Abstract
An important class of structural mechanics problems deals with the stress analysis of bodies in contact. A contact problem occurs when at least two bodies not mechanically joined touch each other without becoming rigidly attached. In most cases, high stress concentrations are developed in the contact areas. This fact and the presence of friction and wear often cause crack initiation and fretting fatigue. Thus, the analysis of elastic bodies in contact is a common concern in engineering practice and it is important to include the effects of friction in this analysis.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Reference
Hertz, H., “Miscellaneous Papers — on the Contact of Elastic Solids translation by Jones”, D.E., macmillan and Co. ltd., London, 1986.
Mindlin, R.D., “Compliance of Elastic Bodies in Contact”, Trans. ASME, J. Appl. Mech., 17, 1949, 259–268.
Lure, A.I., “Three Dimensional Problems of the Theory of Elasticity”, Interscience, New york, 1964
Kalker, J.J., “On Elastic line Contact”, Trans. ASME, J. Appl. Mech., 39, 1972, 1125–1131.
Kalker, J.J., “on Elastic Line contact”, Trans. ASME, J. Appl. Mech., 39, 1972, 1125–1131.
Gladwell, G.M.L., “Contact problems in the Classical theory of Elasticity”, Sijthoff & NoordhoffHBK, 1980.
Timoshenko, S.P., and Goodier, J.N., “Theory of Elasticity”, McGraw-Hill, New York, 1983.
Conry, T.F., and Seireg, A., “A mathematical Programming Method for Design of Elastic Bodies in Contact”, Trans. ASME, J. Appl. Mech., 93, 1971, 387–392.
Kalker, J.J., and Van Randen, Y., “A Minimum Principle for Frictionless Elastic Contact with Applocation to Non-hertzian Half Space Contact Problems”, J. Engag. Math., 6, 1972, 193–206.
Singh, K.P., and Paul, B., “Numerical Solution of Non-Hertzian Elastic Contact Problems”, Trans. ASME, J. Appl. Mech., 41, 1974, 484–490.
Nayak, L., and Johnson, K.L., “Pressure Between Elastic Bodies having a Slender Area of Contact and Arbitrary Profiles”, Int. J. Mech. Sci., 21, 1979, 237–247.
Hartnett, M.J., “The Analysis of Contact Stresses in Rolling Element Bearing”, Trans. ASME, J. Lub. Tech., 101, 1979, 105–109.
Wilson, E.A., and Parson, B., “Finite Element Analysis of Elastic Contact Problems Using Differential Displacements”, Int. J. Num. Meth. Engng.,;2, 1970, 387–395.
Ohte, S., “Finite Element Analysis of Elastic Contact Problems”, Bull. J. ASME,.16, 1973, 797–804.
Chan, S.K., and Tuba, I.S., “A Finite Element Method for for Contact Problems of Solid Bodies, Part I. Theory and Validation”, Int. J. Mech. Sci., 13 1971, 615–626.
Fredriksson, B., “Finite Element Solution of Surface Non-Linearities in Structural Mechanics with Special Emphasis to Contact and Fracture Mechanics Problems”, Comp. ξ Struct., 6, 1976, 281–290.
Gaertner, R., “Investigation of Plane Elastic Contact Allowing for Friction”, Comp. ξ Struct. 1 1977, 59–63.
Okamoto, N., and Nakazawa, M., “Finite Element Incremental Contact Analysis with Various Frictional Conditions”, Int. J. Num. Meth. Engng., 14, 1979, 331–357.
Tseng, J., and Olson, M.D., “The Mixed Finite Element Method Applied to Two-Dimensional Elastic Contact Problems”, Int. J. Num. Meth. Engng., 17, 1981, 991–1014.
Mahmoud, F.F., Salamon, N.J., and Marks, W.R., “A Direct Automated Procedure for Frictionless Contact Problems”, Int. J. Num. Meth. Engng., 18, 1982, 245–257.
Torstenfeit, B., “Contact Problems with Friction in General Purpose Finite Element Computer Programs”, Comp. ξ Struct., 16, 1983, 487–493.
Andersson, T., “The Boundary Element Method Applied to Two-Dimensional Contact Problems with Friction”, in Proc. of the Third International Seminar on Recent Advances in Boundary Element Methods, Irvine, California, C.A. Brebbia (Ed.), Springer Verlag, Berlin, 1981.
Andersson, T., “The Second Generation Boundary Element Contact Problem”, in Proc. of the Fourth International Seminar on Recent Advances in Boundary Element Methods, C.A. Brebbia (Ed.), Southampton, 1982.
Karami, G. and Fenner, R.T., “Application of Boundary Integral Equation (BIE) Method to Two-Dimensional Elastic Contact Problems Using Isoparametric Quadratic Elements”, Iranian Journal of Science and Technology, Vol. 11, No. 2, 1988, pp. 153–176.
Karami, G., and Fenner, R.T., “Analysis of Mixed Mode Fracture and Crack Closure Using the Boundary Integral Equation Method”, International Journal of Fracture, Vol. 30, No. 1, 1986.
Karami, G. and Fenner, R.T., “A Two-Dimensional BEM for Thermo-Elastic Body Force Contact Problems”, in Boundary Elements IX, Vol. 2: Stress Analysis, (Editors, C.A. Brebbia, W.L. Wendland, G. Kuhn), Springer-Verlag, Berlin Heideiber, 1987.
Karami, G., “A Boundary Element Method Formulation for Elasto-Plastic Contact Problems”, in Boundary Element X, Vol. 2: Stress Analysis, (Editor, C.A. Brebbia) CMP ξ Springer-Verlag, Berlin Heidelberg, 1988.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin, Heidelberg
About this chapter
Cite this chapter
Karami, G. (1989). The Contact Problem. In: Lecture Notes in Engineering. Lecture Notes in Engineering, vol 51. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83897-2_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-83897-2_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51562-3
Online ISBN: 978-3-642-83897-2
eBook Packages: Springer Book Archive