYSIS FOR COUPLED PROBLEMS BETWEEN HEAT TRANSFER AND CONTACT PROCESSES

The thermal mechanical analysis for the coupled problems of interaction between heat transfer and contact processes can be found in many engineering fields. The difficult aspect of the problem is the consideration of the coupled interaction on the contact boundaries. To solve this problem, the conditions for heat transfer on the contact boundaries are given in this paper, and two kinds of variational principle for the two different problems, i.e.heat transfer and contact analysis, are respectively put forward. Based on the proposed variational principles, the finite element discretized formulations, where the penalty factor in contact equation can be cancelled, are derived, and an iteration algorithm is shown for the solution of the coupled problems. Two examples are computed and the results demonstrate the validity of the model and algorithm presented here.