Page 276 - Marine Structural Design

252 Part II Ultimate Strength

used, for the ultimate strength analysis of ship hulls by Paik (1991). This method leads to a
considerable reduction in the size of the mathematical model. Furthermore, Valsgm &
Pettersen (1982) and ValsgSud & Steen (1991) developed a non-linear super-element
procedure, which can also model a complicated structure using only a few elements. So far the
ISUM method has not been applied to dynamic response analysis because geometrical
nonlinearities have been accounted for using empirical equations. It is difficult to derive
empirical equations for dynamic geometrically nonlinear analysis.
With regards to collision damages to ship hulls, there is an increasing international concern for
oil pollution from tankers due to different degrees of collision damage. Very little research has
been done on minor ship collisions, as opposed to the extensive investigations in the seventies,
which related to major collisions involving nuclear vessels. McDermott et a1 (1974) and
Kinkead (1980) presented simplified methods for analyzing local deformations of the struck
ships in minor collisions. Van Mater et aZ(1979) reviewed low-energy ship collision damage
theories and design methodologies. It0 et a1 (1984) conducted systematic large-scale static
tests and presented an excellent simplified method, which was used to analyze the strength of
double-hulled structures in collision.
The purpose of this chapter is to develop a procedure to enable the calculation of the ultimate
hull girder strength, which is as accurate as Smith’s method (1977) is for pure bending. It is
based on a FEM approach, and the procedure may save manpower and computer CPU as
much as the ISUM and the super-element approach can do. Combining the plastic node
method (PNM) with the general FEM approach for geometrically nonlinear problems, the
present PNM approach may be applied to dynamic geometrical and material nonlinear analysis
that is useful for both ultimate strength and impact response analysis.
This Chapter first presents an accurate and efficient finite element procedure for the static and
dynamic collapse analyses of ship hulls. This procedure accounts for geometric and material
nonlinearities by combining elastic, large displacement analysis theories with a plastic hinge
model. A set of finite elements such as beam-column, stiffened plate, and shear panel are
developed. Secondly, mathematical equations for the estimation of ultimate moment and
moments interaction are then presented and discussed. Thirdly, the Smith method for hull
girder analysis is modified to account for the effect of corrosion defects and fatigue cracks.
These equations and analysis methods are then compared through ultimate strength analysis of
a couple of ship hull girders. Finally, practical applications to the ultimate longitudinal
strength analysis of ship hulls and response analysis of tankers involved in collisions are also
demonstrated.
This Chapter is based on Bai, Bendiksen and Pedersen (1993) and Sun and Bai (2001).

13.2 Hull Structural Analysis Based on the Plastic Node Method
The finite element formulation for the collapse analysis of ship hulls is described in the
following sections. The analysis is based on a standard beam-column analysis. This involves
formulations for the collapse of plates and stiffened plates, shear panel elements, and non-
linear spring elements.
13.2.1 Beam-Column Element
Figure 13.1 shows a three-dimensional beam-column element. It is a prismatic Timoshenko
beam, which has an arbitrary cross-sectional shape. An updated Lagrangian approach has been