XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX''"> Draping Simulation (Developable Surfaces)
Definition of Developable Surfaces
An important subset of curved surfaces is developable surfaces. These surfaces can always be manufactured using sheet materials without the material needing to shear. At any point, there will be no curvature in one direction and maximum curvature in the orthogonal direction. Mathematically, this means that these surfaces are characterized by zero Gaussian curvature over their entire area. Cylinders are one example of developable surfaces found in many structures.
Note that all developable surfaces are ruled surfaces. However, not all ruled surfaces are developable. For example, a hyperbola of one sheet (such as a cooling tower shape) is not developable.
Although many CAD systems have provision for developing flat patterns from developable surfaces, the definition of material orientation is not trivial, particularly when the curvature is great.
The draping process for development is unique. That means that the cutout profile is always the same, and that definition of fibre orientation at any point uniquely describe the fibre orientations at all other points on the surface.
Example of Waffle Plate
One example of a developable surface with complex fibre orientations is a waffle plate used as a core for sandwich structures. A typical geometry for a circular sandwich structure is shown in
Figure 2‑3. As the core is predominantly loaded in shear, it would be if the majority of fibres lay in the +/-45 directions along the webs. However, if these directions are ideal for one web, they will obviously not be the same for other webs.
Figure 2‑3 Geometry of a Curved Waffle Plate
The MSC.Laminate Modeler can be used to quantify the effect of varying fibre orientation both qualitatively and quantitatively. For example, if a piece of woven fabric is draped from the middle rib so that the average angle is +/-45 along the webs of the central rib, we see that the angle on the webs near the edge of the plate are more like 0/90. This latter direction will obviously result in poor shear stiffness and strength in this direction.
Having understood this limitation, the designer can then make an informed decision whether to specify a quai-isotropic layup for the whole of the waffle plate, or to make the waffle plate out of several different plies oriented in different directions. Both alternatives can be modeled and analyzed rapidly using the MSC.Laminate Modeler, and an informed choice made on the basis of analysis results.
Figure 2‑4 Variation of Fibre Angles over Waffle Plate
Benefits of MSC.Laminate Modeler
1. Visual feedback of fibre orientation.
2. Accurate orientation data for analysis model.
3. Exact flat-pattern generation.
