Trans RINA, Vol 153, Part B2, Intl J Small Craft Tech, 2011 Jul-Dec
bending moment is included and the bending stiffness becomes a function of the axial load [8].
Beam column finite elements are used to simulate spars (masts, spreaders and boom). Running rigging elements (shrouds, stays, vang and mainsheet) are treated as cable finite elements, which are not capable of carrying either bending loads or compressive loads [8]. The stress is assumed to be uniform over the entire element. To compute the forestay sag, the FEM of the forestay itself is composed by a sequence of beam column elements, since cable finite elements would lead to instability of the FEM. To avoid the compression on the cable finite elements a compression check is performed for each iteration, allowing cables to be slack without transferring any reaction to the rig. Cables can be tuned by a virtual turnbuckle, specifying the strain of every finite element. Also the mast
step can be tuned, pushing the mast
upwards or moving it fore and aft. Weight is considered as an external force applied to the rig, computed by the properties of the different
3 rig
elements and taking in account the appropriate heeling angle. The results of the FEM simulation provide:
Compression load on every beam column element (mast, spreaders and boom).
Tensile load on cables and the breaking load ratio. Maximum displacement and position on the mast where it
occurs (from configuration).
Longitudinal and lateral mast bend curve and forestay sag curve and their maximum values.
Reaction on the hull at the mast step and at the stay and shroud chainplates.
Extensive validation of the software has been performed. Non-linear cantilever beam test cases have been found in literature, from Ansys and Patran simulations [9], [10], [11]. The authors have replicated the geometry and load cases in the presented method and have compared the resultant deflection at the tip. The cantilever beam has been loaded with a concentrated force and separately with a concentrated moment. As large deformations appear a non-linear geometric analysis is required. Furthermore,
results have been validated against
commercial available software for a simple fractional rig with and without spreaders. Comparisons between the published results and those calculated with the presented method are very positive, showing differences of less than 1%.
5. OPTIMAL RIG DESIGN - CASE STUDY
At the present time, even for cruising yachts, it is very important
to maximize the sailing performance.
Maximising the contribution of the rig to sailing performance means minimizing the weight of the overall structure and optimizing the section shape. Thus, optimal mast design is driven by a realistic estimation of the maximum operating loading conditions. Rig loads will
©2011: The Royal Institution of Naval Architects Figure 3: TP52 sailplan and rig.
Following the analysis procedure described in section 2 and Table 1 the aerodynamic analysis of the sailplan (Figure 4) was carried out in the sailing and trimming condition displayed in Table 5. Aerodynamic results are displayed in Table 6.
Table 5: Sailing conditions. Sheeting angles
Heeling angle
Apparent Wind Angle (AWA) Apparent Wind Speed (AWS)
Jib Mainsail
8.5° 0°
10° 22°
7.2 m/s
Table 6: Aerodynamic analysis main results. Jib
CP
CDrive CSide
η ( CDrive / CSide ) Heeling moment
2.12 0.52 2.05 0.25
95 kNm
Mainsail 1.69 0.24 1.64 0.15
the undeformed 4 5
define the dimensions of the spars and the stays and the type of material to use. This section describes how the method presented in this paper can be used to optimise a TP52 rig design (Figure 3).
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