On stress function in Saint-Venant beams. (English) Zbl 1293.74114

From the conclusion: A general discussion concerning existence of stress function in Saint-Venant beams with simply or multiply connected cross-sections under shear and torsion has been performed. Significant implications are the following:
Existence of stress function under torsion holds true for any beam cross-section.
Existence of stress function for any non-zero shearing vector holds true only for tubular cross-sections whose hole is centered at the cross-section centroid.


74G50 Saint-Venant’s principle
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74B05 Classical linear elasticity
74G25 Global existence of solutions for equilibrium problems in solid mechanics (MSC2010)


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