Calculation of Combinations for Structural Shapes and Boundary Conditions by Polya Counting Theory.
Yoshihiro NARITA · TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series C · 1992
This paper introduces the Polya counting theory in combinatorial mathematics to engineering problems which may be encountered in the design of structures. The method is based on the group theory, and is used in counting the number of combinations for shapes and boundary conditions of structured. Two specific examples are demonstrated. The first application is counting in the number of patterns of a mechanical component with holes. The second example deals with the combinations of boundary conditions for composite rectangular plates, and the number of combinations is numerically verified by calculating natural frequencies of the plates.