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. Keywords—Non-uniform torsion, Axial symmetric cross-section, Fourier series, Helmholtz equation, FE method.
Time-variant bulk carrier reliability analysis in pure bending intact and damage conditions
Abstract Time-variant reliability analysis of a corroded bulk carrier in intact and damage conditions is performed by First-Order (FORM), Second-Order (SORM) Reliability Methods and Importance Sampling simulation. Annual failure probabilities are determined up to 25-year ship lifetime, accounting for time-variant corrosion wastage of structural members contributing to hull girder strength. Statistical properties of hull girder capacity are determined by Monte Carlo simulation, applying three correlation models among corrosion wastages of structural members contributing to hull girder strength, namely no correlation, full correlation and full correlation among wastages of structural members belonging to the same category of compartments. A modified incremental-iterative method is applied, to account for instantaneous neutral axis rotation, in case of asymmetrical damage conditions, as for collision and grounding events. Incidence of intact/damage condition, as well as correlation among corrosion wastages, on annual sagging/hogging time-variant failure probability is investigated and discussed. Time-variant sensitivity analyses for intact and damage conditions are also performed, to investigate the incidence of random variables' uncertainties on the attained failure probability. Finally, the bulk carrier section scheme, benchmarked in the last ISSC Report, is applied as test case.
LXXXIV. The bifilar property of twisted strips
(1914). LXXXIV. The bifilar property of twisted strips. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Vol. 28, No. 168, pp. 778-787.