1. KDEMO Structural Analysis P. Titus June 26 2013

2. ! KDEMO coil axisymmetric analysis pfcb 21 1, 1.52,0.70,.9,1.3,8,10 !CS1 2, 1.52,2.10,.9,1.3,8,10 !CS2 3, 1.52,3.50,.9,1.3,8,10 !CS3 4, 1.52,4.90,.9,1.3,8,10 !CS4 5, 2.98,8.31,.60,1.25,8,10 !PF1 6, 3.66,8.31,.60,1.25,8,10 !PF2 7, 4.34,8.59,.60,1.25,8,10 !PF3 8, 5.02,8.75,.60,1.25,8,10 !PF4 9, 12.96,7.50,.849,1.5,8,10 !PF5 10, 14.88,2.95,.4,.5,8,10 !PF6 11, 14.88,-2.95,.4,.5,8,10 !PF6 12, 12.96,-7.50,.849,1.5,8,10 !PF5 13, 5.02,-8.75,.60,1.25,8,10 !PF4 14, 4.34,-8.59,.60,1.25,8,10 !PF3 15, 3.66,-8.31,.60,1.25,8,10 !PF2 16, 2.98,-8.31,.60,1.25,8,10 !PF1 17, 1.52,-4.90,.9,1.3,8,10 !CS4 18, 1.52,-3.50,.9,1.3,8,10 !CS3 19, 1.52,-2.10,.9,1.3,8,10 !CS2L 20, 1.52,-0.70,.9,1.3,8,10 !CS1L 21, 6.1,0,2.1,4.2,8,10 !Plasma pfcu 21,3,1,1.0 1,7.68,3.11,-1.55 2,7.68,3.11,-1.55 3,9.65,3.25,-2.25 4,9.65,3.25,-2.25 5,2.323,4.506,5.715 6,3.171,6.235,7.909 7,3.475,6.169,7.897 8,3.663,5.286,6.914 9,0.021,-13.70,-15.95 10,0.184,0.135,-0.223 11,0.184,0.135,-0.223 12,0.021,-13.70,-15.95 13,3.663,5.286,6.914 14,3.475,6.169,7.897 15,3.171,6.235,7.909 16,2.323,4.506,5.715 17,9.65,3.25,-2.25 18,9.65,3.25,-2.25 19,7.68,3.11,-1.55 20,7.68,3.11,-1.55 21,0,13,13 KDEMO Poloidal Coil Analysis

3. Poloidal Field Vectors Kdm1.dat Kdm2.dat Kdm3.dat Not 11 Tesla

4. Nodal ForceVectors Kdm1.dat Kdm3.dat

5. DEMO CS CICC Parameter (Corner Channel) Cable Pattern: (2SC+1Cu)x3x4x4x6 [576 SC Strand + 288 Cu Strand] Void Fraction : 35.85% Strand : –ITER Type (Jc ~ 1000A/mm2) Nb3Sn Strand –Cu/Non-Cu = 1.0 NO COOLING SPIRAL  Corner Channel Jacket Thickness : 5 mm Insulation : 2.0 mm (with Voltage Tap) –0.1 mm Kapton 400% –0.4 mm S-glass 400% Twist Pitch –1 st Stage 20 ± 5 mm –2 nd Stage 4 5 ± 10 mm –3 rd Stage 85 ± 10 mm –4 th Stage 1 50 ± 15 mm –5 th Stage 355 ± 20 mm Wrapping Tape Thickness –Sub-cable : 0.08 mm 40% –Sub-cable wrap width : 15 mm –Cable : 0.5 mm 60% –Final wrap width : 7 mm DEMO CS CICC Cross-section 54 34 20 40 R 3 2 5 50 30 Insulation Jacket

6. Hoop Multiplier = 459/173.7 = 2.64

7. Initial Magnetization Kdm1.txt, kdem1.dat Based on the hoop multiplier 76.1*2.64 = 200 MPa

8. Starts at 662 then propagates into region that is about 200 MPa ITER CS Conductor near Butt WeldITER CS He Penetration Starts at 356 then propagates into region that is about 325 MPa

9. Average Hoop Stress = 5.327e7/1.17/1e6=45.5MPa Initial Magnetization Check of Average Hoop Stress

10. Based on the CS hoop multiplier Applied to PF5 90.6*2.64 = 240 MPa

11. Based on the CS hoop multiplier Applied to PF5 126*2.64 = 332 MPa

12. TF Case 2/3* yield = 666 MPa ½ Ultimate = 750 Mpa 1/3 Ultimate = 500 MPa Sm, Primary Membrane Allowable = 666 Mpa According to ITER MSDC The average stress in the inner leg case should satisfy this Allowable TF Case and Winding Pack Analysis

13. Meshed areas from Tom’s Parasolids Initial Geometry Without Added Outer Structures

14. Base Cross Section, Reflected and Swept Along Tom’s Arcs

15. kdm1 Field Vectors

16. Nodal Force Vectors Field Vectors

17. kdm1

18. Kdm1 Theta Displacement

19. Kdm1 Tresca Stress TF Case 2/3* yield = 666 MPa ½ Ultimate = 750 Mpa 1/3 Ultimate = 500 MPa Allowable = 666 Mpa According to ITER MSDC

20. TF Case 2/3* yield = 666 MPa ½ Ultimate = 750 Mpa 1/3 Ultimate = 500 MPa Allowable = 666 Mpa According to ITER MSDC

21. Added Upper Structure Added Outer Structure Added Lower Structure

22. Model with 16 fold Symmetry, 12 fold symmetry Expansion Model with Added Structure

23. TF Case 2/3* yield = 666 MPa ½ Ultimate = 750 Mpa 1/3 Ultimate = 500 MPa Allowable = 666 Mpa According to ITER MSDC Results with Added Structure Still Doesn’t Pass

24. From the NSTX structural criteria. "An exception to this elastic analysis approach can be when the nature of the structure and its loading make it difficult to decompose the stresses into the above mentioned categories. In such an instance, a detailed, non-linear analysis that accounts for elastic-plastic behavior, frictional sliding and large displacement shall be used to determine the limit load on the structure. The limit load is that load which represents the onset of a failure to satisfy the Normal operating condition as described in Section I-2.6. The safety factor of limit load divided by the normal load shall be greater than 2.0.“ Similar wording is in the ITER Magnet Structural Design Criteria (MSDC)

25. Try Elastic-Plastic Limit Analysis. Must Show a factor of 2 on failure (Non- Convergence in ANSYS Model)

26. Results with Load Factor of 2.0

27. Plastic Strain at Twice Normal Loading

28. Un-Loaded Results After Twice the Normal Loads are Applied

29. Old 2D TF Cross Section

30. An approximation of the options suggested by Keeman Kim is analyzed. The model Inner leg has an inner radius of 2.0m and OR = 3.14m. The inner wedged section is.286 m thick. This section can support the centering load but depending on the position of the outer leg and the stiffness/strength of the outer structures, the inner leg cross section could be acceptable. However with only 27% of the vertical separating force on the inner leg, the cross section is inadequate. Limit analysis is used to evaluate the section. With only the centering load, the load factor is above 3. With 27% of the bursting force applied to the inner leg, the load factor goes to only 1.5. It should be at least 2.0. Heavy/stronger, and stiffer outer structures are needed to support,most of the vertical bursting load.

31. The Bursting Force – is Applied on the Inner Leg Cross Section at a Coupled Node Set. In the runs with the bursting load, 200MN is applied of the 11946/16 = 750 MN per coil, or 27% – The remainder is assumed taken by the outer structures

32. 16 Fold Symmetry Expansion Model Materials Conductor Stress Strain 316 SST Stress Strain

33. Bmax=13.13 ANSYS Nodal Forces

34. ANSYS Displacement Constraints ANSYS CP’s on Top Face

35. Vertical Separating Force is Applied on One of the Coupled Nodes on the Top Face

36. Von Mises Stress 2.5*Load Von Mises Plastic Strain 2.5*Load

37. Excluding Vertical Separating Force /DSCALE,1,20 (20 times actual)

38. Including Scaled 200MN Vertical Separating Force /DSCALE,1,20 (20 times actual)

39. Radial Displacement Under Increasing Load Collapses at Step 7 > 3 times the Nominal Load Including Scaled Vertical Separating Force Excluding Scaled Vertical Separating Force Radial Displacement Under Increasing Load Collapses at Step 3 or 1.5 times the Nominal Load

40. Radial Displacement Under Increasing Load Collapses at Step 7 > 3 times the Nominal Load Plastic Strain in the Nose Remains Elastic up to Load Step 4, 2.0Times the Nominal Load Excluding Scaled Vertical Separating Force

41. Conductor Total Strain Normal Loading Including 200MN Vertical Separating Force

42. Radial Total Strain Theta Total Strain Von Mises Total Strain Axial Total Strain Normal Loading Including 200MN Vertical Separating Force

43. Insulation Von Mises Stress