Computational Technology Resources - CCP

Keywords: shape model, product shape design, non-linear dynamics, phase space.

Summary

The non-uniform structure and the non-uniform density of material of natural objects contributes to the strength, toughness and lightness of the structure. Many natural objects adopt the complex and minute structure to improve the disadvantages of raw material. The microstructure in material improves property of material and many products including very small structures will be produced in future. The suitable complex and minute structure in material contributes to improve the strength, toughness and lightness of the product.

The non-linear dynamics causes the chaotic movement and the chaotic movement makes complex and minute structure of the trajectory in the phase space. In chaotic state, the trajectory in the phase space generates infinitely folded complex minute structure quickly and automatically. The different shape of complex and minute structure is generated by the different kind of chaotic movement and the initial state and parameters of the chaotic movement.

We propose a new shape model, which represents the complex and minute structure generated by non-linear dynamics in the 3 dimensional space. The shape model consists of the points of trajectory of time segments in phase space. The points of trajectory of time segments in phase space are mapped in the 3 dimensional space. A point of trajectory includes a sphere. The sphere occupies the volume of the 3 dimensional space. The spheres with different radiuses create the complex and minute structure in the 3 dimensional space.

References

1: T. Shimojyo, "Introduction to Chaotic Dynamics", Kindaikagaku-sha Company Ltd., Tokyo, Japan, 1998.
2: T. Ohta, "Physics of non-equilibrium system", Shoukabou Company Ltd., Tokyo, Japan, 2000.
3: J.M.T. Thompson, H.B. Stewart, "Nonlinear Dynamics and Chaos Geometrical Methods for Engineers and Scientists", John Wiley & Sons Ltd., 1986.
4: Y. Hagiwara, H. Suzuki, "Fracture Mechanics", Ohmsha Company Ltd., Tokyo, Japan, 2003.
5: M.A. White, "Properties of Materials", Oxford University press, New York, U.S.A., 1999.
6: H. Samet, "The Design and Analysis of Spatial Data Structures", Addison-Wesley Publishing Company, 1989.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 80 PROCEEDINGS OF THE FOURTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: B.H.V. Topping and C.A. Mota Soares Paper 48 A Shape Model using Non-Linear Dynamics for the Shape Design of the Complex and Minute Structure of Products K. Sakita+ and M. Igoshi* +Department of Environmental Engineering for Symbiosis, Soka University, Tokyo, Japan Department of Precision Mechanical Engineering, Tokyo Metropolitan University, Japan doi:10.4203/ccp.80.48 purchase the full-text of this paper Full Bibliographic Reference for this paper K. Sakita, M. Igoshi, "A Shape Model using Non-Linear Dynamics for the Shape Design of the Complex and Minute Structure of Products", in B.H.V. Topping, C.A. Mota Soares, (Editors), "Proceedings of the Fourth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 48, 2004. doi:10.4203/ccp.80.48 Keywords:* shape model, product shape design, non-linear dynamics, phase space. Summary The non-uniform structure and the non-uniform density of material of natural objects contributes to the strength, toughness and lightness of the structure. Many natural objects adopt the complex and minute structure to improve the disadvantages of raw material. The microstructure in material improves property of material and many products including very small structures will be produced in future. The suitable complex and minute structure in material contributes to improve the strength, toughness and lightness of the product. The non-linear dynamics causes the chaotic movement and the chaotic movement makes complex and minute structure of the trajectory in the phase space. In chaotic state, the trajectory in the phase space generates infinitely folded complex minute structure quickly and automatically. The different shape of complex and minute structure is generated by the different kind of chaotic movement and the initial state and parameters of the chaotic movement. We propose a new shape model, which represents the complex and minute structure generated by non-linear dynamics in the 3 dimensional space. The shape model consists of the points of trajectory of time segments in phase space. The points of trajectory of time segments in phase space are mapped in the 3 dimensional space. A point of trajectory includes a sphere. The sphere occupies the volume of the 3 dimensional space. The spheres with different radiuses create the complex and minute structure in the 3 dimensional space. References 1 T. Shimojyo, "Introduction to Chaotic Dynamics", Kindaikagaku-sha Company Ltd., Tokyo, Japan, 1998. 2 T. Ohta, "Physics of non-equilibrium system", Shoukabou Company Ltd., Tokyo, Japan, 2000. 3 J.M.T. Thompson, H.B. Stewart, "Nonlinear Dynamics and Chaos Geometrical Methods for Engineers and Scientists", John Wiley & Sons Ltd., 1986. 4 Y. Hagiwara, H. Suzuki, "Fracture Mechanics", Ohmsha Company Ltd., Tokyo, Japan, 2003. 5 M.A. White, "Properties of Materials", Oxford University press, New York, U.S.A., 1999. 6 H. Samet, "The Design and Analysis of Spatial Data Structures", Addison-Wesley Publishing Company, 1989. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £95 +P&P)
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