ANSYS Workbench Verification Manual

ANSYS Workbench Verification Manual

Release 15.0ANSYS, Inc.

November 2013Southpointe

275 Technology Drive

Canonsburg, PA 15317 ANSYS, Inc. iscertified to ISO

9001:[email protected]

http://www.ansys.com

(T) 724-746-3304

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Table of Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Overview .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Index of Test Cases .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

I. DesignModeler Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1. VMDM001: Extrude, Chamfer, and Blend Features .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2. VMDM002: Cylinder using Revolve, Sweep, Extrude, and Skin-Loft ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3. VMDM003: Extrude, Revolve, Skin-Loft, and Sweep .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

II. Mechanical Application Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1. VMMECH001: Statically Indeterminate Reaction Force Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2. VMMECH002: Rectangular Plate with Circular Hole Subjected to Tensile Loading .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3. VMMECH003: Modal Analysis of Annular Plate .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4. VMMECH004: Viscoplastic Analysis of a Body (Shear Deformation) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

5. VMMECH005: Heat Transfer in a Composite Wall ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

6. VMMECH006: Heater with Nonlinear Conductivity ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

7.VMMECH007:Thermal Stress in a Bar with Temperature Dependent Conductivity ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

8. VMMECH008: Heat Transfer from a Cooling Spine .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

9. VMMECH009: Stress Tool for Long Bar with Compressive Load .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

10. VMMECH010: Modal Analysis of a Rectangular Plate .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

11. VMMECH011: Large Deflection of a Circular Plate with Uniform Pressure .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

12. VMMECH012: Buckling of a Stepped Rod .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

13. VMMECH013: Buckling of a Circular Arch .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

14. VMMECH014: Harmonic Response of a Single Degree of Freedom System ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

15.VMMECH015: Harmonic Response of Two Storied Building under Transverse Loading .... . . . . . . . . . . . . . . . . . . . . 45

16. VMMECH016: Fatigue Tool with Non-Proportional Loading for Normal Stress .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

17. VMMECH017: Thermal Stress Analysis with Remote Force and Thermal Loading .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

18. VMMECH018: A Bar Subjected to Tensile Load with Inertia Relief ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

19.VMMECH019: Mixed Model Subjected to Bending Loads with Solution Combination .... . . . . . . . . . . . . . . . . . . . . . 53

20. VMMECH020: Modal Analysis for Beams .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

21. VMMECH021: Buckling Analysis of Beams .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

22.VMMECH022: Structural Analysis with Advanced Contact Options .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

23. VMMECH023: Curved Beam Assembly with Multiple Loads .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

24. VMMECH024: Harmonic Response of a Single Degree of Freedom System for Beams .... . . . . . . . . . . . . . . . . . . . . . 63

25. VMMECH025: Stresses Due to Shrink Fit Between Two Cylinders .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

26. VMMECH026: Fatigue Analysis of a Rectangular Plate Subjected to Edge Moment .... . . . . . . . . . . . . . . . . . . . . . . . . . 67

27. VMMECH027: Thermal Analysis for Shells with Heat Flow and Given Temperature .... . . . . . . . . . . . . . . . . . . . . . . . . . . 69

28. VMMECH028: Bolt Pretension Load Applied on a Semi-Cylindrical Face .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

29. VMMECH029: Elasto-Plastic Analysis of a Rectangular Beam ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

30. VMMECH030: Bending of Long Plate Subjected to Moment - Plane Strain Model ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

31. VMMECH031: Long Bar with Uniform Force and Stress Tool - Plane Stress Model ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

32. VMMECH032: Radial Flow due to Internal Heat Generation in a Copper Disk - Axisymmetric Model ... . 79

33. VMMECH033: Electromagnetic Analysis of a C-Shaped Magnet .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

34. VMMECH034: Rubber cylinder pressed between two plates .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

35. VMMECH035: Thermal Stress in a Bar with Radiation ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

36. VMMECH036: Thermal Stress Analysis of a Rotating Bar using Temperature Dependant Density .... . . . . . 89

37. VMMECH037: Cooling of a Spherical Body .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

38. VMMECH038: Crashing Blocks Simulation with Transient Structural Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

39. VMMECH039: Transient Response of a Spring-mass System ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

40. VMMECH040: Deflection of Beam using Symmetry and Anti-Symmetry .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

41.VMMECH041: Brooks Coil with Winding for Periodic Symmetry ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

iiiRelease 15.0 - SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information

of ANSYS, Inc. and its subsidiaries and affiliates.

42.VMMECH042: Hydrostatic Pressure Applied on a Square Bar with Fully, Partially Submerged in a Flu-

id .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

43. VMMECH043: Fundamental Frequency of a Simply-Supported Beam ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

44. VMMECH044: Thermally Loaded Support Structure .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

45. VMMECH045: Laterally Loaded Tapered Support Structure .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

46. VMMECH046: Pinched Cylinder .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

47. VMMECH047: Plastic Compression of a Pipe Assembly .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

48. VMMECH048: Bending of a Tee-Shaped Beam ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

49. VMMECH049: Combined Bending and Torsion of Beam ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

50.VMMECH050: Cylindrical Shell under Pressure .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

51. VMMECH051: Bending of a Circular Plate Using Axisymmetric Elements .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

52. VMMECH052: Velocity of Pistons for Trunnion Mechanism ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

53. VMMECH053: Simple Pendulum with SHM motion .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

54. VMMECH054: Spinning Single Pendulum ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

55. VMMECH055: Projector mechanism- finding the acceleration of a point ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

56.VMMECH056: Coriolis component of acceleration-Rotary engine problem ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

57. VMMECH057: Calculation of velocity of slider and force by collar ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

58. VMMECH058: Reverse four bar linkage mechanism ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

59. VMMECH059: Bending of a solid beam (Plane elements) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

60. VMMECH060: Crank Slot joint simulation with flexible dynamic analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

61. VMMECH061: Out-of-plane bending of a curved bar .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

62. VMMECH062: Stresses in a long cylinder .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

63. VMMECH063: Large deflection of a cantilever ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

64. VMMECH064: Small deflection of a Belleville Spring .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

65.VMMECH065:Thermal Expansion to Close a Gap at a Rigid Surface .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

66.VMMECH066: Bending of a Tapered Plate .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

67. VMMECH067: Elongation of a Solid Tapered Bar ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

68. VMMECH068: Plastic Loading of a Thick Walled Cylinder .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

69. VMMECH069: Barrel Vault Roof Under Self Weight .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

70. VMMECH070: Hyperelastic Thick Cylinder Under Internal Pressure .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

71. VMMECH071: Centerline Temperature of a Heat Generating Wire .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

72.VMMECH072: Thermal Stresses in a Long Cylinder .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

73. VMMECH073: Modal Analysis of a Cyclic Symmetric Annular Plate .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

74. VMMECH074: Tension/Compression Only Springs .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

75. VMMECH075: Harmonic Response of Two-Story Building under Transverse Loading .... . . . . . . . . . . . . . . . . . . . . 173

76. VMMECH076: Elongation of a Tapered Shell with Variable Thickness ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

77. VMMECH077: Heat Transfer in a Bar with Variable Sheet Thickness ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

78. VMMECH078: Gasket Material Under Uniaxial Compression Loading-3-D Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . 179

79. VMMECH079: Natural Frequency of a Motor-Generator ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

80. VMMECH080: Transient Response of a Spring-mass System ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

81.VMMECH081: Statically Indeterminate Reaction Force Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

82.VMMECH082: Fracture Mechanics Stress for a Crack in a Plate .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

83. VMMECH083: Transient Response to a Step Excitation .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

84. VMMECH084: Mullins Effect on a Rubber Tube Model Subjected to Tension Loading .... . . . . . . . . . . . . . . . . . . . . 197

85. VMMECH085: Bending of a Composite Beam ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

86. VMMECH086: Stress Concentration at a Hole in a Plate .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

87. VMMECH087: Campbell Diagrams and Critical Speeds Using Symmetric Orthotropic Bearings .... . . . . . 205

88. VMMECH088: Harmonic Response of a Guitar String .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

89.VMMECH089: Delamination Analysis of a Double Cantilever Beam Using Contact-Based Debond-

ing .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

90. VMMECH090: Delamination Analysis of a Double Cantilever Beam Using Interface Delamination .... . 213

III. Design Exploration Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

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Workbench Verification Manual

1.VMDX001: Optimization of L-Shaped Cantilever Beam under Axial Load .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

2.VMDX002: Optimization of Bar with Temperature-Dependent Conductivity ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

3. VMDX003: Optimization of Water Tank Column for Mass and Natural Frequency .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

4. VMDX004: Optimization of Frequency for a Plate with Simple Support at all Vertices .... . . . . . . . . . . . . . . . . . . . . . 225

5.VMDX005: Optimization of Buckling Load Multiplier with CAD Parameters and Young's Modulus .... . . . 227

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Workbench Verification Manual

Introduction

The following topics are discussed in this chapter:

Overview

Index of Test Cases

Overview

This manual presents a collection of test cases that demonstrate a number of the capabilities of the

Workbench analysis environment. The available tests are engineering problems that provide independent

verification, usually a closed form equation. Many of them are classical engineering problems.

The solutions for the test cases have been verified, however, certain differences may exist with regard

to the references. These differences have been examined and are considered acceptable. The workbench

analyses employ a balance between accuracy and solution time. Improved results can be obtained in

some cases by employing a more refined finite element mesh but requires longer solution times. For

the tests, an error rate of 3% or less has been the goal.

These tests were run on an Intel Xeon processor using Microsoft Windows 7 Enterprise 64-bit . These

results are reported in the test documentation. Slightly different results may be obtained when different

processor types or operating systems are used.

The tests contained in this manual are a partial subset of the full set of tests that are run by ANSYS

developers to ensure a high degree of quality for the Workbench product. The verification of the

Workbench product is conducted in accordance with the written procedures that form a part of an

overall Quality Assurance program at ANSYS, Inc.

You are encouraged to use these tests as starting points when exploring new Workbench features.

Geometries, material properties, loads, and output results can easily be changed and the solution re-

peated. As a result, the tests offer a quick introduction to new features with which you may be unfamil-

iar.

Some test cases will require different licenses, such as DesignModeler, Emag, or Design Exploration. If

you do not have the available licenses, you may not be able to reproduce the results. The Educational

version of Workbench should be able to solve most of these tests. License limitations are not applicable

to Workbench Education version but problem size may restrict the solution of some of the tests.

The archive files for each of the Verification Manual tests are available at the Customer Portal. Download

the ANSYS Workbench Verification Manual Archive Files. These zipped archives provide all of the necessary

elements for running a test, including geometry parts, material files, and workbench databases. To open

a test case in Workbench, locate the archive and import it into Workbench.

You can use these tests to verify that your hardware is executing the ANSYS Workbench tests correctly.

The results in the databases can be cleared and the tests solved multiple times. The test results should

be checked against the verified results in the documentation for each test.

ANSYS, Inc. offers the Workbench Verification and Validation package for users that must perform system

validation.

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This package automates the process of test execution and report generation. If you are interested in

contracting for such services contact the ANSYS, Inc. Quality Assurance Group.

Index of Test Cases

Solution OptionsAnalysis TypeElement TypeTest Case Number

LinearStatic StructuralSolidVMMECH001


Free VibrationModalSolidVMMECH003

Nonlinear, Visco-

plastic Materials

StructuralSolidVMMECH004

LinearStatic ThermalSolidVMMECH005

NonlinearStatic ThermalSolidVMMECH006

Nonlinear Thermal

Stress

Static StructuralSolidVMMECH007

LinearStatic ThermalSolidVMMECH008


Free VibrationModalShellVMMECH010

Nonlinear, Large

Deformation

Static StructuralShellVMMECH011

BucklingSolidVMMECH012

BucklingShellVMMECH013

HarmonicSolidVMMECH014


FatigueStatic StructuralSolidVMMECH016

Linear Thermal

Stress


Linear, Inertia reliefStatic StructuralSolidVMMECH018

LinearStatic StructuralBeamVMMECH019

Shell

ModalBeamVMMECH020

BucklingBeamVMMECH021

Nonlinear, ContactStatic StructuralSolidVMMECH022

LinearStatic StructuralBeamVMMECH023

HarmonicBeamVMMECH024


FatigueStatic StructuralShellVMMECH026

Linear Thermal

Stress



Nonlinear, Plastic

Materials


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Introduction


Static Structural2-D Solid, Plane

Strain

VMMECH030


Stress

VMMECH031

Linear Thermal

Stress

Static Structural2-D Solid, Axisym-

metric

VMMECH032

ElectromagneticStatic StructuralSolidVMMECH033

Nonlinear, Large

Deformation


Coupled (Static

Thermal and Static

Stress)

SolidVMMECH035

Sequence LoadingStatic StructuralSolidVMMECH036

Transient Thermal2-D Solid, Axisym-

metric

VMMECH037

Flexible DynamicTransient StructuralSolidVMMECH038


Spring

Static StructuralBeamVMMECH040

ElectromagneticStatic StructuralSolidVMMECH041

Hydrostatic FluidStatic StructuralSolidVMMECH042

ModalBeamVMMECH043

Linear Thermal

Stress




Nonlinear, Plastic

Materials

Static Structural2-D Solid, Axisym-

metric

VMMECH047



Static StructuralAxisymmetric ShellVMMECH050


Rigid DynamicMultipoint Con-

straint

VMMECH052


straint

VMMECH042


straint

VMMECH054


straint

VMMECH055



Index of Test Cases



straint

VMMECH056


straint

VMMECH057


straint

VMMECH058

Static Structural2-D Plane Stress

Shell

VMMECH059


Multipoint Con-

straint



Nonlinear, Large

Deformation



Linear Thermal

Stress

Static StructuralSolid

Shell

VMMECH065



Nonlinear, Plastic

Materials


Strain

VMMECH068


Nonlinear, Large

Deformation

Static Structural2-D SolidVMMECH070

Static Thermal2-D Thermal SolidVMMECH071

Linear Thermal

Stress

Static Structural2-D Thermal SolidVMMECH072

ModalSolidVMMECH073

Rigid Body Dynam-

ics

Solid

Spring

VMMECH074



Static ThermalThermal ShellVMMECH077

Static Structural3-D SolidVMMECH078

3-D Gasket

ModalPipeVMMECH079

Mode Superposi-

tion

Transient DynamicSpring

Mass

VMMECH080


Introduction


ModalPipeVMMECH081

SpectralMass

Fracture MechanicsStatic StructuralSolidVMMECH082

Mode Superposi-

tion

Transient DynamicSpring, MassVMMECH083

Nonlinear, Hypere-

leastic


Composite MaterialStatic StructuralSolidVMMECH085


Submodeling (2D-

2D)

ModalLine BodyVMMECH087

Point Mass

Bearing Connection

Linear PerturbationStatic StructuralBeamVMMECH088

Modal

Harmonic

Contact-Based De-

bonding


Interface Delamina-

tion




Index of Test Cases

Part I: DesignModeler Descriptions

VMDM001: Extrude, Chamfer, and Blend Features

Overview

Extrude, Chamfer, and BlendFeature:

MillimeterDrawing Units:

Test Case

Create a Model using Extrude, Chamfer, and Blend features.

A polygonal area is extruded 60 mm. A rectangular area of 30 mm x 40 mm [having a circular area of

radius 6 mm subtracted] is extruded to 20 mm. Both resultant solids form one solid geometry. A rect-

angular area (24 mm x 5 mm) is subtracted from the solid. Two rectangular areas (40 mm x 10 mm) are

extruded 10 mm and subtracted from solid. Two rectangular areas (25 mm x 40 mm) are extruded 40

mm and subtracted from solid. A Chamfer (10 mm x 10 mm) is given to 4 edges on the resultant solid.

Four Oval areas are extruded and subtracted from Solid. Fillet (Radius 5 mm) is given to 4 edges using

Blend Feature.

Verify Volume of the resultant geometry.

Figure 1: Final Model after creating Extrude, Chamfer, and Blend

Calculations

1. Volume of Solid after extruding Polygonal Area: v1 = 264000 mm3.

2. Volume of rectangular area having circular hole: v2 = 21738.05 mm3.

Net Volume = V = v1 + v2 = 285738.05 mm3.

3. Volume of rectangular (24mm x 5mm) solid extruded 30mm using Cut Material = 3600 565.5 = 3034.5

mm3.

Net volume V = 285738.05 3034.5 = 282703.5 mm3.

4. Volume of two rectangular areas each 40mm x 10mm extruded 10mm = 8000 mm3.



Net volume V = 282703.5 8000 = 274703.5 mm3.

5. Volume of two rectangular areas 25mm x 40mm extruded 40mm = 80000 mm3.

Net volume V = 274703.5 80000 = 194703.5 mm3.

6. Volume of four solids added due to Chamfer = 4 x 500 = 2000 mm3

Net volume V = 194703.5 + 2000 = 196703.5 mm3.

7. Volume of four oval areas extruded 10 mm = 7141.6 mm3.

Net volume V = 196703.5 - 7141.6 = 189561.9 mm3.

8. Volume of 4 solids subtracted due to Blend of radius 5 mm = 429.2 mm3.

Hence Net volume of final Solid body = V = 189561.9 429.2 = 189132.7 mm3.

Results Comparison

Error (%)Design-

Modeler

TargetResults

0189561.95189561.95Volume (mm3)

-0.013544433.344439.29Surface Area (mm2)

05252Number of Faces

011Number of Bodies


VMDM001

VMDM002: Cylinder using Revolve, Sweep, Extrude, and Skin-Loft

Overview

Revolve, Sweep, Extrude, and Skin-LoftFeature:


Test Case

Create a Model using Revolve, Sweep, Extrude, and Skin-Loft features.

A Rectangular area (100 mm x 30 mm) is revolved about Z-Axis in 3600 to form a Cylinder. A circular

area of radius 30 mm is swept 100 mm using Sweep feature. A circular area of radius 30 mm is extruded

100 mm. A solid cylinder is created using Skin-Loft feature between two coaxial circular areas each of

radius 30 mm and 100 mm apart.

Verify Volume of the resultant geometry.

Figure 2: Final Model after creating Revolve, Sweep, Extrude, and Skin-Loft

Calculations

1. Volume of Cylinder created after Revolving Rectangular area (100 mm x 30 mm) = v1 = 282743.3 mm3.

2. Volume of Cylinder created when a circular area (Radius 30mm) is swept 100 mm = v2 = 282743.3 mm3.

Net Volume = V = v1 + v2 = 282743.3 + 282743.3 = 565486.6 mm3.

3. Volume of Cylinder after extruding a circular area (Radius 30 mm) 100 mm = 282743.3 mm3.

Net Volume = V = 565486.6 + 282743.3 = 848229.9 mm3.

4. Volume of Cylinder created after using Skin-Loft feature between two circular areas of Radius 30 mm

and 100 mm apart. = 282743.3 mm3.

Net Volume of the final Cylinder = 848229.9 + 282743.3 = 1130973.2 mm3.



Results Comparison

Error (%)Design-

Modeler

TargetResults

01130973.31130973.3Volume (mm3)

081053.181053.1Surface Area (mm2)

033Number of Faces

011Number of Bodies


VMDM002

VMDM003: Extrude, Revolve, Skin-Loft, and Sweep

Overview

Extrude, Revolve, Skin-Loft, and SweepFeature:


Test Case

Create a Model using Extrude, Revolve, Skin-Loft, and Sweep.

A rectangular area (103 mm x 88 mm) is extruded 100 mm to form a solid box. A circular area of radius

25 mm is revolved 900 using Revolve feature and keeping Thin/Surface option to Yes and 3 mm Inward

and Outward Thickness. A solid is subtracted using Skin-Loft feature between two square areas (each

of side 25 mm) and 100 mm apart. The two solid bodies are frozen using Freeze feature. A circular area

of radius 25 mm is swept using Sweep feature and keeping Thin/Surface option to Yes and 3 mm Inward

and Outward Thickness. Thus a total of 4 geometries are created.

Verify the volume of the resulting geometry.

Figure 3: Final Model after creating Extrude, Revolve, Skin-Loft and Sweep

Calculations

1. Volume of rectangular (103 mm x 88 mm) solid extruded 100mm = 906400 mm3.

2. Volume of solid after revolving circular area of Radius 25 mm through 900 = 29639.6 mm3.

Net Volume of solid box, Va = 906400 - 29639.6 = 876760.3 mm3.

3. Volume of additional body created due to Revolve feature = Vb= 11134.15 mm3.

4. Volume of the rectangular box cut after Skin-Loft between two square areas each of side 25 mm = 62500

mm3.

Net Volume of solid box becomes Va = 876760.3 62500 = 814260.3 mm3.

5. Volume of additional two bodies created due to Sweep feature:



Vc = 47123.9 mm3 and Vd = 28352.8 mm

3.

And total volume that gets subtracted from box due to Sweep Feature = 75476.7 mm3.

Hence Net volume of box, Va = 814260.3 - 75476.7 = 738783.6 mm3.

Sum of volumes of all four bodies = Va+Vb+Vc+Vd = 738783.6 + 11134.15 + 47123.9 +28352.8 =

825394.4 mm3.

Results Comparison

Error (%)Design-

Modeler

TargetResults

0825394.5825394.4Volume (mm3)

0101719.95101719.47Surface Area (mm2)

02222Number of Faces

044Number of Bodies


VMDM003

Part II: Mechanical Application Descriptions

VMMECH001: Statically Indeterminate Reaction Force Analysis

Overview

S. Timoshenko, Strength of Materials, Part 1, Elementary Theory

and Problems, 3rd Edition, CBS Publishers and Distributors, pg.

22 and 26

Reference:

Linear Static Structural AnalysisAnalysis

Type(s):

SolidElement

Type(s):

Test Case

An assembly of three prismatic bars is supported at both end faces and is axially loaded with forces F1and F2. Force F1 is applied on the face between Parts 2 and 3 and F2 is applied on the face between

Parts 1 and 2. Apply advanced mesh control with element size of 0.5.

Find reaction forces in the Y direction at the fixed supports.

Figure 4: Schematic

LoadingGeometric PropertiesMaterial Properties

Force F1 =

-1000 (Y direc-

tion)

Cross section of

all parts = 1 x

1

E = 2.9008e7 psi

= 0.3

= 0.28383 lbm/in3

Length of Part

1 = 4"Force F2 = -500

(Y direction)Length of Part

2 = 3"

Length of Part

3 = 3



Results Comparison

Error (%)MechanicalTargetResults

0.127901.14900Y Reaction Force at Top

Fixed Support (lbf )

-0.190598.86600Y Reaction Force at Bottom

Fixed Support (lbf )


VMMECH001

VMMECH002: Rectangular Plate with Circular Hole Subjected to Tensile Loading

Overview

J. E. Shigley, Mechanical Engineering Design, McGraw-Hill, 1st

Edition, 1986, Table A-23, Figure A-23-1, pg. 673

Reference:


Type(s):

SolidElement

Type(s):

Test Case

A rectangular plate with a circular hole is fixed along one of the end faces and a tensile pressure load

is applied on the opposite face. A convergence with an allowable change of 10% is applied to account

for the stress concentration near the hole. The Maximum Refinement Loops is set to 2 and the Refinement

mesh control is added on the cylindrical surfaces of the hole with Refinement = 1.

Find the Maximum Normal Stress in the x direction on the cylindrical surfaces of the hole.

Figure 5: Schematic


Pressure = -100

Pa

Length = 15 mE = 1000 Pa

Width = 5 m = 0

Thickness = 1

m

Hole radius =

0.5 m

Results Comparison


0.864315.2312.5Maximum Normal X Stress

(Pa)



VMMECH003: Modal Analysis of Annular Plate

Overview

R. J. Blevins, Formula for Natural Frequency and Mode Shape,

Van Nostrand Reinhold Company Inc., 1979, Table 11-2, Case

4, pg. 247

Reference:

Free Vibration AnalysisAnalysis

Type(s):

SolidElement

Type(s):

Test Case

An assembly of three annular plates has cylindrical support (fixed in the radial, tangential, and axial

directions) applied on the cylindrical surface of the hole. Sizing control with element size of 0.5 is applied

to the cylindrical surface of the hole.

Find the first six modes of natural frequencies.

Figure 6: Schematic


Inner diameter

of inner plate =

20"

E = 2.9008e7 psi

= 0.3

= 0.28383 lbm/in3

Inner diameter

of middle plate

= 28"

Inner diameter

of outer plate =

34"

Outer diameter

of outer plate =

40"




Thickness of all

plates = 1"

Results Comparison


-0.23310.21310.9111st Frequency Mode (Hz)

-0.78315.6318.0862nd Frequency Mode (Hz)

-0.77315.64318.0863rd Frequency Mode (Hz)

-1.38346.73351.5694th Frequency Mode (Hz)




VMMECH003

VMMECH004: Viscoplastic Analysis of a Body (Shear Deformation)

Overview

B. Lwo and G. M. Eggert, "An Implicit Stress Update Al-

gorithm Using a Plastic Predictor". Submitted to Computer

Reference:

Methods in Applied Mechanics and Engineering, January

1991.

Nonlinear Structural AnalysisAnalysis

Type(s):

SolidElement

Type(s):

Test Case

A cubic shaped body made up of a viscoplastic material obeying Anand's law undergoes uniaxial shear

deformation at a constant rate of 0.01 cm/s. The temperature of the body is maintained at 400C. Find

the shear load (Fx) required to maintain the deformation rate of 0.01 cm/sec at time equal to 20 seconds.

Figure 7: Schematic

h

Velocity = 0.01 cm/s

Problem Model

h

x

y


Temp = 400C

= 673K

h = 1 cmEx (Young's Modulus) =

60.6 GPa thickness = 1

cm Velocity (x-direc-

tion) = 0.01 (Poisson's Ratio) =

0.4999cm/sec @ y = 1

cmSo = 29.7 MPa

Q/R = 21.08999E3 KTime = 20 sec

A = 1.91E7 s-1

= 7.0




m = 0.23348

ho = 1115.6 MPa

= 18.92 MPa

= 0.07049

a = 1.3

Results Comparison


-6.3-791.76845.00Fx, N


VMMECH004

VMMECH005: Heat Transfer in a Composite Wall

Overview

F. Kreith, Principles of Heat Transfer, Harper and Row Publisher,

3rd Edition, 1976, Example 2-5, pg. 39

Reference:

Linear Static Thermal AnalysisAnalysis

Type(s):

SolidElement

Type(s):

Test Case

A furnace wall consists of two layers: fire brick and insulating brick. The temperature inside the furnace

is 3000F (Tf) and the inner surface convection coefficient is 3.333e-3 BTU/s ft2F (hf). The ambient

temperature is 80F (Ta) and the outer surface convection coefficient is 5.556e-4 BTU/s ft2F (ha).

Find the Temperature Distribution.

Figure 8: Schematic


Cross-section =

1" x 1"

Fire brick wall: k =

2.222e-4 BTU/s ft F

Fire brick wall

thickness = 9"

Insulating wall: k =

2.778e-5 BTU/s ft F

Insulating wall

thickness = 5"

Results Comparison


0.202336.68336Minimum Temperature (F)

0.0072957.22957Maximum Temperature (F)



VMMECH006: Heater with Nonlinear Conductivity

Overview

Vedat S. Arpaci, Conduction Heat Transfer, Addison-Wesley Book

Series, 1966, pg. 130

Reference:

Nonlinear Static Thermal AnalysisAnalysis Type(s):

SolidElement Type(s):

Test Case

A liquid is boiled using the front face of a flat electric heater plate. The boiling temperature of the liquid

is 212F. The rear face of the heater is insulated. The internal energy generated electrically may be as-

sumed to be uniform and is applied as internal heat generation.

Find the maximum temperature and maximum total heat flux.

Figure 9: Schematic


Front face temperat-

ure = 212F

k = [0.01375 * (1 + 0.001 T)]

BTU/s inF

Radius = 3.937

Thickness = 1

Internal heat gener-

ation = 10 BTU/s

in3

Conductiv-

ity (BTU/s

inF)

Temperat-

ure (F)

1.419e-00232

2.75e-0021000

Results Comparison


0.96480.58476Maximum Temperature (F)

-0.0039.999710Maximum Total Heat Flux

(BTU/s in2)



VMMECH007:Thermal Stress in a Bar with Temperature Dependent Conductivity

Overview

Any basic Heat Transfer bookReference:

Nonlinear Thermal Stress AnalysisAnalysis

Type(s):

SolidElement

Type(s):

Test Case

A long bar has thermal conductivity that varies with temperature. The bar is constrained at both ends

by frictionless surfaces. A temperature of TC is applied at one end of the bar (End A). The reference

temperature is 5C. At the other end, a constant convection of h W/m2C is applied. The ambient tem-

perature is 5C. Advanced mesh control with element size of 2 m is applied.

Find the following:

Minimum temperature

Maximum thermal strain in z direction (on the two end faces)

Maximum deformation in z direction

Maximum heat flux in z direction at z = 20 m

Figure 10: Schematic


Rear face tem-

perature T =

100C

Length = 20 mE = 2e11 Pa

Width = 2 m = 0

Breadth = 2 m = 1.5e-05 / C

Film Coefficient

h = 0.005

W/m2C

k = 0.038*(1 +

0.00582*T) W/m C

Conductiv-

ity (W/m C)

Temperat-

ure (C) Ambient tem-

perature = 5C3.91e-0025Reference tem-

perature = 5C0.215800



Analysis

Temperature at a distance "z" from rear face is given by:

z

= +

Thermal strain in the z direction in the bar is given by:

T

= 5

Deformation in the z direction is given by:

=

0

Heat flux in the z direction is given by:

=

Results Comparison


-0.01638.01438.02Minimum Temperature (C)

0.0420.000495210.000495Maximum Thermal strain (z

= 20) (m/m)

0.0000.0014250.001425Maximum Thermal strain (z

= 0) (m/m)

0.9050.0023410.00232Maximum Z Deformation

(m)

0.0420.165070.165Maximum Z Heat Flux (z =

20) (W/m2)


VMMECH007

VMMECH008: Heat Transfer from a Cooling Spine

Overview

Kreith, F., Principles of Heat Transfer, Harper and Row, 3rd Edition,

1976, Equation 2-44a, pg. 59, Equation 245, pg. 60

Reference:

Linear Static Thermal AnalysisAnalysis

Type(s):

SolidElement

Type(s):

Test Case

A steel cooling spine of cross-sectional area A and length L extend from a wall that is maintained at

temperature Tw. The surface convection coefficient between the spine and the surrounding air is h, the

air temper is Ta, and the tip of the spine is insulated. Apply advanced mesh control with element size

of 0.025'.

Find the heat conducted by the spine and the temperature of the tip.



LoadingGeometric

Properties

Material Properties

Tw = 100FE = 4.177e9 psf

Cross section =

1.2 x 1.2

= 0.3 Ta = 0FThermal conductiv-

ity k = 9.71e-3

BTU/s ft F

h = 2.778e-4

BTU/s ft2 F

L = 8

Results Comparison


0.05579.07879.0344Temperature of the Tip (F)

-0.0416.3614e-36.364e-3Heat Conducted by the

Spine (Heat Reaction)

(BTU/s)



VMMECH009: Stress Tool for Long Bar with Compressive Load

Overview

Any basic Strength of Materials bookReference:


Type(s):

SolidElement

Type(s):

Test Case

A multibody of four bars connected end to end has one of the end faces fixed and a pressure is applied

to the opposite face as given below. The multibody is used to nullify the numerical noise near the

contact regions.

Find the maximum equivalent stress for the whole multibody and the safety factor for each part using

the maximum equivalent stress theory with tensile yield limit.


Material Properties

Tensile Yield

(Pa)

E (Pa)Mater-

ial

2.07e801.93e11Part 1

2.8e807.1e10Part 2

2.5e802e11Part 3

2.8e801.1e11Part 4

LoadingGeometric Properties

Pressure = 2.5e8

Pa

Part 1: 2 m x 2

m x 3 m

Part 2: 2 m x 2

m x 10 m

Part 3: 2 m x 2

m x 5 m



Part 4: 2 m x 2

m x 2 m

Results Comparison


0.0002.5e82.5e8Maximum Equivalent Stress

(Pa)

0.0000.8280.828Safety Factor for Part 1


0.00011Safety Factor for Part 3



VMMECH009

VMMECH010: Modal Analysis of a Rectangular Plate

Overview

Blevins, Formula for Natural Frequency and Mode Shape, Van

Nostrand Reinhold Company Inc., 1979, Table 11-4, Case 11,

pg. 256

Reference:

Free Vibration AnalysisAnalysis

Type(s):

ShellElement

Type(s):

Test Case

A rectangular plate is simply supported on both the smaller edges and fixed on one of the longer edges

as shown below. Sizing mesh control with element size of 6.5 mm is applied on all the edges to get

accurate results.

Find the first five modes of natural frequency.



Length = 0.25

m

E = 2e11 Pa

= 0.3

Width = 0.1 m = 7850 kg/m3

Thickness =

0.005 m

Results Comparison


-0.952590.03595.71st Frequency Mode (Hz)

-0.9871118.41129.552nd Frequency Mode (Hz)

-0.6672038.12051.793rd Frequency Mode (Hz)





-0.48933503366.485th Frequency Mode (Hz)


VMMECH010

VMMECH011: Large Deflection of a Circular Plate with Uniform Pressure

Overview

Timoshenko S.P., Woinowsky-Krieger S., Theory of Plates and

Shells, McGraw-Hill, 2nd Edition, Article 97, equation 232, pg.

401

Reference:

Nonlinear Structural Analysis (Large Deformation On)Analysis

Type(s):

ShellElement

Type(s):

Test Case

A circular plate is subjected to a uniform pressure on its flat surface. The circular edge of the plate is

fixed. To get accurate results, apply sizing control with element size of 5 mm on the circular edge.

Find the total deformation at the center of the plate.



Pressure =

6585.18 Pa

Radius = 0.25

m

E = 2e11 Pa

= 0.3

Thickness =

0.0025 m

Results Comparison


-1.0080.00123740.00125Total deformation (m)



VMMECH012: Buckling of a Stepped Rod

Overview

Warren C. Young, Roark's Formulas for Stress & Strains, McGraw

Hill, 6th Edition, Table 34, Case 2a, pg. 672

Reference:

Buckling AnalysisAnalysis

Type(s):

SolidElement

Type(s):

Test Case

A stepped rod is fixed at one end face. It is axially loaded by two forces: a tensile load at the free end

and a compressive load on the flat step face at the junction of the two cross sections. To get accurate

results, apply sizing control with element size of 6.5 mm.

Find the Load Multiplier for the First Buckling Mode.



Force at free

end = 1000 N

Larger diameter

= 0.011982 m

E = 2e11 Pa

= 0.3

Force at the flat

step face = -

2000 N

Smaller diamet-

er = 0.010 m

Length of lar-

ger diameter =

0.2 m

Both forces are

in the z direc-

tionLength of smal-

ler diameter =

0.1 m

Results Comparison


2.035622.95822.5Load Multiplier



VMMECH013: Buckling of a Circular Arch

Overview

Warren C. Young, Roark's Formulas for Stress Strains, McGraw

Hill, 6th Edition, Table 34, Case 10, pg. 679

Reference:


Type(s):

ShellElement

Type(s):

Test Case

A circular arch of a rectangular cross section (details given below) is subjected to a pressure load as

shown below. Both the straight edges of the arch are fixed.

Find the Load Multiplier for the first buckling mode.



Pressure = 1

MPa

Arch cross-sec-

tion = 5 mm x

50 mm

E = 2e5 MPa

= 0

Mean radius of

arch = 50 mm

Included angle

= 90

Results Comparison


0.4546.07544Load Multiplier



VMMECH014: Harmonic Response of a Single Degree of Freedom System

Overview

Any basic Vibration Analysis bookReference:

Harmonic AnalysisAnalysis

Type(s):

SolidElement

Type(s):

Test Case

An assembly where four cylinders represent massless springs in series and a point mass simulates a

spring mass system. The flat end face of the cylinder (Shaft 1) is fixed. Harmonic force is applied on the

end face of another cylinder (Shaft 4) as shown below.

Find the z directional Deformation Frequency Response of the system on the face to which force is

applied for the frequency range of 0 to 500 Hz for the following scenarios using Mode Superposition.

Solution intervals = 20.

Scenario 1: Damping ratio = 0

Scenario 2: Damping ratio = 0.05


Material Properties

(kg/m3

)E (Pa)Material

1e-80.341.1e11Shaft 1

1e-80.341.1e11Shaft 2

1e-80.354.5e10Shaft 3

1e-80.354.5e10Shaft 4


Force = 1e7 N (Z-

direction)

Each cylinder:

Diameter = 20 mm

Point Mass =

3.1044 Kg

Length = 50 mm



Results Comparison


0.5910.141230.1404Maximum Amplitude

without damping (m)

0.000180180Phase angle without damp-

ing (degrees)

0.5770.14080.14Maximum Amplitude with

damping (m)

0.000175.58175.6Phase angle with damping

(degrees)


VMMECH014

VMMECH015: Harmonic Response of Two Storied Building under Transverse

Loading

Overview

W. T. Thomson, Theory of Vibration with Applications, 3rd Edition,

1999, Example 6.4-1, pg. 166

Reference:


Type(s):

SolidElement

Type(s):

Test Case

A two-story building has two columns (2K and K) constituting stiffness elements and two slabs (2M and

M) constituting mass elements. The material of the columns is assigned negligible density so as to make

them as massless springs. The slabs are allowed to move only in the y direction by applying frictionless

supports on all the faces of the slabs in the y direction. The end face of the column (2K) is fixed and a

harmonic force is applied on the face of the slab (M) as shown in the figure below.

Find the y directional Deformation Frequency Response of the system at 70 Hz on each of the vertices

as shown below for the frequency range of 0 to 500 Hz using Mode Superposition. Use Solution intervals

= 50.


Material Properties

(kg/m3

)E (Pa)Material

78500.32e18Block 2

1e-80.354.5e10Shaft 2

157000.32e18Block 1

1e-80.359e10Shaft 1



LoadingGeometric Proper-

ties Force = -1e5 N (y

direction)Block 1 and 2:

40 mm x 40 mm x

40 mm

Shaft 1 and 2:

20 mm x 20 mm x

200 mm

Results Comparison


1.50.211740.20853Maximum Amplitude for

vertex A (m)

1.20.0758380.074902Maximum Amplitude for

vertex B (m)


VMMECH015

VMMECH016: Fatigue Tool with Non-Proportional Loading for Normal Stress

Overview

Any basic Machine Design bookReference:

Fatigue AnalysisAnalysis

Type(s):

SolidElement

Type(s):

Test Case

A bar of rectangular cross section has the following loading scenarios.

Scenario 1: One of the end faces is fixed and a force is applied on the opposite face as shown below

in Figure 19: Scenario 1 (p. 47).

Scenario 2: Frictionless support is applied to all the faces of the three standard planes (faces not seen

in Figure 20: Scenario 2 (p. 47)) and a pressure load is applied on the opposite faces in positive y-

and z-directions.

Find the life, damage, and safety factor for the normal stresses in the x, y, and z directions for non-

proportional fatigue using the Soderberg theory. Use a design life of 1e6 cycles, a fatigue strength factor

or 1, a scale factor of 1, and 1 for coefficients of both the environments under Solution Combination.

Figure 19: Scenario 1


Material Properties

E = 2e11 Pa

= 0.3

Ultimate Tensile Strength = 4.6e8 Pa



Material Properties

Yield Tensile Strength = 3.5e8 Pa

Endurance Strength = 2.2998e6 Pa

Alternating Stress

(Pa)

Number of

Cycles

4.6e81000

2.2998e61e6

LoadingGeometric

Properties Scenario 1: Force

= 2e6 N (y-direc-

tion)

Bar: 20 m x 1 m

x 1m

Scenario 2: Pres-

sure = -1e8 Pa

Analysis

Non-proportional fatigue uses the corresponding results from the two scenarios as the maximum and

minimum stresses for fatigue calculations. The fatigue calculations use standard formulae for the

Soderberg theory.

Results Comparison

Error

(%)

Mechanic-

al

TargetResults

-0.1563329.93335.1049LifeStress Component - Component

X 0.157300.31299.8406Damage

0.1320.0190250.019Safety

Factor

-0.7641465314765.7874LifeStress Component - Component

Y 0.77268.24767.724Damage

-0.6830.0453780.04569Safety

Factor

0.0011476614765.7874LifeStress Component - Component

Z 0.00167.72567.724Damage

0.0130.0456960.04569Safety

Factor


VMMECH016

VMMECH017: Thermal Stress Analysis with Remote Force and Thermal Loading

Overview


Linear Thermal Stress AnalysisAnalysis

Type(s):

SolidElement

Type(s):

Test Case

A cylindrical rod assembly of four cylinders connected end to end has frictionless support applied on

all the cylindrical surfaces and both the flat end faces are fixed. Other thermal and structural loads are

as shown below.

Find the Deformation in the x direction of the contact surface on which the remote force is applied. To

get accurate results apply a global element size of 1.5 m.



Given temperature

(End A) = 1000C

Diameter = 2 mE = 2e11 Pa

Lengths of cylin-

ders in order

= 0

Given temperature

(End B) = 0C

= 1.2e-5/C

from End A: 2

m, 5 m, 10 m,

and 3 m.

Remote force =

1e10 N applied on

the contact surface

at a distance 7 m

from end A.

Location of remote

force = (7,0,0) m

Results Comparison


-1.50.100250.101815Maximum X Deformation

(m)



VMMECH018: A Bar Subjected to Tensile Load with Inertia Relief

Overview


Linear Static Structural Analysis (Inertia Relief On)Analysis

Type(s):

SolidElement

Type(s):

Test Case

A long bar assembly is fixed at one end and subjected to a tensile force at the other end as shown

below. Turn on Inertia Relief.

Find the deformation in the z direction



Force P = 2e5 N

(positive z direc-

tion)

Cross-Section =

2 m x 2 m

E = 2e11 Pa

= 0.3

Lengths of bars

in order from = 7850 kg/m

3

End A: 2 m, 5

m, 10 m, and 3

m.

Analysis

z

= 2

where:

L = total length of bar

A = cross-section

m = mass



Results Comparison


0.1722.5043E-062.5e-6Maximum Z Deformation

(m)


VMMECH018

VMMECH019: Mixed Model Subjected to Bending Loads with Solution Combination

Overview



Type(s):

Beam and ShellElement

Type(s):

Test Case

A mixed model (shell and beam) has one shell edge fixed as shown below. Bending loads are applied

on the free vertex of the beam as given below. Apply a global element size of 80 mm to get accurate

results.

Scenario 1: Only a force load.

Scenario 2: Only a moment load.

Find the deformation in the y direction under Solution Combination with the coefficients for both the

environments set to 1.




Force F = -10 N (y

direction)

Shell = 160 mm

x 500 mm x 10

mm

E = 2e5 Pa

= 0




Moment M = -

4035 Nmm @ z-ax-

is

Beam rectangu-

lar cross section

= 10 mm x 10

mm

Beam length =

500 mm

Analysis

y

= +3 2

l l

where:

I = total bending length of the mixed model

I = moment of inertia of the beam cross-section

Results Comparison


0.929-7.2542-7.18742Maximum Y-Deformation

(mm)


VMMECH019

VMMECH020: Modal Analysis for Beams

Overview


Modal AnalysisAnalysis

Type(s):

BeamElement

Type(s):

Test Case

Two collinear beams form a spring mass system. The density of the longer beam is kept very low so

that it acts as a massless spring and the smaller beam acts as a mass. The end vertex of the longer

beam (acting as a spring) is fixed. The cross section details are as shown below.

Find the natural frequency of the axial mode.

Figure 25: Cross Section Details for Both Beams


Material Properties

(kg/m3)E (Pa)Material

1e-80.341.1e11Spring

7.85e502e11Mass




Spring beam length =

500 mm

Mass beam length = 5

mm

Results Comparison


0.1601190.51188.6Natural Frequency of Axial

Mode (Hz)


VMMECH020

VMMECH021: Buckling Analysis of Beams

Overview

Warren C. Young, Roark's Formulas for Stress and Strains, McGraw

Hill, 6th Edition, Table 34, Case 3a, pg. 675

Reference:


Type(s):

BeamElement

Type(s):

Test Case

A beam fixed at one end and is subjected to two compressive forces. One of the forces is applied on

a portion of the beam of length 50 mm (L1) from the fixed end and the other is applied on the free

vertex, as shown below.

Find the load multiplier for the first buckling mode.



Force on L1 =

-1000 N (x direc-

tion)

L1 = 50 mmE = 2e11 Pa

= 0.3 Total length =

200 mm

Force on free ver-

tex = -1000 N (x

direction)

Rectangular

cross section =

10 mm x 10

mm

Results Comparison


-0.40710.19810.2397Load Multiplier



VMMECH022: Structural Analysis with Advanced Contact Options

Overview

Any basic Strength of Material bookReference:

Nonlinear Static Structural AnalysisAnalysis

Type(s):

SolidElement

Type(s):

Test Case

An assembly of two parts with a gap has a Frictionless Contact defined between the two parts. The end

faces of both the parts are fixed and a given displacement is applied on the contact surface of Part 1

as shown below.

Find the Normal stress and Directional deformation - both in the z direction for each part for the following

scenarios:

Scenario 1: Interface treatment - adjust to touch.

Scenario 2: Interface treatment - add offset. Offset = 0 m.

Scenario 3: Interface treatment - add offset. Offset = 0.001 m.

Scenario 4: Interface treatment - add offset. Offset = -0.001 m.

Validate all of the above scenarios for Augmented Lagrange and Pure Penalty formulations.



Given displace-

ment = (0, 0,

0.0006) m

Gap = 0.0005 mE = 2e11 Pa

Dimensions for

each part: 0.1

m x 0.1 m x

0.5m

= 0

Results Comparison

The same results are obtained for both Augmented Lagrange and Pure Penalty formulations.



Er-

ror

(%)

Mechan-

ical

Tar-

get

Results

0.0006e-46e-4Maximum directional z de-

formation Part 1 (m)

Adjust To Touch

-0.3575.9786e-

4

6e-4Maximum directional z de-


0.0002.4e82.4e8Maximum normal z stress

Part 1 (Pa)

-0.354-2.3915e8-2.4e8Maximum normal z stress

Part 2 (Pa)



Add Offset. Offset = 0 m

-0.3560.99644e-

4

1e-4Maximum directional z de-



Part 1 (Pa)

-0.355-3.9858e7-4e7Maximum normal z stress

Part 2 (Pa)



Add Offset. Offset =

0.001 m

-0.3551.0961e-

3

1.1e-

3

Maximum directional z de-



Part 1 (Pa)

-0.357-4.3843e8-4.4e8Maximum normal z stress

Part 2 (Pa)



Add Offset. Offset = -

0.001 m

0.00000Maximum directional z de-



Part 1 (Pa)

000Maximum normal z stress

Part 2 (Pa)


VMMECH022

VMMECH023: Curved Beam Assembly with Multiple Loads

Overview



Type(s):

BeamElement

Type(s):

Test Case

An assembly of two curved beams, each having an included angle of 45, has a square cross-section. It

is fixed at one end and at the free end a Force F and a Moment M are applied. Also, a UDL of "w " N /

mm is applied on both the beams. Use a global element size of 30 mm to get accurate results. See the

figure below for details.

Find the deformation of the free end in the y direction.


Equivalent Loading:


Force F = -1000 N

(y direction)

For each beam:Beam 1:

Cross-section =

10 mm x 10

mm

E1 = 1.1e5 MPa

Moment M = -

10000 Nmm

(about z-axis)

1 = 0

1 = 8.3e-6

kg/mm3

Radius r = 105

mm




UDL w = -5 N/mm

(y direction) on

both beams

Included angle

= 45

Beam 2:

E2 = 2e5 MPa

2 = 0This UDL is applied

as an edge force2 = 7.85e-6

kg/mm3

on each beam

with magnitude =

-5 (2 x 3.14 x 105)

/ 8 = -412.334 N

Analysis

The deflection in the y direction is in the direction of the applied force F and is given by:

=

+ +

+

1

3 2 4

2

3 2 4+ +

where:

= deflection at free end in the y direction

I = moment of inertia of the cross-section of both beams

Results Comparison


0.619-8.4688-8.416664Minimum Y Deformation

(mm)


VMMECH023

VMMECH024: Harmonic Response of a Single Degree of Freedom System for

Beams

Overview



Type(s):

BeamElement

Type(s):

Test Case

Two collinear beams form a spring-mass system. The density of the longer beam is kept very low so

that it acts as a massless spring and the smaller beam acts as a mass. The end vertex of the longer

beam (acting as a spring) is fixed. A Harmonic force F is applied on the free vertex of the shorter beam

in z direction. Both beams have hollow circular cross-sections, as indicated below.

Scenario 1: Damping ratio = 0

Scenario 2: Damping ratio = 0.05

Find the z directional deformation of the vertex where force is applied at frequency F = 500 Hz for the

above scenarios with solution intervals = 25 and a frequency range of 0 to 2000 Hz. Use both Mode

Superposition and Full Method.


Material Properties

(kg/m3)

E

(Pa)

Mater-

ial

1e-80.341.1e11Spring

7.85e502e11Mass


Harmonic force F

= 1 e6 N (z-direc-

tion)

Cross-section of

each beam:

Outer radius =

10 mm




Inner radius =

5 mm

Length of

longer beam =

100 mm

Length of

shorter beam =

5 mm

Results Comparison

Er-

ror

(%)

Mechan-

ical

TargetResults

-0.8594.078e-34.11332e-

3

Maximum z directional deforma-

tion without damping (m)

Mode Superposi-

tion

-0.8764.0765e-

3

4.11252e-

3


tion with damping (m)

-0.0034.1132e-

3

4.11332e-

3


tion without damping (m)

Full Method

-1.0464.0695e-

3

4.11252e-

3


tion with damping (m)


VMMECH024

VMMECH025: Stresses Due to Shrink Fit Between Two Cylinders

Overview

Stephen P. Timoshenko, Strength of Materials, Part 2 - Advanced

Theory and Problems, 3rd Edition, pg. 208-214

Reference:


Type(s):

SolidElement

Type(s):

Test Case

One hollow cylinder is shrink fitted inside another. Both cylinders have length L and both the flat faces

of each cylinder are constrained in the axial direction. They are free to move in radial and tangential

directions. An internal pressure of P is applied on the inner surface of the inner cylinder. To get accurate

results, apply a global element size of 0.8 inches.

Find the maximum tangential stresses in both cylinders.

Note

Tangential stresses can be obtained in the Mechanical application using a cylindrical coordin-

ate system.

To simulate interference, set Contact Type to Rough with interface treatment set to add offset

with Offset = 0.



P = 30000 psiInner Cylinder:Both cylinders

are made of ri = 4

the same mater-

ialro = 6.005

Ri = 6E = 3e7psi




Ro = 8 = 0

= 0.28383

lbm/in3

Length of both

cylinders = 5

Results Comparison


1.03573835396.67Maximum normal y stress, inner

cylinder (psi)

0.04227942281.09Maximum normal y stress, outer

cylinder (psi)

Note

Here y corresponds to direction of a cylindrical coordinate system.


VMMECH025

VMMECH026: Fatigue Analysis of a Rectangular Plate Subjected to Edge Moment

Overview

Any standard Machine Design and Strength of Materials bookReference:

Fatigue AnalysisAnalysis

Type(s):

ShellElement

Type(s):

Test Case

A plate of length L, width W, and thickness T is fixed along the width on one edge and a moment M

is applied on the opposite edge about the z-axis.

Find the maximum Bending Stress (Normal X Stress) and maximum Total Deformation of the plate. Also

find the part life and the factor of safety using Goodman, Soderberg, & Gerber criteria. Use the x-stress

component. Consider load type as fully reversed and a Design Life of 1e6 cycles, Fatigue Strength factor

of 1, and Scale factor of 1.


Material Properties

E = 2e11 Pa

= 0.0

Ultimate tensile strength =

1.29e9 Pa

Endurance strength = 1.38e8 Pa

Yield Strenth = 2.5e8 Pa

Alternating Stresses

(Pa)

No. of Cycles

1.08e91000

1.38e81e6


Moment M = 0.15

Nm (counterclock-

wise @ z-axis)

Length L = 12e-

3 m

Width W = 1e-3

m




Thickness T = 1

e-3 m

Results Comparison

Er-

ror

(%)

Mechan-

ical

TargetResults

0.0009e89e8Maximum normal x-stress (Pa)

0.2796.4981e-

4

6.48e-4Maximum total deformation (m)

0.0200.153330.1533Safety factorSN-Goodman

0.0051844.41844.3Life

0.0200.153330.1533Safety factorSN-Soderberg

0.0051844.41844.3Life

0.0200.153330.1533Safety FactorSN-Gerber

0.0051844.41844.3Life


VMMECH026

VMMECH027:Thermal Analysis for Shells with Heat Flow and Given Temperature

Overview

Any standard Thermal Analysis bookReference:

Thermal Stress AnalysisAnalysis

Type(s):

ShellElement

Type(s):

Test Case

A plate of length (L), width (W), and thickness (T) is fixed along the width on one edge and heat flow

(Q) is applied on the same edge. The opposite edge is subjected to a temperature of 20 C. Ambient

temperature is 20 C. To get accurate results, apply a sizing control with element size = 2.5e-2 m.

Find the maximum temperature, maximum total heat flux, maximum total deformation, and heat reaction

at the given temperature.



Heat flow Q = 5 WLength L = 0.2

m

E = 2e11 Pa

Given Temperature

= 20C

= 0.0

Width W = 0.05

m

Coefficient of

thermal expan-

sion = 1.2e-

5/C

Thickness T =

0.005 m

Thermal con-

ductivity k =

60.5 W/mC

Analysis

Heat Reaction = -(Total heat generated)

Heat flow due to conduction is given by:

h l=



where:

Th = maximum temperature

T1 = given temperature

Total heat flux is:

=

Temperature at a variable distance z from the fixed support is given by:

z h

h=

1

Thermal deformation in the z-direction is given by:

l

=

0

Results Comparison

Er-

ror

(%)

Mechan-

ical

TargetResults

0.00086.11686.1157Maximum Temperature (C)

0.0002e42e4Maximum Total Heat Flux (W/m2)

0.7817.9958e-

5

7.93386e-

5

Maximum Total Deformation (m)

0.000-5-5Heat Reaction (W)


VMMECH027

VMMECH028: Bolt Pretension Load Applied on a Semi-Cylindrical Face

Overview

Any standard Strength of Materials bookReference:

Static Structural An

ANSYS Workbench Verification Manual

Documents

Transcript of ANSYS Workbench Verification Manual