ON THE SOLUTION OF 3D FRICTIONAL CONTACT PROBLEMS WITH BOUNDARY ELEMENT METHOD AND DISCONTINUOUS ELEMENTS USING A GENERALIZED NEWTON METHOD WITH LINE SEARCH

Authors

  • Cristiano J. B. Ubessi
  • Rogério J. Marczak

DOI:

https://doi.org/10.26512/ripe.v2i7.21719

Keywords:

Frictional Contact. Boundary Element Method. Discontinuous Elements. Generalized Newton Method with line search.

Abstract

This paper presents the implementation of an algorithm for the solution of 3D elastic contact problems with friction using the Boundary Element Method (BEM) with discontinuous elements. A standard BEM implementation is used, and the coupling of the potential contact zone is imposed through a projection function which treats each region independently, and is updated along with the changes to the contact state. The contact restrictions are fulfilled through the augmented Lagrangian, and the solution is found using the Generalized Newton Method with line search. With this method is possible to avoid the calculation of the non-linear derivatives, allowing for a fast solution of the problem. A classic contact problem is solved to evaluate the accuracy of the method and to provide a comparison with analytic solution.

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References

Alart, P. & Curnier, A., 1991. A mixed formulation for frictional contact problems prone to newton like solution methods. Comput. Methods Appl. Mech. Eng., vol. 92, no. 3, pp. 353”“375.

Andersson, T., 1981. The boundary element method applied to two-dimensional contact problems with friction. In Boundary element methods, pp. 239”“258, Springer.

Beer, G., Smith, I., & Duenser, C., 2008. The Boundary Element Method with Programming. Springer Wien, New York.

Brebbia, C., Telles, J., & Wrobel, L., 2012. Boundary Element Techniques: Theory and Applications in Engineering. Springer Berlin Heidelberg.

Fichera, G., 1963. Sul problema elastostatico di Signorini con ambigue condizioni al contorno. Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat., vol. 34, pp. 138”“142.

Fichera, G., 1973. Boundary value problems of elasticity with unilateral constraints. In Linear Theories of Elasticity and Thermoelasticity, pp. 391”“424, Springer.

Garrido, J., Foces, A., & Paris, F., 1991. B.e.m. applied to receding contact problems with friction. Mathematical and Computer Modelling, vol. 15, no. 3, pp. 143 ”“ 153.

Gonz´alez, J. A., Park, K., Felippa, C. A., & Abascal, R., 2008. A formulation based on localized lagrange multipliers for bem”“fem coupling in contact problems. Computer Methods in Applied Mechanics and Engineering, vol. 197, no. 6, pp. 623”“640.

Johnson, K. L. & Johnson, K. L., 1987. Contact mechanics. Cambridge university press.

Man, K., Aliabadi, M., & Rooke, D., 1993a. Bem frictional contact analysis: load incremental technique. Computers & structures, vol. 47, no. 6, pp. 893”“905.

Man, K., Aliabadi, M., & Rooke, D., 1993b. Bem frictional contact analysis: modelling considerations. Engineering analysis with boundary elements, vol. 11, no. 1, pp. 77”“85.

Pang, J.-S., 1990. Newton’s method for b-differentiable equations. Mathematics of Operations Research, vol. 15, no. 2, pp. 311”“341.

Paris, F., Blazquez, A., &Canas, J., 1995. Contact problems with nonconforming discretizations using boundary element method. Computers & structures, vol. 57, no. 5, pp. 829”“839.

Paris, F. & Garrido, J., 1989. An incremental procedure for friction contact problems with the boundary element method. Engineering Analysis with Boundary Elements, vol. 6, no. 4, pp. 202 ”“ 213.

Rodr´Ä±guez-Tembleque, L. & Abascal, R., 2010. A fem-bem fast methodology for 3d frictional contact problems. Comput. Struct., vol. 88, no. 15-16, pp. 924”“937.

Rodriguez-Tembleque, L., Buroni, F., Abascal, R., & S´aez, A., 2011. 3d frictional contact of anisotropic solids using bem. European Journal of Mechanics-A/Solids, vol. 30, no. 2, pp. 95”“ 104.

Rodr´Ä±guez-Tembleque, L., Gonza´lez, J. A´ ., & Abascal, R., 2008. A formulation based on the localized lagrange multipliers for solving 3d frictional contact problems using the BEM . Numerical Modeling of Coupled Phenomena in Science and Engineering: Practical Use and Examples, p. 359.

Yamazaki, K., Sakamoto, J., & Takumi, S., 1994. Penalty method for three-dimensional elastic contact problems by boundary element method. Computers & structures, vol. 52, no. 5, pp. 895”“903.

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Published

2017-01-25

How to Cite

Ubessi, C. J. B., & Marczak, R. J. (2017). ON THE SOLUTION OF 3D FRICTIONAL CONTACT PROBLEMS WITH BOUNDARY ELEMENT METHOD AND DISCONTINUOUS ELEMENTS USING A GENERALIZED NEWTON METHOD WITH LINE SEARCH. Revista Interdisciplinar De Pesquisa Em Engenharia, 2(7), 186–198. https://doi.org/10.26512/ripe.v2i7.21719

Issue

Vol. 2 No. 7 (2016): BOUNDARY ELEMENT AND MESH REDUCED METHODS (II)

Section

Artigos

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