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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.

MSC:

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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[1] Andreaus, UA; Ruta, G, A review of the problem of the shear centre(s), Contin Mech Thermodyn, 10, 369-380, (1998) · Zbl 0937.74038
[2] Baniassadi, M; Ghazavizadeh, A; Rahmani, R; Abrinia, K, A novel semi-inverse solution method for elastoplastic torsion of heat treated rods, Meccanica, 45, 375-392, (2010) · Zbl 1258.74122
[3] Barretta, R; Barretta, A, Shear stresses in elastic beams: an intrinsic approach, Eur J Mech A/Solids, 29, 400-409, (2010)
[4] Barretta, R, On the relative position of twist and shear centres in the orthotropic and fiberwise homogeneous Saint-Venant beam theory, Int J Solids Struct, 49, 3038-3046, (2012)
[5] Barretta, R, On Cesàro-Volterra method in orthotropic Saint-Venant beam, J Elast, (2013) · Zbl 1267.74002
[6] Brnic, J; Turkalj, G; Canadija, M, Shear stress analysis in engineering beams using deplanation field of special 2-D finite elements, Meccanica, 45, 227-235, (2010) · Zbl 1258.74124
[7] de Saint-Venant AJCB (1855) Mémoire sur la torsion des prismes. Mém Savants Étrangers Acad Sci Paris 14:233-560
[8] de Saint-Venant AJCB (1856) Mémoire sur la flexion des prismes. J Math Pures Appl 1(2):89-189
[9] Ecsedi, I, A formulation of the centre of twist and shear for nonhomogeneous beam, Mech Res Commun, 27, 407-411, (2000) · Zbl 0984.74042
[10] Goodier, JN, A theorem on the shearing stress in beams with applications to multicellular sections, J Aeronaut Sci, 11, 272-280, (1944) · Zbl 0063.01695
[11] Lacarbonara, W; Paolone, A, On solution strategies to Saint-Venant problem, J Comput Appl Math, 206, 473-497, (2007) · Zbl 1151.74355
[12] Muskhelishvili NI (1953) Some basic problems of the mathematical theory of elasticity. Nordhoff, Groningen · Zbl 0052.41402
[13] Novozhilov VV (1961) Theory of elasticity. Pergamon, London · Zbl 0098.37604
[14] Prandtl L (1903) Zur Torsion Von Prismatischen Stäben. Phys Z 4:758-770 · JFM 34.0852.03
[15] Romano G (2007) Continuum mechanics on manifolds. Lecture notes. University of Naples Federico II, Naples. http://wpage.unina.it/romano
[16] Romano, G; Barretta, R; Barretta, A, On maupertuis principle in dynamics, Rep Mat Phys, 63, 331-346, (2009) · Zbl 1230.37067
[17] Romano, G; Barretta, R; Diaco, M, Algorithmic tangent stiffness in elastoplasticity and elastoviscoplasticity: a geometric insight, Mech Res Comm, 37, 289-292, (2010) · Zbl 1272.74071
[18] Romano, G; Barretta, R, Covariant hypo-elasticity, Eur J Mech A/Solids, 30, 1012-1023, (2011) · Zbl 1278.74015
[19] Romano, G; Barretta, R, On euler’s stretching formula in continuum mechanics, Acta Mech, 224, 211-230, (2013) · Zbl 1401.74007
[20] Romano, G; Barretta, R, Geometric constitutive theory and frame invariance, Int J Non-Linear Mech, 51, 75-86, (2013)
[21] Romano, G; Barretta, A; Barretta, R, On torsion and shear of Saint-Venant beams, Eur J Mech A/Solids, 35, 47-60, (2012) · Zbl 1349.74225
[22] Sokolnikoff IS (1956) Mathematical theory of elasticity. McGraw-Hill, New York · Zbl 0070.41104
[23] Solomon L (1968) Élasticité lineaire. Masson, Paris · Zbl 0165.27501
[24] Stephen, NG; Maltbaek, JC, The relationship between the centres of flexure and twist, Int J Mech Sci, 21, 373-377, (1979) · Zbl 0408.73049
[25] Timoshenko SP, Goodier JN (1951) Theory of elasticity. McGraw-Hill, New York · Zbl 0045.26402
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