1. Chapter 9 2D 實體結構分析 Analysis of 2D Structural Solids

2. 2/46 Contents 9.1 何謂 2D 結構 ? When is a Structure Modeled as 2D? 9.2PLANE42: 2D 實體結構元素 PLANE42: 2D Structural Solid Element 9.3 實例 : 平面應力問題 Example: Plane Stress Case 9.4 實例 : 平面應變問題 Example: Plane Strain Case 9.5 實例 : 軸對稱問題 Example: Axisymmetric Case 9.62D 實體元素瀏覽 Overview of 2D Solid Elements 9.7 練習題 : 懸臂樑的 2D 分析 2D Analysis of a Cantilevel Beam

3. 3/46 第 9.1 節 何謂 2D 結構 ? When is a Structure Modeled as 2D?

4. 4/46 9.1.1 平面應力問題 Fixed pin hole, 0.8 in diameter Tapered pressure load: 50 to 500 psi approximates a 130 lb pin load force 6 in 2 in 4 in 2 in 0.4 in radius Thickness = 1/2 in

5. 5/46 9.1.2 平面應變問題

6. 6/46 9.1.3 軸對稱問題

7. 7/46 第 9.2 節 PLANE42: 2D 實體結構元素 PLANE42: 2D Structural Solid Element

8. 8/46 9.2.1 PLANE42 元素描述

9. 9/46 9.2.2 PLANE42 輸入資料 Element NamePLANE42 NodesI, J, K, L Degrees of FreedomUX, UY Real ConstantNone, if KEYOPT (3) = 0, 1, 2 Thickness, if KEYOPT (3) = 3 Material PropertiesEX, NUXY, GXY, ALPX, DENS, DAMP, etc. Surface LoadsPressure: face 1 (JI), face 2 (KJ), face 3 (LK), face 4 (IL) Body LoadsTemperature -- T(I), T(J), T(K), T(L) Special FeaturesPlasticity, Creep, Stress stiffening, Large deflection, Large strain, etc. KEYOPT(1)Key for element coordinate system: 0 -- Element C.S. is parallel to the global C.S. 1 -- Element C.S. is based on the element I-J side KEYOPT(2)Key to include extra shapes: 0 -- Include extra displacement shapes 1 -- Suppress extra displacement shapes KEYOPT(3)0 -- Plane stress 1 -- Axisymmetric 2 -- Plane strain 3 -- Plane stress with thickness input

10. 10/46 第 9.3 節 實例 : 平面應力問題 Example: Plane Stress Case

11. 11/46 9.3.1 問題描述 Fixed pin hole, 0.8 in diameter Tapered pressure load: 50 to 500 psi approximates a 130 lb pin load force 6 in 2 in 4 in 2 in 0.4 in radius Thickness = 1/2 in

12. 12/46 9.3.2 ANSYS Procedure (1/5) 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 FINISH /CLEAR /TITLE, Corner Bracket (in-lbf-s) /PREP7 ET, 1, PLANE82,,, 3 R, 1, 0.5 MP, EX, 1, 30E6 MP, NUXY, 1, 0.27 RECTNG, 0, 6, -1, 1 RECTNG, 4, 6, -3, -1 PCIRC, 1 WPOFFS, 5, -3 PCIRC, 1 AADD, ALL

13. 13/46 9.3.2 ANSYS Procedure (2/5) 18 19 20 21 22 23 24 25 26 27 28 29 WPOFFS, -5, 3 PCIRC, 0.4 WPOFFS, 5, -3 PCIRC, 0.4 ASBA, 5, ALL LFILLT, 8, 17, 0.4 AL, 12, 13, 14 AADD, ALL APLOT /PNUM, LINE, ON /PNUM, KP, ON LPLOT

14. 14/46 9.3.2 ANSYS Procedure (3/5) 30 31 32 33 34 /PNUM, DEFAULT SMRTSIZE, 5 AMESH, ALL EPLOT FINISH

15. 15/46 9.3.2 ANSYS Procedure (4/5) 36 37 38 39 40 41 42 43 44 45 46 47 48 /SOLU DK, 7, ALL, 0,, 1 DK, 9, ALL, 0,, 1 DK, 10, ALL, 0,, 1 DK, 12, ALL, 0,, 1 SFL, 10, PRES, 50, 500 SFL, 11, PRES, 500, 50 /PBC, U,, ON /PSF, PRES, NORM, 2 APLOT SOLVE FINISH

16. 16/46 9.3.2 ANSYS Procedure (5/5) 50 51 52 53 /POST1 PLDISP, 2 PLNSOL, S, EQV

17. 17/46 第 9.4 節 實例 : 平面應變問題 Example: Plane Strain Case

18. 18/46 9.4.1 問題描述

19. 19/46 9.4.2 ANSYS Procedure (1/6) 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 FINISH /CLEAR /TITLE, STRESSES IN A LONG CYLINDER /UNITS, BIN /PREP7 ET, 1, PLANE42,,, 2 MP, EX, 1, 30E6 MP, DENS, 1,.00073 MP, NUXY, 1, 0.3 CSYS, 1 K, 1, 4, 0 K, 2, 8, 0 K, 3, 4, 45 K, 4, 8, 45 A, 3, 1, 2, 4 ESIZE,.25 MSHKEY, 1 MSHAPE, 0, 2D AMESH, 1 NROTAT, ALL FINISH

20. 20/46 9.4.2 ANSYS Procedure (2/6) 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 /SOLU NSEL, S, LOC, Y, 0 NSEL, A, LOC, Y, 45 D, ALL, UY, 0 NSEL, S, LOC, X, 4 SF, ALL, PRES, 30000 ALLSEL /PBC, U,, ON /PSF, PRES, NORM, 2 EPLOT SOLVE NSEL, S, LOC, X, 4 SF, ALL, PRES, 0 ALLSEL OMEGA,,, 1000 SOLVE FINISH

21. 21/46 9.4.2 ANSYS Procedure (3/6) 50 51 52 53 54 55 56 /POST1 SET, 1 PLDISP, 2 RSYS, 1 PLNSOL, S, X PLNSOL, S, Y

22. 22/46 9.4.2 ANSYS Procedure (4/6) 58 59 60 61 62 63 64 65 66 PATH, R-DIR, 2 PPATH, 1,, 4, 0 PPATH, 2,, 8, 0 PDEF, R-STRESS, S, X PDEF, H-STRESS, S, Y /GRID, 1 /AXLAB, Y, STRESS /TITLE, STRESS UNDER PRESSURE PLPATH, R-STRESS, H-STRESS

23. 23/46 9.4.2 ANSYS Procedure (5/6) 68 69 70 71 SET, 2 PLDISP, 2 PLNSOL, S, X PLNSOL, S, Y

24. 24/46 9.4.2 ANSYS Procedure (6/6) 73 74 75 76 PDEF, R-STRESS, S, X PDEF, H-STRESS, S, Y /TITLE, STRESS UNDER ROTATION PLPATH, R-STRESS, H-STRESS

25. 25/46 第 9.5 節 實例 : 軸對稱問題 Example: Axisymmetric Case

26. 26/46 9.5.1 問題描述

27. 27/46 9.5.2 ANSYS Procedure (1/6) 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 FINISH /CLEAR /TITLE, STRESSES IN A LONG CYLINDER /UNITS, BIN /PREP7 ET, 1, PLANE42,,, 1 MP, EX, 1, 30E6 MP, DENS, 1,.00073 MP, NUXY, 1, 0.3 K, 1, 4, 0 K, 2, 8, 0 K, 3, 4, 1 K, 4, 8, 1 A, 3, 1, 2, 4 ESIZE,.25 MSHK, 1 MSHA, 0, 2D AMESH, 1 FINISH

28. 28/46 9.5.2 ANSYS Procedure (2/6) 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 /SOLU NSEL, S, LOC, Y, 0 NSEL, A, LOC, Y, 1 D, ALL, UY, 0 NSEL, S, LOC, X, 4 SF, ALL, PRES, 30000 ALLSEL /PBC, U,, ON /PSF, PRES, NORM, 2 EPLOT SOLVE NSEL, S, LOC, X, 4 SF, ALL, PRES, 0 ALLSEL OMEGA,, 1000 SOLVE FINISH

29. 29/46 9.5.2 ANSYS Procedure (3/6) 48 49 50 51 52 53 /POST1 SET, 1 PLDISP, 2 PLNSOL, S, X PLNSOL, S, Z

30. 30/46 9.5.2 ANSYS Procedure (4/6) 55 56 57 58 59 60 61 62 63 PATH, R-DIR, 2 PPATH, 1,, 4, 0 PPATH, 2,, 8, 0 PDEF, R-STRESS, S, X PDEF, H-STRESS, S, Z /GRID, 1 /AXLAB, Y, STRESS /TITLE, STRESS UNDER PRESSURE PLPATH, R-STRESS, H-STRESS

31. 31/46 9.5.2 ANSYS Procedure (5/6) 65 66 67 68 SET, 2 PLDISP, 2 PLNSOL, S, X PLNSOL, S, Z

32. 32/46 9.5.2 ANSYS Procedure (6/6) 70 71 72 73 PDEF, R-STRESS, S, X PDEF, H-STRESS, S, Z /TITLE, STRESS UNDER ROTATION PLPATH, R-STRESS, H-STRESS

33. 33/46 第 9.6 節 2D 實體元素瀏覽 Overview of 2D Solid Elements

34. 34/46 9.6.1 General 2D Structural Solids

35. 35/46 9.6.2 Axisymmetric Harmonic Solids

36. 36/46 9.6.3 Large Strains

37. 37/46 9.6.4 P-Elements

38. 38/46 9.6.5 Hyperelasticity

39. 39/46 9.6.6 Viscoelasticity and Viscoplasticity

40. 40/46 9.6.7 Thermal Solids

41. 41/46 9.6.8 Axisymmetric Harmonic Thermal Solids

42. 42/46 9.6.9 Fluid Elements

43. 43/46 9.6.10 Electrostatic Fields

44. 44/46 9.6.11 Magnetic Fields

45. 45/46 9.6.12 Coupled-Field Elements

46. 46/46 第 9.7 節 練習題 : 懸臂樑的 2D 分析 2D Analysis of a Cantilever Beam