A semi-analytical approach to three-dimensional normal contact problems with friction

Computational Mechanics

Volumn 30, Issue 4, 2003, Pages 310-322

  Li, J ^a   Berger, E J ^a  

^a University of Cincinnati   (United States)

Author keywords

Contact; Elasticity; Friction; Semi analytical methods

Indexed keywords

BOUNDARY ELEMENT METHOD; ELASTICITY; FINITE ELEMENT METHOD; ITERATIVE METHODS;

CONTACT; MESHLESS METHOD; SEMI-ANALYTICAL METHOD; STICK ZONE SIZE;

FRICTION;

EID: 0038298847     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-002-0407-y     Document Type: Article

References (44)

1. Andersson L-E (1991) A quasistatic frictional problem with normal compliance. Nonlinear Analysis 16: 347-369
2. Andersson L-E (1995) A global existence result for a quasistatic contact problem with friction. Adv. Mat. Sci. Appl. 5: 249-286
3. Andersson L-E (1999) A quasistatic frictional problem with a normal compliance penalization term. Nonlinear Analysis 37: 689-705
4. Atluri SN, Kim H-G, Cho JY (1999) A critical assessment of the truly meshless local petrov-galerkin (mlpg) and local boundary integral equation (lbie) methods. Comput. Mech. 24: 348-372
5. Babuska I, Melenk JM (1997) The partition of unity method. Int. J. Num. Meth. Eng. 40: 727-758
6. Campos LT, Oden JT, Kikuchi N (1982) A numerical analysis of a class of contact problems with friction in elastostatics. Comp. Meth. Appl. Mech. Eng. 34: 821-845
7. Cattaneo C (1938) Sul contatto di due corpi elastici: Distribuzione locale degli sforzi. Reconditi dell Academia Nazionale dei Lincei 27: 342-348, 434-436, 474-478
8. Ciavarella M (1998a) The generalized cattaneo partial slip plane contact problem: i-theory. Int. J. Solids Struct. 35(18): 2349-2362
9. Ciavarell M (1998b) Tangential loading of general three-dimensional contacts. J. Appl. Mech. 65: 998-1003
10. Duarte C, Oden JT (1996) Hp-cloud: a meshless method to solve boundary-value problems. Comp. Meth. Appl. Mech. Eng. 139: 237-262
11. Dydo JR, Busby HR (1995) Elasticity solutions for constant and linearly varying load applied to a rectangular surface patch on the elastic half-space. J. Elast. 38: 153-163
12. Eterovic AL, Bathe KJ (1991) On the treatment of inequality constraints arising from contact conditions in finite element analysis. Comp. Struct. 40: 203-209
13. Guyot N, Kosior F, Maurice G (2000) Coupling of finite elements and boundary elements methods for study of the frictional contact problem. Comp. Meth. Appl. Mech. Eng. 181: 147-159
14. Hills DA, Sackfield A (1987) The stress field induced by normal contact between dissimilar spheres. J. Appl. Mech. 54: 8-14
15. Hills DA, Sackfield A (1987) The stress field induced by normal contact between dissimilar spheres. J. Appl. Mech. 54: 8-14
16. Hills DA, Nowell D, O'Connor JJ (1988) On the mechanics of fretting fatigue. Wear 125: 129-146
17. Johnson KL (1961) Energy dissipation at spherical surfaces in contact transmitting oscillating forces. J. Mech. Eng. Sci. 3(4): 362-368
18. Johnson KL (1985) Contact Mechanics. Great Britain: Cambridge University Press
19. Kalker JJ, van Randen Y (1972) A minimum principle for frictionless elastic contact with application to non-hertzian half-space contact problems. J. Eng. Math. 6(2): 193-206
20. Kikuchi N, Oden JT (1988) Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods. Society for Industrial and Applied Mathematics, Philadelphia
21. Klarbring A (1986a) General contact boundary conditions and the analysis of frictional systems. Int. J. Solids Struct. 22(12): 1377-1398
22. Klarbring A (1986b) A mathematical programming approach to three-dimensional contact problems with friction. Comp. Meth. Appl. Mech. Eng. 58: 175-200
23. Klarbring A (1990) Examples of non-uniqueness and non-existence of solutions to quasistatic contact problems with friction. Ingenieur-Archiv 60: 529-541
24. Kosior F, Guyot N, Maurice G (1999) Analysis of frictional contact problem using boundary element method and domain decomposition method. Int. J. Num. Meth. Eng. 46: 65-82
25. Lancaster P, Salkauskas K (1981) Surface generated by moving least squares methods. Math. Comp. 37: 141-158
26. Li J (2002) Three-dimensional nonconformal contact problems, part i: Formulation and solution of integral equations for some fundamental loading elements, Case report 2002-201, University of Cincinnati Computer-Aided Engineering Laboratory.
27. Li J, Berger EJ (2001) A boussinesq-cerruti solution set for constant and linear distribution of normal and tangential load over a triangular area. J. Elast. 63: 137-151
28. Li S, Qian D, Liu W-K, Belytschko T (2001) A meshfree contact-detection algorithm. Comp. Meth. Appl. Mech. Eng. 190: 3271-3292
29. Litewka P, Wriggers P (2002) Frictional contact between 3d beams. Comp. Mech. 28: 26-39
30. Love AEH (1929) The stress produced in a semi-infinite solid by pressure on part of the boundary. Phil. Trans. Roy. Soc. (London) A228: 377
31. Mindlin RD (1949) Compliance of elastic bodies in contact. J. Appl. Mech. 16: 259-268
32. Mindlin RD, Dereciewics H (1953) Elastic spheres in contact under varying oblique forces. J. Appl. Mech. 20: 327-344
33. Mindlin RD, Mason WP, Osmer TF, Dereciewicz H (1952) Effect of an oscillatory tangential force on the contact surfaces of elastic spheres. Proceedings of the First National Congress of Applied Mechanics
34. Munisamy RL, Hills DA, Nowell D (1994) Static axisymmetric hertzian contacts subject to shearing forces. J. Appl. Mech. 61: 278-283
35. Oden JT, Pires EB (1983) Nonlocal and nonlinear friction laws and variational principles for contact problems in elasticity. J. Appl. Mech. 50: 67-76
36. Pantuso D, Bathe KJ, Bouzinov PA (2000) A finite element procedure for the analysis of thermo-mechanical solids in contact. Comp. Struct. 75: 551-573
37. Paris F, Garrido JA (1989) An incremental procedure for friction contact problems with the boundary element method. Eng. Anal. Boun. Elem. 6(4): 202-213
38. Rabier P, Martin JAC, Oden JT, Campos L (1986) Existence and local uniqueness of solutions to contact problems in elasticity with nonlinear friction laws. Int. J. Eng. Sci. 24(11): 1755-1768
39. Saeedvafa M, Dundurs J (1988) An example for load-path dependence in elasticity with friction. J. Theo. Appl. Mech. 7(2): 211-226
40. Spence DA (1968) Self-similar solutions to adhesive contact problems. Proc. the Roy. Soc. (London) A305(1480): 55-80
41. Spence DA (1975) The hertz contact problem with finite friction. J. Elast. 5(4): 297-319
42. Svec OJ, Gladwell GML (1971) An explicit boussinesq solution for a polynomial distribution of pressure over a triangular region. J. Elast. 1: 167-170
43. Young WC (1989) Roark's Formulas for Stress and Strain. 6th edn, McGraw-Hill, Inc., New York
44. Zavarize G, Wriggers P, Schrefler A (1998) A method for solving contact problems. Int. J. Num. Meth. Eng. 42: 473-498