Abstract
Special complex variables techniques are used to obtain the six flexure functions (one of which is the torsion function) of a certain isotropic cylinder under flexure. The cross section is bounded by the closed curver=a sin4(θ/4) (−π<θ⩽π). The torsional rigidity, moment integrals, and the associated twist are also evaluated for this beam. It is worthy to mention that these techniques work successfully when they are applied to any of the cross sections bounded byr=a∥sin(θ/n)∥n·(−π<θ⩽π), wheren is a positive integer (n>1).
Résumé
On utilisie des techniques spéciales sur les variables complexes pour obtenir six functions du fléchissement (l'une d'elles est la fonction de torsion) d'un certain cylindre isotrope. La section est bordée par la courbe ferméer=a sin4(θ/4), −π<θ⩽π. La rigidité à la torsion de cette barre, les intégrales des moments et le moment de torsion sont aussi évalués. Mentionons encore que ces techniques s'appliquent aussi avec succès aux barres de sectionr=a∥sin(θ/v)∥n, −π<θ⩽π, oùn est un entier positif.
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Obaid, S.A. Flexure of beams with certain curvilinear cross sections. Z. angew. Math. Phys. 34, 439–449 (1983). https://doi.org/10.1007/BF00944707
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DOI: https://doi.org/10.1007/BF00944707