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

在1995年财政年度，基本思想是开发应用组合学方法，这是基于群论，在机械工程力学和设计问题。特别地，对“波利亚计数理论”进行了推广，并将其应用于作者以往研究中的一些问题。为此，循环多项式方法被扩展到包括“索引”多项式。在某些工程问题中，建立了用循环多项式方法求解的算法流程和软件技术，并在1996年应用于复合材料层合板壳力学性能组合等更实际的工程问题。本文还提出了一些有效计算复合材料层合构件力学性能的分析方法。两篇稿件正在进行最后的准备工作，将提交给国外工程期刊。题目是“一般边界条件下复合材料矩形板动力特性的组合”和“层合扁壳动力特性的组合学研究”。

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".