Figure 2 Typical comparison, vertical shear and bending.
to be rearranged for FE application. Several tuning options are available which, may as well be used to get the total LCG equal to the FEM determined LCB instead of to the reference LCG. Tis depends on the specific particulars of the project. In case the weight and buoyancy in FEM
are not exactly the same (which will oſten be the case for practical considerations) a balance has to be found in order to model the free floating situation correctly (i.e. no residual reaction forces). Tis can be done by either a hydrostatic correction using a mesh of soſt springs or by correcting the weight distribution through a slightly modified gravity acceleration. Te first option will be the most representative of reality. Finally, the resemblance between FEM
and hydrostatic hull girder loads should be ‘reasonable’. A balance between accuracy and speed of analysis should be pursued on a project basis. Te plots shown in figure 2 offer a typical comparison (vertical shear and bending), which meets Bureau Veritas requirements of deviations in a bending moment of less than 10%[1]. In the plots, ‘PIAS’ refers to the reference hydrostatic calculation, ‘ANSYS’ and ‘AQWA’ are the FE and diffraction tools used, respectively [2 and 3]. In assessing the still water load case, the
shear force distribution should be leading, because it is the most direct representation of the load distribution (i.e. the first integral, without any compromising assumptions). The bending moment distribution is not only the second integration step but, is also prone to more errors due to uncertainties in the neutral line in the FEA and the effect of hydrostatic end loads on the bending (which can be substantial). For large hopper dredgers, the effectiveness
of the mid-ship cross section in overall vertical bending is an issue, due to the large opening of the hopper. Figure 3 shows the FEA results of the longitudinal stresses in the mid-ship
Figure 3 The FEA results of the longitudinal stresses in the mid-ship section (looking from aft to fore).
The Naval Architect July/August 2009 39
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