1. Finite Element Study of Structural Discontinuities Presented By: Ike Lee and Nick Lin Project Advisor: Ioannis Korkolis

2. Presentation Objectives Discuss background of structural discontinuities Discuss background of structural discontinuities Introduce the finite element method Introduce the finite element method Explain how to generate a finite element model Explain how to generate a finite element model Review previous work Review previous work Present new work Present new work Discuss possibilities for future work Discuss possibilities for future work Answer questions Answer questions

3. What is a Structural Discontinuity? A break or gap within a structural component that alters its behavior under load A break or gap within a structural component that alters its behavior under load

4. Examples of Structural Discontinuities Holes:Often used to lighten an aerospace structure or to rivet components together Holes:Often used to lighten an aerospace structure or to rivet components together Cracks:Usually a result of material imperfections or areas of high stress Cracks:Usually a result of material imperfections or areas of high stress

5. Concerns Uniform loading of a square plate results in a uniform stress distribution Uniform loading of a square plate results in a uniform stress distribution

6. Concerns Holes alter the stress distribution and induce stress concentrations. Holes alter the stress distribution and induce stress concentrations. Study of Mesh Refinement EM 360 Fall 2002

7. Concerns Stress concentrations at crack tips Stress concentrations at crack tips Crack propagation Crack propagation

8. Possible Consequences Stress fields around discontinuities can interact with each other and cause failure. Stress fields around discontinuities can interact with each other and cause failure. Cessna 402C Mishap Investigation, 1999

9. Solution Method Structural discontinuity problems are often very difficult to solve analytically, sometimes impossible. Structural discontinuity problems are often very difficult to solve analytically, sometimes impossible. Our method is to use ABAQUS, a finite element program. Our method is to use ABAQUS, a finite element program.

10. The Finite Element Method (FEM) General technique for constructing approximate solutions to boundary value problems General technique for constructing approximate solutions to boundary value problems Study of Mesh Refinement EM 360 Fall 2002

11. How to Generate a Finite Element Model An input file must be written containing the following two parts: An input file must be written containing the following two parts: Model Data: This portion defines the geometry of the model and material properties. Model Data: This portion defines the geometry of the model and material properties. History Data: This portion defines how the model will be loaded and what values should be outputted. History Data: This portion defines how the model will be loaded and what values should be outputted.

12. Some Important Factors to Consider Boundary Conditions Boundary Conditions Load Type and Directions Load Type and Directions Mesh Refinement Mesh Refinement Study of Mesh Refinement EM 360, Fall 2002

13. Some Important Factors to Consider : Mesh Refinement Peterson’s Stress Concentration Factors, 1997 11 Elements 1 Second K=4.342 Finite Element Study of Structural Discontinuities, 2003 K=  max____ 

14. Some Important Factors to Consider : Mesh Refinement Finite Element Study of Structural Discontinuities, 2003 67 Elements 1 second K=4.41

15. Some Important Factors to Consider : Mesh Refinement Finite Element Study of Structural Discontinuities, 2003 211 Elements 1 second K=4.47

16. Some Important Factors to Consider : Mesh Refinement Finite Element Study of Structural Discontinuities, 2003 823 Elements 2 seconds K=4.512

17. Some Important Factors to Consider : Mesh Refinement Finite Element Study of Structural Discontinuities, 2003 Approx. 3000 Elements 4 seconds K=4.517

18. Some Important Factors to Consider : Mesh Refinement Finite Element Study of Structural Discontinuities, 2003 Approx. 19000 Elements 21 seconds K=4.520

19. Mesh Convergence Curve Finite Element Study of Structural Discontinuities, 2003

20. Computation Time Finite Element Study of Structural Discontinuities, 2003

21. Mesh Convergence Refining a coarse finite element mesh will result in a more accurate solution at the cost of computation time. Refining a coarse finite element mesh will result in a more accurate solution at the cost of computation time.

22. Caveat and Approach Just because a solution is obtained does not necessarily mean it is correct. Therefore, it is important to study the results and compare your solution with a known, correct solution. Just because a solution is obtained does not necessarily mean it is correct. Therefore, it is important to study the results and compare your solution with a known, correct solution.

23. Previous Work Model 1 Model 1 Finite Element Study of Structural Discontinuities, 2003 Peterson’s Stress Concentration Factors, 1997

24. Previous Work Model 1 (continued) Model 1 (continued) Finite Element Study of Structural Discontinuities, 2003

25. Previous Work Model 2 Model 2 Finite Element Study of Structural Discontinuities, 2003 Peterson’s Stress Concentration Factors, 1997

26. Previous Work Model 2 (continued) Model 2 (continued) Finite Element Study of Structural Discontinuities, 2003

27. New Work Reduction of stress concentrations from edges of holes Reduction of stress concentrations from edges of holes Finite element modeling of cracks Finite element modeling of cracks Reduction of crack stress intensity factor Reduction of crack stress intensity factor

28. Reducing Stress Concentrations from Holes Method: Add another hole to alleviate the stress concentration. Method: Add another hole to alleviate the stress concentration. Constant:Radius of original hole = 2 in Tensile Load = 1 psi in horizontal direction Constant:Radius of original hole = 2 in Tensile Load = 1 psi in horizontal direction Variables:R = radius of added hole L = distance between centers of holes Variables:R = radius of added hole L = distance between centers of holes

29. Reducing Stress Concentrations from Holes Finite Element Study of Structural Discontinuities, 2003

30. Reducing Stress Concentrations from Holes Finite Element Study of Structural Discontinuities, 2003

31. Reducing Stress Concentrations from Holes Finite Element Study of Structural Discontinuities, 2003

32. Reducing Stress Concentrations from Holes Finite Element Study of Structural Discontinuities, 2003

33. Reducing Stress Concentrations from Holes Conclusion: Conclusion: Adding holes in a plane perpendicular to the loading direction does not reduce the stress concentration factor.

34. Reducing Stress Concentrations from Holes Finite Element Study of Structural Discontinuities, 2003

35. Reducing Stress Concentrations from Holes Finite Element Study of Structural Discontinuities, 2003

36. Reducing Stress Concentrations from Holes Finite Element Study of Structural Discontinuities, 2003

37. Reducing Stress Concentrations from Holes Finite Element Study of Structural Discontinuities, 2003

38. Reducing Stress Concentrations from Holes Finite Element Study of Structural Discontinuities, 2003

39. Reducing Stress Concentrations from Holes Finite Element Study of Structural Discontinuities, 2003

40. Reducing Stress Concentrations from Holes Finite Element Study of Structural Discontinuities, 2003

41. Reducing Stress Concentrations from Holes Conclusion: Conclusion: Adding holes in a plane parallel to the loading direction does reduce the stress concentration factor.

42. Finite Element Analysis of Cracks Crack configuration models: Crack configuration models: Tada The Stress Analysis of Cracks Handbook Model 1 Model 2 Model 3

43. Finite Element Analysis of Cracks Crack Model 1 (Center Cracked Plate) Crack Model 1 (Center Cracked Plate)

44. Finite Element Analysis of Cracks Crack Model 2 (Edge Cracked Plate)

45. Finite Element Analysis of Cracks Crack Model 3

46. Finite Element Analysis of Cracks Crack Model 3 Tada, The Stress Analysis of Cracks Handbook

47. Finite Element Analysis of Crack Repair Crack repair models: Crack repair models: Finite Element Study of Structural Discontinuities, 2003

48. Finite Element Analysis of Cracks Center Cracked Plate with Stop Holes

49. Finite Element Analysis of Cracks Center Cracked Plate with an Array of Holes Near the Crack Tip

50. Finite Element Analysis of Cracks Patch Repair of Center Cracked Plate

51. Finite Element Analysis of Cracks Arrester Repair of Center Cracked Plate

52. Finite Element Analysis of Cracks Variation in Stress Intensity Factor with Arrester Strip Distance

53. Summary of Work Completed This Semester Used the FEM to determine how holes and cracks affect stress distributions. Used the FEM to determine how holes and cracks affect stress distributions. Devised a method to alleviate stress concentrations around holes. Devised a method to alleviate stress concentrations around holes. Investigated crack repair methods. Investigated crack repair methods.

54. Possibilities for Future Work Finite element modeling of structural discontinuities under cyclic loading Finite element modeling of structural discontinuities under cyclic loading Finite element modeling of structural discontinuities in more complex structures Finite element modeling of structural discontinuities in more complex structures Adaptation of scripting feature in ABAQUS Adaptation of scripting feature in ABAQUS

55. Questions?