section (looking from aſt to fore). Using class rules, an effectiveness of 90%
in bending has to be assumed in this case. From the FE results, the mean outer fibre stresses can be extracted. In combination with the total bending moment (also an FE output), the effective bending moduli can be calculated. Tese values are compared to the geometrical section properties as defined in the FE model. Te values appeared practically similar, indicating a 100% effectiveness of the section in bending. Tis finding is qualitatively supported by the stress gradients shown in the plot above. Te plot also shows the cross beams which are probably responsible for the favorable bending response.
Figure 4 A typical diffraction mesh.
Wave loads Te ship rules of the classification societies provide reference values for design wave hull girder loads. Tese sectional loads are best reproduced in the FE model using an appropriate wave pressure distribution on the outer shell, e.g. generated by a 3D diffraction tool.
Te FEA hull shape serves as the basis
for the diffraction mesh, guaranteeing full compatibility between the FE and diffraction analyses. A typical diffraction mesh is shown in figure 4. Te results of the diffraction analysis are
Figure 5 The hydrodynamic pressure distribution of the regular wave which reproduces the mid-ship vertical wave bending in sagging.
used to generate RAO data of all hull girder loads of interest. At the very least, the vertical mid-ship bending and the quarter length vertical shear should be included. Given the large opening introduced by the hopper in combination with the large length of the vessel (190m), horizontal bending and torsion are also evaluated. From the RAO data the direction and
period of the regular waves inducing maximum values for the sectional loads are determined. Tese waves are then scaled (by means of the wave height) in order to attain the reference value of the section load. Figure 5 shows the hydrodynamic
pressure distribution of the regular wave which reproduces the mid-ship vertical wave bending in sagging. Te wave has a height of 10.7m, a period of
12.6 seconds and approaches the vessel from the bow (180degs). A phase angle (-176degs)
Table 1: The design waves with the sectional loads for 190m long trailing suction hopper dredger.
The Naval Architect July/August 2009 41
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