An asymptotic numerical algorithm for frictionless contact problems
Keywords:
asymptotic numerical method, contact, elastic structures, perturbation technique, Pade approximantsAbstract
Perturbation techniques have been successfully developed to solve problems in non-linear structural mechanics. Based on asymptotic expansions, these techniques lead to analytic representation of the solution branches. In elasticity, when solving contact problems, two non-linearities can occur due to contact constraints and to geometry. The aim of this paper is to propose an asymptotic numerical method for frictionless contact problems. Three examples of 2-D contact problems will be studied to establish the efficiency of our algorithm.
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References
(ABA 94] Hmnrrr, I
Hibbitt, Karlsson and Sorens n Inc., V rsion 5.4 .
(BAK 96] BAKER G.A., RAVES-MORRIS P. (1996). Pade approximants, Encyclopedia
of Math matics and its Applications, second clition , ambridge Universi ty Press,
ambridge.
(CO 94-1) OCfiELIN B., DAMIL N. and POTIER-FERRY M. (1994). The asy mptoticnum
rica) method : an fficient pertubation technique for non-linear structw·al
mechanics, Revue Europeenne des Elements Finis, 3(2) :281-297.
94-2) OCHELIN B., DAMIL N. and POTIER-FERRY M. (1994) . Asymptotic
numerical methods and Pade approx.imants for non-linear elastic structures, International
Journal for Numerical Methods in Engin ering, 37:1187-12l3.
[ELH 98] ELHAGE HusSEIN A. (1998). Modelisation des problemes de contact par une
Methode Asymptotique Numerique, These: Universite de Metz, France.
[FAR 90] FARIN G. (1990). urves and Surfac s for Computer Aided Geometric
Design, Computer Science and Scientific Computing, second edition.
(FEN 91] FENO Z.Q. (1991) . Contribution a Ia modelisation des problemes non lineaires:
contact, plasticite et endommagement, These: Universite de Teclmologie
de Compiegne, France.
[I
methode des elements finis dans un cadre grandes deformations elastoplastiques,
These: &ole Nationale superieure des Arts et Metiers, France.
(KIK 88] KIKUCHI N., and ODEN J.T. (1988). Contact Problems in Elasticity: A Study
of Variational Inequalities and Finite Element Methods, SIAM, Philadelphia.
(NAJ 98) NAJAH A., CoCHELIN B., 0AMIL N. and POTIER-FERRY M. (1998). A critical
review of Asymptotic Numerical Methods, to appear: Archives of Computational
Methods in Engineering, Vol. 5, 1, 3-22.