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

热弹性问题的新边界元方法及其在奇异应力场中的应用

• 批准号: 61550077
• 负责人: TANAKA Masataka
• 金额: $ 1.22万
• 依托单位: SHINSHU UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1986
• 资助国家: 日本
• 起止时间: 1986 至 1987
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-61550077/
• 关键词: BOUNDARY INTEGRAL EQUATION; BOUNDARY ELEMENT METHOD; SINGULAR STRESS FIELD; STRESS INTENSITY FACTOR; THERMAL STRESS; TRANSIENT HEAT CONDUCTION; 定常熱伝導

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.

尝试建立一种求解热弹性体问题的新边界元方法。首先，本文提出了一种新的边界元方法，用于求解具有温度变材料常数的非线性暂态热传导问题，将Kirchhoff变换应用于热弹性问题，得到一个伪线性微分方程组，然后用通常的边界元方法求解得到的积分方程组。将该方法应用于一系列非线性暂态问题，验证了该方法的有效性。其次，用常规的边界元方法分析了稳态和暂态热传导状态下裂纹尖端产生的热应力，并采用两步法求解。文中给出了一些实际问题的计算结果，为基于断裂力学的设计提供了有用的图表。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。新方法利用HERMANDER方法推导出问题的积分方程式所需的基本解。得到了一组边界积分方程组，并用通常的边界元方法进行了离散。在这项研究中，首先对新方法的理论方面进行了研究。在此基础上，开发了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对于完全耦合的热弹性问题仍然是开放的，这可以作为本项目未来的研究工作。

项目成果

田中正隆: "境界要素法の応用" (株)コロナ社, 260 (1987)

田中正孝：《边界元法的应用》Coronasha Co., Ltd.，260（1987）

田中正隆: 材料システム. 6. 157-162 (1987)

田中正孝：材料系统。6. 157-162 (1987)

MASASHI KIKUTA: "A BOUNDARY ELEMENT METHOD FOR NONLINEAR TRANSIENT HEAT CONDUCTION PROBLEMS" BOUNDARY ELEMENTS VIII, ED. BY M. TANAKA AND C.A. BREBBIA, SPRINGER-VERLAG. 47-58 (1986)

MASASHI KIKUTA：“非线性瞬态热传导问题的边界元方法”边界元 VIII，ED。

田中正隆: 境界要素法論文集. 4. 93-98 (1987)

田中正孝：边界元法论文集 4. 93-98 (1987)。

MASASHI KIKUTA: "BOUNDARY ELEMENT ANALYSIS OF NONLINEAR TRANSIENT HEAT CONDUCTION PROBLEMS" COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING. 62. 321-329 (1987)

MASASHI KIKUTA：“非线性瞬态热传导问题的边界元分析”应用力学和工程中的计算机方法。