Nonlinear analysis of elastic round rods. (English) Zbl 0663.73032

Algostino, Franco; Bigi, Dante; Cicala, Placido

Meccanica 22, 203-209 (1987).

The nonlinear theory of elastic round rods is split into a vector equation concerning the properties of finite inextensional flexural deflections and a scalar equation concerning torsional deformations. In particular, the related boundary conditions examined for the case of a Cardan joint. The buckling configurations of a rod under tension and torsion, constrained at both ends by Cardan joints, are determined by the linearized form of the above theory and compared with previous findings about the rod with cylindrical end hinges.

MSC:

74G60	Bifurcation and buckling
74K10	Rods (beams, columns, shafts, arches, rings, etc.)

Keywords:

nonlinear theory; elastic round rods; vector equation; finite inextensional flexural deflections; scalar equation; torsional deformations; boundary conditions; Cardan joint; cylindrical end hinges

References:

[1]	Algostino F.,Stati critici della verga soggetta a trazione e torsione, AIMETA, Res. Rep. No. 12, 1985.
[2]	Cicala P.,Helicoidal buckling of an elastic rod, Meccanica, 1985, pp. 124–126.
[3]	Cicala P.,Teoria non lineare delle verghe e delle travi elastiche, Memorie Acc. d. Scienze Torino, Genn. 1985.
[4]	Greenwood D.C.,Mechanical power transmissions, Mc. Graw-Hill, London, 1962.
[5]	Koiter W.T.,Buckling of a flexible shaft under torque loads transmitted by Cardan joints, Ingenieur Archiv, 1980, pp. 369–373. · Zbl 0438.73035
[6]	Landau L.D., Lifshitz E.M.,Theory of Elasticity, Pergamon Press, London, 1959.
[7]	Zachmann D.W.,Nonlinear analysis of a twisted axially loaded elastic rod, Quart. Appl. Math., April 1979, pp. 67–72. · Zbl 0403.73062
[8]	Ziegler H.,Linear elastic stability, Z.A.M.P., 1953, pp. 89–115, 168–185.