1993 Fiscal Year Final Research Report Summary
DEVLOPMENT OF THE METHOD OF BOUNDARY DISCRETIZATION OF ANALYTIC SOLUTIONS FOR STATIC AND DYNAMIC ANALYSIS OF ELASITIC STRUCTURES
| Project/Area Number |
04805023
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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 |
機械力学・制御工学
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| Research Institution | SHIZUOKA INSTITUTE OF SCIENCE AND TECHNOLOGY |
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Principal Investigator |
URATA Yohihiko SHIZUOKA INSTITUTE OF SCIENCE AND TECHNOLOGY, Faculty of Science and Technology, Professor, 理工学部, 教授 (60024329)
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| Project Period (FY) |
1992 – 1993
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| Keywords | Analytic Solution / Discretization / Boundary / Vibration / Static Problems / Computaional Time / Accuracy / 重調和方程式 |
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| Research Abstract |
1. It was clarified that a linear combination of plane waves traveling in all directions may be used for an appoximate general solutions of the twodimensional Helmholtz's equation which describes eigenvalue problems in domains with arbitrary shaped boundaries. This representaion of the general solution can be transformed into relations of potential and concentrated flux at nodal points located on the boundary. The resulted relations have similar forms to FEM equations. In this method, small size matrices are required because nodal points are located only on the boundary. However calculated results are very precise.
2. As an example of application of this method to the one-dimensional problems, vibration analysis of a three-dimensionally crooked pipe containing fluids was done. Analytic solutions were used for straiht parts. Usual finite elements were used for elbows. Natural frequencies calculated by this method were very close to measured ones.
3. Problems described by various differential equations such as plate vibration, Laplace equation, biharmonic euation and so on are can be analyzed by the mothod proposed in this investgation.
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