Page 281 - Marine Structural Design

Chapter 13 Collapse Analysis ofship Hulls 257

13.2.3 Shear Panel Element
The shear stiffness is lost when a stiffened plate structure is modeled as a grillage. Considering
this, an additional element that only has shear stiffness is used. The increment of the shear
strain dy in the local coordinate system is related to the increments of nodal displacements
(du, 1 as follows (Bathe, 1982):
dY = [B, XdUS f (13.20)

where [B, ]denotes the strain-displacement matrix.
The tangent stress-strain relationship is taken as:
dt = G,dy (13.21)

where,

(13.22)

where yy denotes the shear strain for yielding.
Finally, the element stiffness matrix is obtained:

(13.23)

where V is the volume of the element. The local coordinate system of the element is updated
and a coordinate transformation is carried out at each time step.
The element and their interaction are best understood in Figure 13.4.
13.2.4 Non-Linear Spring Element

In addition to the three element types, a spring with non-linear stiffness may also be employed.
Any node may be connected, in any of the six degrees of freedom, by non-linear springs. The
stiffness is given by points on the force-displacement curve. Stiffness as a function of
displacement is the slope of the force displacement curve (see Figure 13.5). In addition to the
points on this curve, the unloading stiffness must be defined.
13.2.5 Tension Tearing Rupture

Fatigue cracks and/or welding defects may initiate cleavage, ductile tearing, plastic collapse,
or a combination of these events during the collapse. This paper determines the capacity of
cracked members by either the CTOD design curve approach (Burdekin, & Dawes, 1971), or
the level-3 CTOD method (Andersen, 1988).
In terms of the applied strain E, the CTOD design curve is expressed as:

(13.24)