Trans RINA, Vol 153, Part B2, Intl J Small Craft Tech, 2011 Jul-Dec 6. IMPACT OF WRINKLING
Wrinkling has a dramatic impact on the shape of the sail. As shown in [9], in the case of upwind sails the occurrence of wrinkling, voluntary or involuntary, can have a significant effect on the amount of draft, its position and entry and exit angles. In [9] this is attributed to the physical model as well as grid kinematics effects.
In the case of a spinnaker, where the sail’s displacements and changes in surface curvature are significantly larger, the effect of including a
observed in a dramatic fashion. To show the
effects flying shapes wrinkling model can be under constant
pressure difference were calculated for a symmetric spinnaker with significant tack displacement and sheet length change. In Figure 5 the designed shape of the investigated spinnaker is shown. For discretization a triangular net of 7250 elements is used.
Figure 6 gives the flying shapes without and with wrinkling model.
Figure 7: Principal stress 1 without and with wrinkling model
sheet of plastic or metal under compression. Figure 6, right does not show this behaviour. Wrinkling is not visible as it occurs on a sub-element scale.
Figures 7 and 8 show principal stresses in direction 1 and 2. With wrinkling model the principal stresses 1 mostly radiate out from the corners and go up the side leeches, dissipating towards the centre of the sail.
Principal
stresses 2 are oriented perpendicular to them and equal or larger than zero. Without wrinkling model the principal stresses 1 are primarily oriented along the folds with significantly folds.
negative principal stresses 2 across the
Figure 5: Mould of tested spinnaker (design shape)
Figure 8: Principal stress 2 without and with wrinkling model
The folds can be attributed to an effect known as grid- locking. This effect typically occurs on low-order triangular membrane or shell elements without a wrinkling model. These elements have the particular property that compressive deformation is accompanied by opposing nodal forces. Higher order elements can deform conically (e.g. buckling), the wrinkling model contains the condition that compression is free of force.
Figure 6: Flying shapes without (left) and with (right) wrinkling model
It can be seen that without accounting for wrinkling (Figure 6, left), significant folds radiate from the tack. Under strong Gaussian
deformations the membrane without wrinkling model appears to behave like a thin
This grid-locking effect imposes a restriction on nodal motion in the affected areas and therefore erroneous nodal forces and deformed shape. It is important to note that the folds cannot be seen as a representation of folds occurring on the real sail in any way as the particular size and geometry of these folds is dictated purely by the mesh resolution. To evaluate the real shape of folds occurring on the sail would necessitate modelling the sail using higher order shell elements combined with a buckling analysis.
©2011: The Royal Institution of Naval Architects B-75
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