Page 304 - Marine Structural Design

280 Part II Ultimate Strength

assumptions about the position of the neutral axis for the hull beam are made when
progressive collapse is analyzed. By using this transformation, the shifting of the neutral axis
in the plate elements is also taken into account.
The results obtained !?om this PNM method have been compared with experimental results
and other numerical solutions, which have experienced problems with plate and overall
buckling. The comparison appears to be in good agreement with these simple examples.
The present PNM method has been compared with experiments that deal with the ultimate
longitudinal strength of a tanker. Calculations have been performed with and without initial
plate imperfections. When disregarding the plate imperfections, the ultimate load is 16%
higher.
The calculation of the ultimate longitudinal strength of an existing double hull product tanker
is shown. The ratio between the ultimate moment and the plastic moment was compared with
an empirical prediction and the results showed to be in good agreement. The result of the
analysis is not only the ultimate bending moment, but is also the ultimate failure mode. A
failure in sagging would be the most dramatic.
Finally, the PNM method was used to derive the force-indentation curve for a double-hulled
product tanker subjected to a concentrated force in the middle of the side. The force-
indentation curve derived by a quasi-static analysis is in agreement with the approximate
method.
This work has shown that the Plastic Node Method, along with the new element, is in
agreement with existing approximate methods for hull collapse loads and moreover, provides
much more information about the progressive failure. In this respect, the Plastic Node Method
approaches the general finite element method while using a much simpler element mesh,
which is considered to be more efficient.
A modified Smith method to compute the ultimate value of the longitudinal bending moment
at the midship section was introduced using an effective width formula for the plating. The
modified Smith method accounts for the manufacturing imperfections, including initial
eccentricity of stiffeners, the plating’s initial residual stress, and deflection. The corrosion
defect was considered as an exponential time function with a random steady corrosion rate,
which is assumed to uniformly reduce the plate thickness. Crack propagation was predicted
based on the Paris-Erdogen equation. Crack initiation time and coating lifetime were also
taken into account.
An equation for estimating ultimate strength of hull girders was suggested. The hull girders
used in the ISSC benchmark calculations by Yao et al (2000), were used to examine the
accuracy of this equation. It has been demonstrated that the equation provides quite reasonable
results and may be useful in estimating the bending moment strength.

13.8 References
1. Andersen, T. L., (1988), “Ductile and Brittle Fracture Analysis of Surface Flows Using
CTOD”, Experimental Mechanics, pp. 188-193.
2. Bai, Y., Bendiksen, E. and Pedersen, P. Temdrup (1993) “Collapse Analysis of Ship
Hull”, J. of Marine Structures, Vo1.6, pp. 485-507.