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A.1 Preliminary Calculation of the Honeycomb plate using finite element Analysis
A.1.4 Model description
The proposed honeycomb struture has two aluminum skins of 0.5 mm thickness separated by a low density aluminum honeycomb core of 50 mm thickness. On the sides of the plate is an aluminum frame with vertical ribs. This frame, made of 2 mm thick aluminum, reinforces the plate. On top of that, a triangle aluminum piece maintains this frame to the brackets fixed to the USS members.
Since our software does not allow a stress calculation in a real honeycomb structure, we therefore have simulated this honeycomb plate by using a sort of "volumic" model with an aluminum core made from a collection of 3-D solid elements in between the two aluminum skins represented by some shell elements. The model is presented in Figures A-6 and A-7
- Types of finite elements
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The present version is a 3-D model. It requires a multi spacial shell as a special option. The finite element used is either a shell element or a solid one, so it can be either bidimensional or tridimensional, but its degree of freedom is always six as for the shell element. Its particularity is that we can put together a shell and a solid element.
In the type of problem we have, taking into account the ratio of thicknesses between the skin and the core, we can claim that a shell-solid-shell assembly is reasonably conceivable. Moreover, since the aluminum skins are completely sticked to the aluminum core, we have geometrically sticked the nodes of the shell elements to the corresponding nodes of the solid elements.
- Material Characteristics
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Table A-1 shows the characteristics of the materials to be used for the construction of the honeycomb plate.
Material characteristics for the honeycomb structure
| | Aluminum skin | Aeroweb 5052 aluminum core | Aluminum frame | Aluminum triangle |
| Density r0 (kg/m3) | 2700 | 49.6 | 2700 | 2700 |
| Young modulus (N/m2) | 72x109 | see Table A-2 | 72x109 | 72x109 |
| Poisson coefficient | 0.33 | see Table A-2 | 0.33 | 0.33 |
| Thickness (m) | 0.0005 | 0.05 | 0.002 | 0.002 |
Table A-2 represents the values of the symmetric tensor D which links stresses to strains by the formula: s=D e
Values of the symmetric tensor D
| Ex | 0 | 0 | 0 | 0 | 0 |
| | Ey | 0 | 0 | 0 | 0 |
| | | Ez | 0 | 0 | 0 |
| | | | Gyz | 0 | 0 |
| | | | | Gxz | 0 |
| | | | | | Gxy |
with the following values: Ex = 5 x 106 N/m2; Ey = 5 x 106 N/m2; Ez = 517 x 106 N/m2, Gxy = 10 x 106 N/m2; Gxz= 310 x 106 N/m2; Gyz = 152 x 106 N/m2
- Boundary Conditions
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The aluminum triangle is fixed to the brackets by four rivets; therefore, all translations and rotations in this fixed region are completely blocked.
- Loads
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We have three different load cases corresponding to a permutation of three load factors applied simultaneously on the weight supported by the honeycomb plate (half weight of the counter estimated to 40 kg: a little bit more heavy than the real weight), which are:
- LOAD CASE 1
- 17 g along the global X axis of the detector Fx = 6670.8 N
- 4.25 g along the global Y axis of the detector Fy = 1667.7 N
4.25 g along the global Z axis of the detector Fz = 1667.7 N
- LOAD CASE 2
- 4.25 g along the global X axis of the detector Fx = 1667.7 N
- 17 g along the global Y axis of the detector Fy = 6670.8 N
- 4.25 g along the global Z axis of the detector Fz = 1667.7 N
- LOAD CASE 3
- 4.25 g along the global X axis of the detector Fx = 1667.7 N
- 4.25 g along the global Y axis of the detector Fy = 1667.7 N
- 17 g along the global Z axis of the detector Fz = 6670.8 N
All these different loads are applied on both face to face rectangular surfaces in the middle of the plate corresponding to the surface of the Cerenkov counter. As these areas contain 2484 nodes, for each load case, we have distributed each force described above one each node, that means we have divided the value obtained by 2484.
Issue: Draft - Revision: 04 - Last Modified: 20 April 1997