Trans RINA, Vol 154, Part A2, Intl J Maritime Eng, Apr-Jun 2012
Figure 6 shows element number setting for Nt, Nl and Ns. Figure 7 and Table 5 shows the average stress-shortening curves and the ultimate strength of the stiffened panel FS2-A21 with different Nt and Nl when Ns is equal to 5. It can be seen that the Su3 and Su4 are almost the same, namely the mesh size setting as Nt=8 and Nl=16 for the plates is fine enough. Figure 8 show the ultimate strength of the stiffened panel with different Ns, which illustrates that the Ns affect
slightly the ultimate strength.
According to the mesh sizes convergence study, the mesh sizes are set as Nt=8, Nl=16, Ns=5 and 3 elements in the flange of the frame.
3.4 INITIAL IMPERFECTIONS
It has generally been found that initial imperfections tend to decrease the rigidity and ultimate strength of plates. These initial imperfections affect
significantly the
ultimate strength of stiffened panel and should be accounted for. The imperfections are caused during a complex fabrication process and are subject to significant uncertainty related to the magnitude and spatial variation.
Kmiecik [15] modelled the initial deflection as the superimposition
of the Fourier components. The
behaviour of plates subjected to buckling loads depends to a considerable degree on the shape of their initial deflection [16-19]. The most accurate method is to use real measured data, but it is not always available. For design purposes some sort
of representative initial
imperfection is used [20, 21]. The numerical analysis in this paper aims to investigate the influence of the boundary condition and geometric model on the ultimate strength and thus, the equivalent initial imperfections are assumed as plate initial deflection, column-type initial distortions of stiffeners and sideways initial distortions of stiffeners as follows [22] :
Hungry horse mode initial deflection (wopl) of the local plate with the shape corresponding to buckling mode due to uniaxial compressive load having the magnitude of b/200.
Column-type initial deflection (woc) of the stiffeners with the shape corresponding to buckling mode due to uniaxial compressive load having the magnitude of a/1000.
Side-ways initial deflection (vos) of the stiffeners with the shape corresponding to buckling mode due to uniaxial compressive load having the magnitude of a/1000.
To impose the initial imperfection in the FE analysis, linear buckling analysis
is performed for the target
stiffened panel to find out the related buckling modes of the plate and the stiffeners. The geometry properties, for example the thickness of the plates and the stiffeners, are changed to decouple those deformations from lower eigenmodes and to obtain the desired shapes for the plate
100 200 300 400 500 600
0 FS2A
3Bay-C1 3Bay-C2 3Bay-C3 3Bay-C4 2Bay1-C5 2Bay1-C6 2Bay2-C7 2Bay2-C8 1Bay-C9
0 2 4 6 8 10 12 14 dL/L(103
) Figure 9 Average stress-shortening curves for FS2-A
100 200 300 400 500 600
0 BS2A
3Bay-C1 3Bay-C2 3Bay-C3 3Bay-C4 2Bay1-C5 2Bay1-C6 2Bay2-C7 2Bay2-C8 1Bay-C9
Figure 10 Average stress-shortening curves for BS2-A
0 2 4 6 8 10 12 14 dL/L(103
)
100 200 300 400 500
0 LS2A
and the stiffener out-of-plane deformations. The three types of distortions are superimposed altogether in the FE model as equivalent initial imperfection of
the
stiffened panels. 4. RESULTS OF THE FEM ANALYSIS
The strength of each panel is obtained by summing the reaction force on each node on the opposite boundary where the load is applied and divided by the sectional area of the stiffened panel. These calculations must be performed for each step of the non-linear analysis.
3Bay-C1 3Bay-C2 3Bay-C3 3Bay-C4 2Bay1-C5 2Bay1-C6 2Bay2-C7 2Bay2-C8 1Bay-C9
0 246 8 dL/L(103 ) Figure 11 Average stress-shortening curves for LS2-A
Figure 9 - 12 show the average stress-shortening curves of the stiffened panels with B0 = 300 mm for different models and boundary conditions. It can be seen that a linear behaviour for the FS2-A panels and nonlinear behaviour for the LS2-A, BS2-A and US2-A panels until the ultimate compressive stress are achieved. This main
©2012: The Royal Institution of Naval Architects A-71 10 12 14
Stress (Mpa)
Stress (Mpa)
Stress (Mpa)
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