On the Exact Solution of Non-Uniform Torsion for Beams with Axial Symmetric Cross-Section
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.
[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.
[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.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:52037", author = "A.Campanile and M. Mandarino and V. Piscopo and A. Pranzitelli", title = "On the Exact Solution of Non-Uniform Torsion for Beams with Axial Symmetric Cross-Section", abstract = "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 = "Non-uniform torsion, Axial symmetric cross-section,
Fourier series, Helmholtz equation, FE method.", volume = "3", number = "7", pages = "751-10", }