Figure 1 – NSTX Upper Umbrella Assembly Baseline Upgrade Design

1. Figure 1 – NSTX Upper Umbrella Assembly Baseline Upgrade Design

2. G10 Support G10 Support Figure 2 – Single Segment Strap Assembly with Baseline Design G10 Supports

3. Figure 3 – Single Segment Strap Assembly w/o G10 Supports

4. Figure 4 – Single Segment Strap Assembly: Center Strap Only

5. Rout = 5.688” 38 Laminations: - .060” thk; .005” gap Mat’l: Copper Wtfull = 37.4 lb (Wtarch = 20.4 lb) Rin = 3.160” 7.5” Bpol= .3 T 5” I = 130 kA Uvertthermal = .3 in Btor = 1 T Uradthermal = .018 in 2.523” 2” Figure 5 – Single Laminated Strap Assembly with Applied Fields and Current

6. Calculated EMAG Loads Fop Out-of-Plane Load (z-direction) I+ R Fop = 2*I*Bpol*R Fop = 2 x 130,000 A/ 38 x .3 T x 5.688/39.37 m Fop = 296.4 N = 66.6 lbf [per lamination] Bpol In-Plane Load (y-direction) pressip Fip/ L = I*Btor Fip/ L = 130,000 A/ 38 x 1 T [per lamination] Fip/ L = 3,421 N/ m x .2248 lbf/ N x 1 m/ 39.37 in Fip/ L = 19.53 lbf/ in pressip = (Fip/ L)/ w pressip = 19.53 lbf/in / 2 in pressip = 9.77 lbf/ in2 (applied to inside cylindrical faces) x x x x x x x x x x x x x x x x x x I+ w Btor

7. Force = 66.6 lbf Ux = .018 in Uy = .3 in Uz = 0 Press = 9.7 psi Fixed 3 Elements thru Thickness Figure 6A – Single Lamination FEA Model: Mesh

8. Figure 6B – Single Lamination Linear Results: von Mises Stress Loads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)

9. Figure 6C – Single Lamination Linear Results: von Mises Stress Loads: Thermal Displacements Only

10. Figure 6D – Single Lamination Linear Results: von Mises Stress Loads: In-Plane (Pressure) Load Only

11. Figure 6E – Single Lamination Linear Results: von Mises Stress Loads: Out-of-Plane (Force) Load Only

12. Large deflection = On Figure 6F – Single Lamination Nonlinear Results: von Mises Stress Loads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)

13. Large deflection = On Figure 6G – Single Lamination Nonlinear Results: Z-Deformations Loads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)

14. Large deflection = On Figure 6H – Single Lamination Nonlinear Results: Z-Deformations_Front Loads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)

15. σhoop = P*R/ t = 9.77 psi x 5.688 in/ .060 in = 924 psi Large deflection = On Figure 6J – Single Lamination Nonlinear Results: von Mises Stress Loads: Emag Pressure (In Plane) Only

16. 1st Mode Load Multiplier = 58.4 1st Mode Load Multiplier = 58.4 3rd Mode Load Multiplier = 117.6 (Nonlinear 1st Mode Load Multiplier = 50) Large deflection = Off 2nd Mode Load Multiplier = 73.0 Figure 6K – Single Lamination Pre-Stressed Linear Buckling Results Load multiplier LMF applies to all Emag loads and thermal displacements

17. Y LMF = 14 0 80 Large deflection = On Figure 6L – Single Lamination Nonlinear Buckling: Y-Deformation at Onset (1) Load multiplier factor LMF applies only Out-of-Plane Emag load

18. Y LMF = 26 0 80 Large deflection = On Figure 6M – Single Lamination Nonlinear Buckling: Y-Deformation at Onset (2) Load multiplier factor LMF applies only to Out-of-Plane Emag load

19. Conclusions • Buckling due mostly to out-of-plane load. In-plane load (pressure outward) reduces buckling; thermal displacements slightly increase buckling. • Good agreement between linear and nonlinear buckling results with load multiplier factor applied to both Emag loads and to thermal displacements. • Load multiplier factor over 14 for nonlinear analysis with constant in-plane load and increasing out-of-plane load (conservative).

20. 3 Elements / Lamination Figure 7A – 3 Lamination FEA Model: Mesh

21. Large deflection = On Frictional contact (COF = .4) Figure 7B – 3 Lamination Nonlinear Results: von Mises Stress Loads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)

22. Large deflection = On Frictional contact (COF = .4) Figure 7C – 3 Lamination Nonlinear Results: Z-Deformations Loads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)

23. Large deflection = On Frictional contact (COF = .4) Figure 7D – 3 Lamination Nonlinear Results: Z-Deformations_Front Loads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)

24. Large deflection = On Frictional contact (COF = .4) Figure 7E – 3 Lamination Nonlinear Results: Contact Status Loads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)

25. 3rd Mode Load Multiplier = 61.8 1st Mode Load Multiplier = 58.2 Large deflection = Off Frictional contact (COF = .4) 2nd Mode Load Multiplier = 60.7 Figure 7F – 3 Lamination Results: Linear Buckling Mode Multiplier Load Multiplier factor LMF applies to all Emag loads and thermal displacements

26. Figure 8A – Single Laminated Strap Assembly FEA Model: Bonded and Frictionless Contact Areas

27. 3 elements/ lamination # Nodes = 850423 # Elements = 152895 Figure 8B – Single Laminated Strap Assembly FEA Model: Mesh

28. Large deflection = Off Frictional contact (COF = 0) Fig. 8C –Laminated Strap Assembly FEA Results - Thermal Displacements Only: von Mises Stress

29. Large deflection = Off Frictional contact (COF = 0) Fig. 8D –Laminated Strap Assembly FEA Results – Thermal Displacements Only: Total Deformation

30. 0 V 130,000 A Fig. 9A – Single Segment_Center Strap Electric Model: Boundary Conditions

31. By = .3T Bz = 1 T ux = .018” uy = .30” I = 130 kA JS FLorentz Non-Linear Large Deflection Non-Linear Large Deflection Heat Gen Tnodes Fig. 9B – Upper Flex Strap ANSYS Multiphysics Analysis Work Flow Diagram

32. Figure 9C – Single Segment_Center Strap Assembly: Mesh

33. Figure 9D – Single Segment_Center Strap Electric Model Results: Voltage

34. Fig. 9E – Single Segment_Center Strap Electric Model Results: Current Density

35. Fig. 9F – Single Segment_Center Strap Electric Model Results: Joule Heat