Sliding Roof Deflection Analysis of Villo Motor Yacht
Gerard Petersen gerard@rhinocentre.nl September 2010
Goal Find out what the maximum deflection of the roof will be just before it will be supported by the mast. Secondary is to locate maximum stresses in the geometry and optimize the geometry or structure to minimize hotspot locations.
Introduction The Villo design (www.villo.nl) features a sliding roof and windows that slide down in order to open up the saloon and turn it into a cockpit. The roof slides with roll wheels, two wheels on the sides and one on the end of the beam. At the front end the roof is supported by a mast and will be fixed with a catch mechanism to prevent the roof to be blown upwards in strong winds and storm. The roof itself will be made from aluminum or wood/epoxy composites. Both solutions show a structure with an estimated weight of approx. 250 kg.
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Setting up calculation 01 Scan & Solve asks for a single solid as input, therefore the first analysis is set up with the roof only being a shell, as if the roof is made of solid wood or aluminum. This keeps the geometry simple and calculation time short. In this case Aluminum 6061 is chosen. For the restraints three small surfaces are created representing the contact area with the rollers. The load which is applied is set to a Scalar Load of 3000 Newton. The Gravity option is not checked as the ‘solid’ roof will then weigh more than 8000 kg. The first calculation is done with a resolution of 10000 elements. This calculation of Geometry-01 shows a z-displacement near the mast of 4,744 mm.
Danger Level Von Mises
Von Mises Stress
z-displacement
The calculation is now repeated with a resolution of 28000 elements resulting in a displacement of 6,538 mm. Calculated with 50000 elements the displacement is 8,000 mm. See attached a table with an overview of the calculations and results. Hot Spots
Hot Spots
Magnified Deflection
The Hot Spot locations are a little forward of the side rollers and more important at the topside of the beam connection to the roof. The bending of the beam is an important factor for the total deflection of the roof at the front end near the mast. Is it an option to change the shape of the beam in order to minimize stresses and deflection?
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Alternative Geometry- 02 By increasing the area moment of inertia of the beam, the maximum stresses will decrease, but more important is whether this leads to less deflection of the roof near the mast. Therefore the beam geometry is now a more triangular shape. After running several calculations with the same input as the original geometry The picture shows less stress near the connection of the beam and roof. The deflection is 3,815 mm. This is 80% of the deflection of Geometry01 with a small beam.
Von Mises Stress
Hollow Geometry-03 The next challenge is to calculate the roof based on a hollow structure of aluminum frames, stiffeners and shell plating. Due to the expected complexity of the structure the time to calculate a solution will increase dramatically. Therefore a simplified 3d structure is applied with less frames and stiffeners than in reality would exist. This might lead to a calculation with a more elastic/plastic structure. It is interesting to find out what the calculation results will be. Modeling this type of structure offers another Scan & Solve issue which is the creation of a single solid which is fully closed. If a structure of frames and stiffeners is covered with plating, inside the object hollow spaces, cavities, will occur. When modeled properly in Rhino this leads to independent volumes inside the shell without any connection to the shell. This problem is tackled by small rectangular pipes connecting the outer shell with inner cavities. Thus creating an open cell structure.
detail structure
Calculation results And yes, this calculation takes much more time to compute. At the lowest resolution of elements it takes a few hours. For curiosity reasons also calculations were executed at a higher resolution which took one night to compute. The results show a larger deflection with a maximum of nearly 10 mm. for the calculation at a higher amount of elements. Von Mises Stress
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Calculation results Case 1 2 3 4 5 6 7 8 9
Geometry Solid 01 Solid 01 Solid 01 Solid 02 Solid 02 Solid 02 Solid 02 Solid 03 Solid 03
Aluminum 6061 6061 6061 6061 6061 6061 6061 6061 6061
elements 10000 28000 50092 10000 28000 50092 70000 10000 20635
Calcution Z-displacment 4,744 6,538 7,994 3,815 5,202 5,954 6,582 6,403 9,360
delta deflection compared to case 100% 138% 1 169% 1 80% 1 136% 4 156% 4 173% 4 168% 4 146% 8
wider beam connection wider beam connection wider beam connection wider beam connection Hollow Structure Hollow Structure
Conclusion With my limited theoretical knowledge of FEA, Scan & Solve shows the largest deflection at the most realistic situation of a hollow structure with only a few frames and stiffeners. As the final structure will contain much more frames and stiffeners the roof will be stiffer and less deflection is expected then. Furthermore the top of the mast will be shaped with a slope of approx. 25 mm. Therefore a deflection of 10 mm. will never be problematic when the roof touches the slope and is then supported by the mast when it slides out to the maximum position. Unless this document shows that fundamental FEA mistakes were made, it is expected that this roof will work well in this layout.
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