Polya Counting Theory Applied to Combination of Edge Conditions for Generally Shaped Isotropic Plates

  • Yoshihiro Narita Hokkaido University (Professor Emeritus), C-BEST Project, Center of Technology, UNHAS
Keywords: Counting problem, combinatory mathematics, plate shape, Polya counting theory, structural response

Abstract

Structural behaviors of plate components, such as internal stress, deflection, buckling and dynamic response, are important in the structural design of aerospace, mechanical, civil and other industries. These behaviors are known to be affected not only by plate shapes and material properties but also by edge conditions. Any one of the three classical edge conditions in bending, namely free, simply supported and clamped edges, may be used to model the constraint along an edge of plates. Along the entre boundary with plural edges, there exist a wide variety of combinations in the entire plate boundary, each giving different values of structural responses. For counting the total number of possible combinations, the present paper considers Polya counting theory in combinatorial mathematics. For various plate shapes, formulas are derived for counting exact numbers in combination. In some examples, such combinations are confirmed in the figures by a trial and error approach.

Published
2019-08-31
How to Cite
Narita, Y. (2019, August 31). Polya Counting Theory Applied to Combination of Edge Conditions for Generally Shaped Isotropic Plates. EPI International Journal of Engineering, 2(2), 194-202. https://doi.org/https://doi.org/10.25042/epi-ije.082019.16