Numerical Treatment of Nonmonotone Quasi-Static Frictional Contact Problems Via D.C. Energy Decomposition and Multiphase Methods

  • Georgios E. Stavroulakis


Theoretical and numerical study of quasistatic numerical contact problems with nonmonotone Coulomb-like friction is considered through difference convex (d.c.) decomposition of the nonconvex superpotential energy function. Separate handling of convexity and concavity. whenever this information is explicitly (d.c. Hiriart-Urruty, 1985) or implicitly (quasidifferentials Demya.nov, 1989) available, is currently considered to be a reasonable approach for the study of nonconvex optimization problems, since results of convex analysis and optimization can be fully utilized. The impact of this approach on the development of numerical algorithms for frictional contact problems is studied here.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Auchmuty, G., 1989, Duality algorithms for nonconvex variational principles. Num. Funct. Anal. and Optimization, 10:211–264.MathSciNetMATHCrossRefGoogle Scholar
  2. Demyanov, V.F., 1989, Smoothness of nonsmooth functions, in:“Nonsmooth Optimization and Related Topics”, F.II. Clarke, V.F. Deuiyanov and F. Giannessi eds., Plenum Press, New York, London.Google Scholar
  3. Hiriart-Urruty, J.-B., 1985, Generalized differentiability, duality and optimization for problems dealing with differences of convex functions,in: “Convexity and Duality in Optimization”, J. Ponstein ed., Lect. Notes in Econ. and Math. Systems Vol. 256, Springer 1985.Google Scholar
  4. Moreau, J.J., 1968, La notion de sur-potentiel et les liaisons unilaterales en elastostatique. C.R. Acad. Sc., Paris, 267A:954–957.MathSciNetGoogle Scholar
  5. Panagiotopoulos, P.D. and Stavroulakis, G.E., 1992, New type of variational principles based on the notion of quasidifferentiability, Acta lllechanica 94:171–194.MathSciNetMATHCrossRefGoogle Scholar
  6. Panagiotopoulos, P.D., 1994, “Hemivariational Inequalities. Applications in Mechanics and Engineering”, Springer Verlag, New York, Berlin.Google Scholar
  7. Stavroulakis, G.E. and Panagiotopoulos, P.D., 1993 Convex multilevel decomposition algorithms for non-monotone problems, Intern. Journal of Numerical Methods in Engineering 36(11): 1945–1961.MathSciNetMATHCrossRefGoogle Scholar
  8. Tao, P.D. and Sonad, EI.B., 1988, Duality in D.C. optimization. Subgradient methods, in: “Intern. Series of Numerical Mathematics” Vo91:276–294, Birkhäuser Verlag, Basel.Google Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Georgios E. Stavroulakis
    • 1
  1. 1.Faculty of Mathematics and PhysicsAachen University of Technology, RWTHAachenF.R. Germany

Personalised recommendations