1987 Fiscal Year Final Research Report Summary
NEW BOUNDARY ELEMENT METHOD FOR THERMOELASTIC PROBLEMS AND ITS APPLICATION TO SINGULAR STRESS FIELDS
| Project/Area Number |
61550077
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
材料力学
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| Research Institution | SHINSHU UNIVERSITY |
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Principal Investigator |
TANAKA Masataka SHINSHU UNIVERSITY, PROFESSOR, 工学部機械工学科, 教授 (40029319)
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| Project Period (FY) |
1986 – 1987
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| Keywords | BOUNDARY INTEGRAL EQUATION / BOUNDARY ELEMENT METHOD / SINGULAR STRESS FIELD / STRESS INTENSITY FACTOR / THERMAL STRESS / TRANSIENT HEAT CONDUCTION / 定常熱伝導 |
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| Research Abstract |
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.
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