Trans RINA, Vol 154, Part A2, Intl J Maritime Eng, Apr-Jun 2012
large strain nonlinear. Both full and reduced integration schemes are supported. This element is suitable for analyzing thin-walled structures.
The residual stresses are not included in the FE analyses. The geometric and material nonlinearities are both taken into account, including elastic-plastic large deflection. The assumed material properties use the characteristic values of yield stress and Young’s modulus. Where appropriate, a bi-linear isotropic elastic-plastic material model excluding strain rate effects is to be used. A plastic tangent modulus of 1,000 MPa is acceptable for normal and high strength steel [1]. The following are the other material properties: Young’s modulus E = 200 GPa and Poisson’s ratio v= 0.3.
3.2 BOUNDARY CONDITIONS AND LOADING
The coordinate system and load in the FE analyses is shown in Figure 5.
analysis. The pressure Px in the x direction is applied on the edge of the plate and the stiffeners.
Table 4 Description for the boundary conditions NBC
Description
1 A-A1:ux, uy, uz, θx, θy and θz 2 A-A1: ux, uy, uz 3 B-B1: uy, uz, θx, θy, θz and equal ux 4 B-B1: uy, uz, and equal ux 5 F, F1, D, and D1 on frame (for 3 and 1/2+1+1/2 bays model): uz
6 F, F1 on frame (for 1+1 bays model): uz 7 The intersection between frame and plate: uz 8
AB edge: ux, θz and θx 9 A1B1 edge: θz, θx and equal ux
3.3 SENSITIVITY ANALYSIS OF ELEMENT SIZE DEFINITION
It has been realized that the incorrect modelling
techniques in FE analysis may cause a significant amount of computational errors. The shell elements mesh should be fine enough to properly describe the model shape, also after deformation. A balance between required accuracy and efforts is needed. The FS2-A21 stiffened panel with C1 condition is used to study the convergence of the mesh sizes in the plate and web of the stiffeners.
Table 5 Ultimate strengths (Ns=5) No.
Figure 5 Coordinate system and load in the FE analyses Table 3 Boundary conditions in the FE analyses NBC
3 bays
2 bays 2 bays (1+1)
C1 C2 C3 C4 C5 C6 C7 C8 C9 Note:
1 √ √ √ × √ × √ × × 2 × × × √ × √ × √ √ 3 √ √ √ × √ × √ × × 4 × × × √ × √ × √ √ 5 √ √ √ √ √ √ × × × 6 × × × × × × √ √ × 7 × √ √ √ √ √ √ √ × 8 × × √ √ √ √ √ √ √ 9 × × √ √ √ √ √ √ √ Different models and boundary conditions
correspond to different location of the stiffeners.
The stiffened panel models, including 3 bays, 1/2+1+1/2 bays, 1+1 bays and 1 bay, are simulated with different boundary conditions as shown in Table 3 and 4. The NBC is the number of the boundary conditions description. To investigate the effect of model geometry and boundary condition on the collapse behaviour of the stiffened panels, nine configurations are calculated in the FE
A-70 455
450 12 345 Ns
Figure 8 Ns - ultimate strength (Su) ©2012: The Royal Institution of Naval Architects
1 2 3 4 5
1bay
100 200 300 400 500
Figure 6 Element setting 460 Ns=5
0 01 234 5 dL/L
Nt=2,Nl=4 Nt=4,Nl=8 Nt=8,Nl=16 Nt=12,Nl=24 Nt=16,Nl=32
Figure 7 Average stress- shortening curves
Nt Nl 2 4 8
4 8
12 16
16 24 32
Su (MPa) 480 460 455 454 455
Su (MPa)
Average stress
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