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。首先，针对材料常数与温度有关的非线性瞬态热传导问题，提出了一种新的边界元方法。将kirchhoff变换应用于热弹性问题，得到伪线性微分方程，然后用边界元法求解得到的积分方程。将该方法应用于一系列非线性暂态问题，从而证明了该方法的潜在有效性。其次，采用边界元法研究了裂纹尖端在稳态和瞬态热传导状态下产生的热应力。由此得到的一些实际问题的结果总结为基于断裂力学的设计有用的图表。最后，对耦合和非耦合热弹性问题提出了一种新的边界元方法。新方法采用霍曼德法推导出问题的积分方程公式所需要的基本解。得到了一组边界积分方程，并用通常的边界元法进行了离散。在本研究中，首先对新方法的理论方面进行了研究。然后，开发了用于稳态热传导热应力分析的边界元软件。然而，新方法的进一步发展仍然对完全耦合热弹性问题开放，这可以作为本项目未来的研究工作。

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.