Boundary element hyper-singular formulation for elastoplastic contact problems. (English) Zbl 0974.74072

Aliabadi, M. H.; Martin, D.

Int. J. Numer. Methods Eng. 48, No. 7, 995-1014 (2000).

Summary: We present a new formulation for solving elastoplastic frictional contact problems by the boundary element method using non-conforming discretization. The initial strain approach, together with the von Mises yield criterion, is adopted. Two different methods are developed for the evaluation of contact parameters. The first utilizes the local interpolation functions to approximate the contact parameters at the non-nodal contact points. In the second method the unknowns at these contact points are computed by using a boundary integral displacement equation which contains a strongly singular integral, or by using a boundary integral traction equation, which has a hyper-singular integral. The resulting system of equations includes the unknowns of a node within the contact zone of one body expressed in terms of all nodal values of tractions and displacements of the other body. Comparisons are made between the new approaches and conforming discretizations.

MSC:

74S15	Boundary element methods applied to problems in solid mechanics
74M15	Contact in solid mechanics
74C05	Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74M10	Friction in solid mechanics

Keywords:

elastoplastic frictional contact problems; boundary element method; non-conforming discretization; initial strain approach; von Mises yield criterion; boundary integral displacement equation; strongly singular integral; boundary integral traction equation; hyper-singular integral

References:

[1]	Boundary elements in two-dimensional contact and friction. Dissertations No. 85, Link?ping University, 1982.
[2]	A two-dimensional BEM method for thermo-elastic body forces contact problems. In Boundary Elements IX, vol. 2: Stress Analysis Applications, (eds). Computational Mechanics Publications: Southampton, Springer: Berlin, 1987; 417-437.
[3]	On the use of discontinuous elements in 2D contact problems. In Boundary Elements VII. Computational Mechanics Publications: Southampton, 1985; 13-27 to 13-39.
[4]	Analysis of contact friction using the boundary element method. In Computational Methods in Contact Mechanics, (eds). Computational Mechanics Publications: Southampton, Elsevier Applied Science: London, 1993; 1-60.
[5]	Leitao, International Journal for Numerical Methods in Engineering 38 pp 315– (1995) · Zbl 0831.73072 · doi:10.1002/nme.1620380210
[6]	Non-conform discretisation of the contact region applied to two-dimensional boundary element method. In Boundary Elements XVI, (ed.). Computational Mechanics Publications: Southampton, 1994; 353-360. · Zbl 0842.73071
[7]	Martin, Engineering Analysis with Boundary Elements 21 pp 349– (1998) · Zbl 0957.74069 · doi:10.1016/S0955-7997(98)00023-X
[8]	An algorithm for frictionless contact problems with non-conforming discretizations using BEM. In Boundary Elements XIV, (eds). Computational Mechanics Publications: Southampton, 1992; 409-420. · Zbl 0831.73066
[9]	Olukoko, International Journal for Numerical Methods in Engineering 36 pp 2625– (1993) · Zbl 0780.73095 · doi:10.1002/nme.1620361508
[10]	Martin, Computers and Structures 69 pp 557– (1998) · Zbl 0940.74065 · doi:10.1016/S0045-7949(98)00138-2
[11]	Par?s, Computers and Structures 57 pp 829– (1995) · Zbl 0900.73903 · doi:10.1016/0045-7949(95)92007-5
[12]	Numerical Recipes in FORTRAN. Cambridge University Press: Cambridge, MA 1992. · Zbl 0778.65002
[13]	Aliabadi, International Journal for Numerical Methods in Engineering 21 pp 2221– (1985) · Zbl 0599.65011 · doi:10.1002/nme.1620211208
[14]	Guigginai, Journal of Applied Mechanics 57 pp 906– (1990) · Zbl 0735.73084 · doi:10.1115/1.2897660
[15]	Aliabadi, Communications in Applied Numerical Methods in Engineering 3 pp 123– (1987) · Zbl 0617.65006 · doi:10.1002/cnm.1630030208