1. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 1 Design, Manufacture, Transport and Integration on-site in Chile of ALMA Antennas Elevation Membrane Verification PM#04- 17-18 May 2006 Dated November 18 h, 2005

2. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 2 ►Membrane: element typeSHELL63 thickness 0.005 m ► Fictitious beams: element typeBEAM4 Area0.001 m 2 Ixx=Iyy=Izz1e-5 m 4 thickness 0.001 m ► Material model: linear, isotropic Elastic modulus206 GPa Poisson ratio0.3 ► Constraints: ux, uy, uz, rotx, roty, rotzalong the external perimeter of the membrane FEM MODEL

3. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 3 Loads have been assessed from the antenna global model and they have been applied at the central node of the fictitious beams dial

4. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 4 1gx σ VM,max =141MPa 1gy σ VM,max =42MPa 1gz σ VM,max =43MPa STATIC VERIFICATION

5. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 5 ΔT=20°C σ VM,max =54.7 MPa U x =1mm σ VM,max =401 MPa STATIC VERIFICATION

6. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 6 BUCKLING VERIFICATION ►Critical Load ► F cr =5.70E6 N ►Worst load condition ►4g vertical shock acceleration ►Fz~0.45E6 N ►Safety factor ~12.5

7. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 7 FATIGUE VERIFICATION ►Thermic stress fatigue verification ►Assumptions (in advantage of safety) ►Daily ΔT=±20°C ►cycle no =365×30~1.1e4 ►Loads are reduced to F x component ►Biaxial stress ►Principal stress in radial and circumferential directions ►Verification performed as unidirectional by imposing σ a =σ 1,max, R=0

8. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 8 Radial stress σ r,max =60 MPa Circumferential stress σ c,max =18 MPa Shear stress  r,c ~0 MPa FATIGUE VERIFICATION

9. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 9 FATIGUE VERIFICATION R=-1 UTS=680 MPa σ A,-1 =0.35×UTS=240 MPa n=1.1e4 σ a =60 MPa σ L =490 MPa  σ =490/60~8 σ k N=const σLσL

10. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 10

11. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 11