This paper presents a new method to determine an optimum topology of plate structure using coordinate transformation by conformal mapping. We have already proposed a method to determine an optimum topology of planar structure using coordinate transformation by conformal mapping. In that study first we defined simple design domain in which analysis and optimization were performed easily. We calculated optimum topology in this simple design domain. Then we applied coordinate transformation by conformal mapping to optimum topology calculated in simple design domain, and obtained some optimum topologies in complex design domain. We also showed that the invariants of stresses which were the sum and difference of principal stress satisfied Laplace equation and relationshi p between fluid mechanics and electromagnetic could be valid in the theory of elasticity. In this study we clarify two invariants of bending moments satisfy Laplace equation under a certain condition. We note the similarity between Airy stress function of 2-D elastic body and deflection of plate, and will show that the two invariants of bending moments which are the sum and difference of principal bending moments satisfy Laplace equation using this similarity. As a result we will show that corresponding relationship between fluid mechanics, electromagnetic and elasticity may be valid in the theory of plate. Then by using this relationship, we proposed a new method to determine optimum topology using coordinate transformation by conformal mapping. Our proposed method will be useful to determine optimum topology easily in complex design domain. Through numerical examples, we can examine the effectiveness of the proposed method.
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ASME 2002 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
September 29–October 2, 2002
Montreal, Quebec, Canada
Conference Sponsors:
- Design Engineering Division and Computers and Information in Engineering Division
ISBN:
0-7918-3622-3
PROCEEDINGS PAPER
A Study on Optimum Topology of Plate Structure Using Coordinate Transformation by Conformal Mapping Available to Purchase
Satoshi Kitayama,
Satoshi Kitayama
Kanazawa University, Kanazawa, Japan
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Hiroshi Yamakawa
Hiroshi Yamakawa
Waseda University, Tokyo, Japan
Search for other works by this author on:
Satoshi Kitayama
Kanazawa University, Kanazawa, Japan
Hiroshi Yamakawa
Waseda University, Tokyo, Japan
Paper No:
DETC2002/DAC-34053, pp. 169-174; 6 pages
Published Online:
June 18, 2008
Citation
Kitayama, S, & Yamakawa, H. "A Study on Optimum Topology of Plate Structure Using Coordinate Transformation by Conformal Mapping." Proceedings of the ASME 2002 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 2: 28th Design Automation Conference. Montreal, Quebec, Canada. September 29–October 2, 2002. pp. 169-174. ASME. https://doi.org/10.1115/DETC2002/DAC-34053
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