1. Results of Linear Stress Analyses for Modular Coils and Coil structure For 2T High Beta Currents at 0 Seconds and Initial Coil Shrinkage of 0.0004 in/in with Coil Equivalent E of 63,000 MPa H.M. Fan PPPL March 15, 2005

2. FEA Model 120° sector model Appropriate boundary conditions Smeared property for modular coils. Pro/E geometry provided by ORNL Small features in the geometry were removed to improve meshing Model includes shells with tees and wings, wing bags, poloidal break spacers, toroidal flange spacers, and modular coils Bonded contact elements were assumed at the component interfaces Upper shell C Upper shell B Upper shell A Lower shell A Lower shell B Lower shell C

3. Boundary Conditions Cyclic symmetry between edges at -60° and +60° (see Fig.A) Cyclic symmetry for wing bags outside the 120° range and their rotational images (see Fig.B) Displacement constraints at the bottom shell stiffeners in the vertical and toroidal directions Figure A Figure B

4. Material Properties, Loading, and Assumptions Use the following material properties:. Tee/shell:modulus of elasticity = 193,000 MPa Poissoin’s ratio = 0.31 Modular coil:modulus of elasticity = 63,000 MPa Poissoin’s ratio = 0.20 Coef. of thermal expansion = 0.172e-4 / °C Toroidal spacer:modulus of elasticity = 150,000 MPa Poissoin’s ratio = 0.27 poloidal spacer:modulus of elasticity = 193,000 MPa Poissoin’s ratio = 0.31 Wing bag:modulus of elasticity = 68,940 MPa Poissoin’s ratio = 0.32 Wing bag image:modulus of elasticity = 689 MPa Poissoin’s ratio = 0.32 Magnetic loads are based on currents of 2T high beta scenario at 0.0 seconds. Initial cooling shrinkage of coil strain is 0.0004 in/in that is equivalent to a temperature difference of -23.2558 °C. No temperature change for the modular coil winding form. Contact elements are always bonded and the solution is a linearly elastic analysis.

5. Currents, Materials, and Element Type Numbers ComponentCurrentTurnMaterial Elem. Type (A/turn) Number Number M1 40908 20 73 M2 41561 20 42 M3 40598 18 11 PF1-15274 72 104 PF2-15274 72 105 PF3 -5857 72 106 PF4 -9362 80 107 PF5 1080 24 108 PF6 -24 14 109 TF -1301 12 11 10 Plasma 0 1 11 11 Shell - - 10,13,16 10,13,16 19,22,25 19,22,25 Toroidal spacer - - 98 Poloidal spacer - - 11,15,17 11,15,17 20,24,26 20,24,26 Wing bag - - 12,14,18 12,14,18 21,23,27 21,23,27 Wing bag - - 69,70 18,27

6. Von Mises Stress Plots of Modular Coils Maximum stress Unit of stress in pascal

7. Unit of displacement in meter Shell Displacements Total Displacement Vertical Displacement

8. Von Mises Stress Plots of Shells Unit of stress in pascal

9. Von Mises Stress Plots of Upper Shell A Unit of stress in pascal

10. Von Mises Stress Plots of Upper Shell B Maximum stress

11. Von Mises Stress Plots of Upper Shell C Unit of stress in pascal Maximum stress

12. Von Mises Stress Plots of Lower Shell C Maximum stress Unit of stress in pascal

13. Contact Pressure on Wing Bag at Upper Shell A Unit of pressure in pascal Note – Positive pressure indicates load toward the surface and therefore is in compression

14. Unit of pressure in pascal Contact Pressure on Wing Bags at Upper Shell B

15. Unit of pressure in pascal Contact Pressure on Wing Bags at Upper Shell C Rotational image of wing bag outside the 120° range in the upper shell C

16. Unit of pressure in pascal Contact Pressure on Wing Bag at Lower Shell A

17. Unit of pressure in pascal Contact Pressure on Wing Bags at Lower Shell B

18. Unit of pressure in pascal Contact Pressure on Wing Bags at Upper Shell C Rotational image of wing bag outside the 120° range in the lower shell C

19. 1.Adding rotational images of the wing bags that locate outside the 120° section range provide correct cyclic symmetry boundary condition. The stiffness of the wing bag image was set at one percent of the material property of wing bag that should give negligible effects on the results. 2.Small features in the geometry such as chamfers and fillets were removed to improve the meshing and to minimize the node and element number. 3.Maximum stress occurs at coil lead opening corner in the shell type C, which will be reduced if the chamfer is provided. The higher stress level in the lead opening of lower shell C is because of its higher elevation that possess higher deformation. 4.Pressures on the wing bags are not uniform. The plots provide the informations for a most effective shim support location. 5.Because of bonding, the pressure on wing bags may yield tension. The nonliners contact elements are needed to eliminate tension. 6.The tension on the wing bag is of no use. It may be able to break the wing bag into several discontinuous pieces. 7.It should be noted that the stiffness of wing bags will affect the stresses of wing and the pressure on the wing bags. Discussions