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".