First-kind and the second-kind boundary integral equation systems for solution of frictionless contact problems

Engineering Analysis with Boundary Elements

Volumn 24, Issue 5, 2000, Pages 407-426

  Vodicka R ^a  

^a TECHNICAL UNIVERSITY OF KO ICE   (Slovakia)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; BOUNDARY ELEMENT METHOD; GALERKIN METHODS; INTEGRAL EQUATIONS; PRESSURE MEASUREMENT; PROBLEM SOLVING;

DISPLACEMENT BOUNDARY INTEGRAL EQUATIONS (BIE); ELASTIC CONTACTS; TRACTION HYPERSINGULAR BOUNDARY INTEGRAL EQUATIONS (HBIE);

ELASTICITY;

EID: 0343826053     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0955-7997(00)00012-6     Document Type: Article

References (39)

1. Andersson T. The boundary element method applied to two-dimensional contact problems with friction. In: Brebbia CA, editor. Boundary element method, Berlin: Springer, 1981.
2. Andersson T, Fredricksson B, Persson BGA. The boundary element method applied to two-dimensional contact problems. In: Brebbia CA, editor. Proceedings of the Second International Seminar on Recent Advances in Boundary Element Method, Southampton: Computational Mechanics Publications, 1980 (March).
3. Baláš J, Sládek J, Sládek V. Stress analysis by boundary element method. Amsterdam: Elsevier, 1989.
4. Blázquez A, París F, Cañas J, Garrido JA. An algorithm for frictionless contact problems with non-conforming discretizations using BEM. In: Brebbia CA, Dominguez M, Paris F, editors. Boundary elements, vol. XIV, Sevilla: Computational Mechanics Publications, 1992.
5. Blázquez A, París F, Mantič V. BEM solution of two dimensional contact problems by weak application of contact conditions with non-conforming discretizations. Int J Solids Struct 1998;35(24):3259-78.
6. Chan SK, Tuba IS. A finite element method for contact problems of solid bodies. I. Theory and validation. Int J Mech Sci 1971;13:615-25.
7. Chen WH, Chen TC. Boundary element analysis for contact problems with friction. Comp Struct 1992;45(3):431-8.
8. Dundurs J, Lee MS. Stress concentration at a sharp edge in contact problems. J Elast 1972;2(2):109-12.
9. Fredriksson B. Finite element solution of surface nonlinearities in structural mechanics with special emphasis to contact and fracture mechanics problems. Comp Struct 1976:281-90.
10. Golub GH, van Loan CF. Matrix computations. Baltimore, MD: The Johns Hopkins University Press, 1983.
11. Gray LJ, Paulino GH. Symmetric Galerkin boundary integral formulation for interface and multi-zone problems. Int J Numer Meth Engng 1997;40:3085-101.
12. Hartmann F. Introduction to boundary elements. Berlin: Springer, 1989.
13. Hertz H. Miscellaneous papers on the contact of elastic solids. London: McMillan, 1896 (translated by Jones).
14. Holzer SM. How to deal with hypersingular integrals in the symmetric BEM. Commun Numer Meth Engng 1993;9:219-32.
15. Holzer SM. On engineering analysis of 2D problems by the symmetric Galerkin boundary element method and coupled BEM/ FEM. Advances in boundary element techniques, Berlin: Springer, 1992. p. 187-208 (chap. 10).
16. Hörmander L. The analysis of partial differential operators, vol. I. Berlin: Springer, 1983.
17. Johnson KL. Contact mechanics. Cambridge: Cambridge University Press, 1985.
18. Khutoryanskiy NM. Boundary-contact integro-differential equations of the elasticity theory for articulately homogenious bodies. Applied problems of strength and plasticity, methods of solution of elasticity and plasticity problems, Gorkiy: Soviet-union Proceedings, University of Gorkiy, 1981. p. 11-8 (in Russian).
19. Khutoryanskiy NM. Boundary integral and integro-differential equations of the second kind for basic mixed boundary value problem of the elasticity theory. Applied problems of strength and plasticity, statics and dynamics of deformable systems, Gorkiy: Soviet-union Proceedings, University of Gorkiy, 1981. p. 3-13 (in Russian).
20. Klarbring A. Mathematical programming in contact problems. In: Aliabadi MH, Brebbia CA, editors. Computational methods in contact mechanics, Southampton; Boston: Computational Mechanics Publications, 1993. p. 233-63 (chap. 7).
21. Layton JB, Ganguly S, Balakrishna C, Kane JH. A symmetric Galerkin multi-zone boundary element formulation. Int J Numer Meth Engng 1997;40:2913-31.
22. Maier G, Diligenti M, Carini A. A variational approach to boundary element elastodynamic analysis and extension to multidomains problems. Comp Meth Appl Mech Engng 1991;92:193-213.
23. Maier G, Novati G, Cen Z. Symmetric Galerkin boundary element method for quasi-brittle-fracture and frictional contact mechanics. Comp Mech 1993;13:74-89.
24. Man K, Aliabadi MH, Rooke DP. Analysis of contact friction using boundary element method. In: Aliabadi MH, Brebbia CA, editors. Computational methods in contact mechanics, Southampton; Boston: Computational Mechanics Publications, 1993. p. 1-59 (chap. 1).
25. Mantic V. Computer implementation of the boundary element method with multilevel substructuring. PhD thesis, TU Košice, Faculty of mechanical engineering, September 1992.
26. Oden JT, Pires EB. Algorithms and numerical results for finite element approximations of contact problems with non-classical friction laws. Comp Struct 1984;19:137-47.
27. Olukoko OA, Becker AA. A new boundary element approach for contact problems with friction. Int J Numer Meth Engng 1993;36: 2625-42.
28. París F, Foces A, Garrido JA. Application of BEM to solve three-dimensional elastic contact problems without friction. Comp Struct 1992;43(1): 19-30.
29. París F, Garrido JA. An incremental procedure for friction contact problems with the boundary element method. Engng Anal Boundary Element 1989;6(4):202-13.
30. París F, Garrido JA. On the use of discontinuous elements in two-dimensional contact problems. In: Brebbia CA, editor, Boundary elements Berlin: Springer, vol. VII, 1985. p. 1327-30.
31. Sirtori G, Maier G, Novati G, Miccoli S. Galerkin symmetric boundary element method. Int J Numer Meth Engng 1992;35:255-82.
32. Sirtori S, Miccoli S, Korach E. Symmetric coupling of finite elements and boundary elements. Advances in boundary element techniques, Berlin: Springer, 1993. p. 407-27.
33. Ugodchicoff AG, Khutoryanskiy NM. Boundary element method in solid mechanics, Kazan: Kazan University Press, 1986 (in Russian).
34. Vladimirov VS. Equations of mathematical physics. Moscow: Mir, 1984.
35. Vodička R. Conforming contact singular tractions by coupled boundary integral equations. In: Proceedings of the International Conference TRANSCOM'99, University of Zilina, Section 7, June 1999. p. 149-52.
36. Vodička R. Coupled formulations of boundary integral equations for solving contact problems of elasticity. PhD thesis, Technical University of Košice, Faculty of mechanical engineering, January 1999 (in Slovak).
37. Vodička R. Iterative methods for solution of systems of linear equations in the boundary element method. Masters thesis, CTU Faculty of nuclear science and physical engineering, Prague, 1993 (in Slovak).
38. Vodička R. On discretization of boundary integral equations. In: Proceedings of the Third Conference of Doctoral Students of Faculty of Mechanical Engineering, Technical University of Košice, June 1997. p. 76-8 (in Slovak).
39. Wendland WL. In: Whiteman J, editor. On some mathematical aspects of boundary element methods for elliptic problems, Mathematics of finite elements and applications, vol. V. London: Academic Press, 1985. p. 193-227.