Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31100
On the Exact Solution of Non-Uniform Torsion for Beams with Axial Symmetric Cross-Section

Authors: A.Campanile, M. Mandarino, V. Piscopo, A. Pranzitelli


In the traditional theory of non-uniform torsion the axial displacement field is expressed as the product of the unit twist angle and the warping function. The first one, variable along the beam axis, is obtained by a global congruence condition; the second one, instead, defined over the cross-section, is determined by solving a Neumann problem associated to the Laplace equation, as well as for the uniform torsion problem. So, as in the classical theory the warping function doesn-t punctually satisfy the first indefinite equilibrium equation, the principal aim of this work is to develop a new theory for non-uniform torsion of beams with axial symmetric cross-section, fully restrained on both ends and loaded by a constant torque, that permits to punctually satisfy the previous equation, by means of a trigonometric expansion of the axial displacement and unit twist angle functions. Furthermore, as the classical theory is generally applied with good results to the global and local analysis of ship structures, two beams having the first one an open profile, the second one a closed section, have been analyzed, in order to compare the two theories.

Keywords: Fourier Series, Helmholtz equation, Non-uniform torsion, Axial symmetric cross-section, FE method

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2029


[1] R. Fiorenza, Appunti delle lezioni di Analisi Funzionale, Gli Strumenti di Coinor, 2005.
[2] V. Vlasov, Thin-walled elastic beams, Jerusalem: Israel program for Scientific Translation Ltd , 1961.
[3] A.D. Polyanin, Linear partial differential equations for Engineers and Scientists, CHAPMAN & HALL/CRC.
[4] C.J. Burgoyne, H. Brown, ÔÇÿÔÇÿNon uniform elastic torsion", International Journal of Mechanical Sciences, Vol. 36, No. 1, pp. 23- 38, 1994.
[5] T. Coppola, E. Fasano, M. Mandarino, A. Turtoro, "The restrained warping applied to catamarans", Fast -97 Papers, 1997.
[6] K. Haslum, A. Tonnensen, ÔÇÿÔÇÿAn analysis of torsion in ship hulls", European Shipbuilding, No. 5/6, pp. 67-90, 1972.