Abstract
Combinatorial identities, trigonometric formulas, together with complex variable techniques are used to derive exact and closed expressions for the six flexure functions of certain isotropic cylinders under flexure. The cross sections are bounded either by the closed curvesr=a cosn (θ/n) (−π<θ≦) or the closed curvesr=a∣sin(θ/n)∣n(−π<θ≦), wheren isa positive integer (n>1).
Résumé
Des identiteés combinatoires et des formules trigonométriques avec des techniques de variables complexes sont utilisées pour dériver des expressions exactes et simples pour les six fonctions de flexion de quelques cylindres isotropiques. Les sections sont limitées par les courbes ferméesr=a cosn θ/n(−π≦θ≦π) et les courbesr=a∣sinθ/n∣n(−π≦θ≦π) où est un entier positif (n>1).
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Rung, D.C., Obaid, S.A. Combinatorics and flexure. Z. angew. Math. Phys. 36, 443–459 (1985). https://doi.org/10.1007/BF00944635
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DOI: https://doi.org/10.1007/BF00944635