NEW BOUNDARY ELEMENT METHOD FOR THERMOELASTIC PROBLEMS AND ITS APPLICATION TO SINGULAR STRESS FIELDS

试图建立一种新的热弹性问题边界元方法。本文首先提出了一种新的边界元法，用于求解材料常数依赖于材料性质的非线性瞬态热传导问题，将Kirchhoff变换应用于热弹性问题，得到一个拟线性微分方程，然后用通常的边界元法求解拟线性积分方程。将所提出的方法应用于一系列非线性瞬态问题，证明了该方法的潜在实用性。其次，用通常的边界元法求解了稳态和瞬态热传导状态下裂纹尖端附近产生的热应力。本文对一些实际问题的计算结果作了归纳，并给出了断裂力学设计中的有用图表。最后，本文提出了一种新的边界元法，它可用于耦合和非耦合热弹性问题。新方法利用霍曼德程序导出问题积分方程的基本解。本文用通常的边界元法导出并离散了一组边界积分方程。在这项研究中，新方法的理论方面首先进行了阐述。在此基础上，编制了稳态热传导热应力分析的边界元软件。然而，对于完全耦合的热弹性问题，新方法的进一步发展仍然是开放的，这可以作为本项目未来的研究工作推荐。

ATTEMPT IS MADE TO ESTABLISH A NEW BOUNDARY ELEMENT APPROACH TO THERMOELASTIC PROBLEMS. FIRST, A NEW BOUNDARY ELEMENT METHOD IS PROPOSED FOR THE NONLINEAR TRANSIENT HEAT CONDUCTION PROBLEMS WITH TEMPERATURE-DEPENDENT MATERIAL CONSTANTS.THE KIRCHHOFF TRANSFORMATION IS APPLIED TO THE THERMOELASTIC PROBLEMS TO PRODUCE A PSEUDO LINEAR DIFFERENTIAL EQUATION, AND THEN THE RESULTING INTEGRAL EQUATION IS SOLVED BY MEANS OF THE USUAL BOUNDARY ELEMENT METHOD. THE PROPOSED METHOD IS APPLIED TO A SERIES OF NONLINEAR TRANSIENT PROBLEMS WHEREBY THE POTENTIAL USEFULNESS OF THE METHOD IS DEMONSTRATED. SECOND, THE THERMAL STRESSES PRODUCED NEARTHE CRACK TIPS IN STEADY AND ALSO TRANSIENT HEAT CONDUCTION STATES ARE INVESTIGATED BY THE USUAL BOUNDARY ELEMENT METHOD IN WHICH THE TWO-STEP SOLUTION PROCEDURE IS EMPLOYED. THE RESULTS THUS OBTAINED FOR A NUMBER OF PRACTICAL PROBLEMS ARESUMMARIZED AS CHARTS USEFUL FOR DESIGN BASED ON FRACTURE MECHANICS.FINALLY, A NEW BOUNDARY ELEMENT METHOD IS PROPOSED FOR BOTH THE COUPLED AND UNCOUPLED THERMOELASTIC PROBLEMS. THE NEW METHOD EMPLOYS HOERMANDER'S PROCEDURE TO DERIVE THE FUNDAMENTAL SOLUTIONS NEEDED FOR THE INTEGRAL EQUATION FORMULATION OF THE PROBLEMS. A SET OF BOUNDARY INTEGRAL EQUATIONS ARE OBTAINED AND DISCRETIZED BY MEANS OF THE USUAL BOUNDARY ELEMENT METHOD. IN THIS STUDY, THEORETICAL ASPECTS OF THE NEW APPROACH ARE FIRST INVESTIGATED. THEN, A BOUNDARY ELEMENT SOFTWARE IS DEVELOPED FOR THERMAL STRESS ANALYSIS IN STEADY STATE HEAT CONDUCTION. HOWEVER, FURTHER DEVELOPMENT OF THE NEW APPROACH IS STILL OPEN TO FULLY COUPLED THERMOELASTIC PROBLEMS, WHICH CAN BE RECOMMENDED AS THE FUTURE RESEARCH WORK OF THIS PROJECT.