Research on Applications of the Group Theory Based Combinatorics Methods to Design Engineering

基于群论的组合方法在设计工程中的应用研究

• 批准号: 07805016
• 负责人: NARITA Yoshihiro
• 金额: $ 0.19万
• 依托单位: HOKKAIDO UNSTITUTE OF TECHNOLOGY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1995
• 资助国家: 日本
• 起止时间: 1995 至 1996
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07805016/
• 关键词: Group Theory; Combinatorics; Design Engineering; Polya Counting Theory; Composite Materials; Optimization

In the fiscal year of 1995, basic ideas were developed to apply the combinatorics methods, which were based on the group theory, to mechanics and design problems in mechanical engineering. Particulary, an extension of "Polya Counting Theory", which was applied to some problems in the author's previous studies, was investigated. For the purpose, the cyclic polynomial approach was extended to include "indexed" polynomials. The alogorithm flows and software techniques were established by using the indexed cyclic polynomials, when some engineering problems were concerned.In the fiscal year of 1996, the approach was applied to more realistic problems in engineering, such as combinations in mechanical behaviors of laminated composite plates and shells. Some analytical methods were also developed to effciently calculate the mechanical behaviors of laminated composite components. Two manuscripts are under final preparation to be submitted to foreign engineering journals. The titles are "Combinations of Dynamic Behaviors of Composite Rectangular Plates Under General Boundary Conditions" and "The combinatorics Study in Dynamic Behaviors of Laminated Shallow Shells".

在1995财政年度，提出了将以群论为基础的组合学方法应用于机械工程中的力学和设计问题的基本思想。特别是对作者以往研究中应用于某些问题的“Polya计数理论”的推广进行了研究。为此，对循环多项式方法进行了扩展，以包括“索引”多项式。针对一些工程问题，利用指数循环多项式建立了相应的算法流程和软件技术，并在1996财政年度将其应用于更实际的工程问题，如复合材料层合板壳的力学性能组合问题。为了有效地计算复合材料层合构件的力学行为，还提出了一些分析方法。两份手稿正在最后准备中，将提交给外国工程期刊。题目分别是《复合材料矩形薄板在一般边界条件下的动力行为组合》和《叠层扁壳动力行为的组合学研究》。

项目成果

成田吉弘・伊藤吉保・清水信行: "FD活用材料力学" 共立出版, 159 (1996)

Yoshihiro Narita、Yoshiyasu Ito、Nobuyuki Shimizu：“FD 利用材料力学”Kyoritsu Shuppan，159 (1996)

Y.NARITA,M.ITOH and X.ZHAO: "Optimal Design by Genetic Algorithm for Maximum fundamental Frequency of Laminated shallow Shell" Advanced Composite Letters. Vol.5, No.1. 21-24 (1996)

Y.NARITA、M.ITOH 和 X.ZHAO：“叠层浅壳最大基频的遗传算法优化设计”高级复合字母。

Y.NARITA: "Appllication of the Three Dimensional Analysis to Cross-ply Thick Cylinders and Circular Plates" Proc.17th European Conf.on Comp.Mat.Vol.2. 271-276 (1996)

Y.NARITA：“三维分析在交叉层厚圆柱体和圆板中的应用”Proc.17th European Conf.on Comp.Mat.Vol.2。

Y.Narita: "Some Unsolved Problems in Dynamics of Mechanical Systems (in Japanese)" J.JSME. vol.100, No.939. 211-214 (1997)

Y.Narita：“机械系统动力学中一些未解决的问题（日语）”J.JSME。

成田吉弘・伊藤吉保・清水信行: "FD活用材料力学" 共立出版(株), 205 (1996)

成田义宏、伊藤义康、清水伸行：《FD利用材料力学》共立出版株式会社，205（1996）