Ph.D. Dissertation Presentation

1. Determination of Contact Stress Distribution in Pin Loaded Orthotropic Plates Neville A. Tomlinson Department of Mechanical Engineering Howard University Washington D C December 2006

10. Problem Definition region of no contact region of contact Plate thickness = unity Hole radius = Clearance = Pin radius = Pin force = Pin displacement = Hole center = A Contact point = B Contact angle =

11. Mathematical Formulations For the Pin Loaded Plate with Clearance and Friction Equation of ellipse Point B has coordinates Contact Equation

12. Boundary Conditions at the Pin-plate Interface

14. Trigonometric displacement function y Traction conditions on the hole boundary requires that Assumed three terms displacement field along the contact region as

15. Trigonometric Displacement Function (continued)

16. Trigonometric Displacement Function (continued) Using the following relation, Evaluate at

17. Determination of the Stress Functions and Stresses Constants

18. Determination of the Stress Functions and Stresses (continued) mapping function Introduce unit circle to satisfy boundary conditions

19. Determination of the Stress Functions and Stresses (continued) Comparing coefficients yields

21. Determination of the Stress Functions and Stresses (continued) Functions of material parameters, the displacement coefficients and the hole radius

23. Determination of Given Substitute Re-stated as

27. Contact angle analysis Fixed clearance and varying friction (Plate A) 72.19 17.0 0.4 71.05 14.0 0.2 0.02 76.58 20.6 0.4 76.18 15.05 0.2 0.01 88.80 21.0 0.4 88.52 15.6 0.2 0.0 (degrees) (GN)

28. Contact angle analysis Fixed friction and varying clearance (Plate A) 72.19 17.0 0.02 76.58 20.6 0.01 88.80 21.0 0.0 0.4 71.05 14.0 0.02 76.18 15.05 0.01 88.52 15.6 0.0 0.2 (degrees) (GN)

29. Fixed Friction and Clearance (Plate C) 76.07 0.05 17.0 71.8 0.035 12.0 63.1 0.02 7.0 (degrees) (GN)

30. Radial Streses for Plate A for Fixed Clearance

31. Radial Streses for Plate A for Fixed Friction

32. Shear Stress for Plate A for Fixed Clearance

33. Shear Stress for Plate A for Fixed Friction

34. Hoop Stress for Plate A for Fixed Clearance

35. Hoop Stress for Plate A for Fixed Friction

36. Radial Stress for Plate B for Fixed Clearance

37. Shear Stress for Plate B for Fixed Clearance

38. Shear Stress for Plate B for Fixed Friction

39. Hoop Stress for Plate B for Fixed Clearance

40. Hoop Stress for Plate B for Fixed Friction

41. Stresses for Plate C for varying Pin displacement