Abstract: This paper deals with the problem of non-uniform
torsion in thin-walled elastic beams with asymmetric cross-section,
removing the basic concept of a fixed center of twist, necessary in the
Vlasov-s and Benscoter-s theories to obtain a warping stress field
equivalent to zero. In this new torsion/flexure theory, despite of the
classical ones, the warping function will punctually satisfy the first
indefinite equilibrium equation along the beam axis and it wont- be
necessary to introduce the classical congruence condition, to take into
account the effect of the beam restraints. The solution, based on the
Fourier development of the displacement field, is obtained assuming
that the applied external torque is constant along the beam axis and
on both beam ends the unit twist angle and the warping axial
displacement functions are totally restrained.
Finally, in order to verify the feasibility of the proposed method
and to compare it with the classical theories, two applications are
carried out. The first one, relative to an open profile, is necessary to
test the numerical method adopted to find the solution; the second
one, instead, is relative to a simplified containership section,
considered as full restrained in correspondence of two adjacent
transverse bulkheads.
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.