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Unilateral contact applications using FEM software

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Nonsmooth analysis, inequality constrained optimization and variational inequalities are involved in the modelling of unilateral contact problems. The corresponding theoretical and algorithmic tools, which are part of the area known as nonsmooth mechanics, are by no means classical. In general purpose software some of these tools (perhaps in a simplified way) are currently available. Two engineering applications, a rubber-coated roller contact problem and a masonry wall, solved with MARC, are briefly presented, together with elements of the underlying theory.








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  • Laboratory of Applied Mechanics, Department of Engineering Sciences, Technical University of Crete, GR–73100 Chania, Greece
  • Division of Applied Mathematics and Mechanics, University of Ioannina, GR-45110 Ioannina, Greece


  • Adly S. and Goeleven D. (2000): A discretization theory for a class of semi-coercive unilateral problems. - Numer. Math., Vol. 87, No. 1, pp. 1-34.
  • Antes H. and Panagiotopoulos P.D. (1992): The Boundary Integral Approach to Static and Dynamic Contact Problems. Equality and Inequality Methods. - Basel: Birkhauser.
  • Bathe K.J. (1996): Finite Element Procedures. -New Jersey: Prentice-Hall.
  • Batra R.C. (1980): Rubber covered rolls. The nonlinear elastic problem. - J. Appl. Mech., Vol. 47, pp. 82-86.
  • Bertsekas D.P. (1996): Constrained optimization and Lagrange multiplier methods. - Athena Scientific Press, MA.
  • Chaudhary A.B. and Bathe K.-J. (1986): Asolution method for static and dynamic analysis of three-dimensional contact problems with friction. - Comput. Struct., Vol. 24, No. 6, pp. 855-873.
  • Christensen P.W., Klarbring A., Pang J.S., and N. Stromberg (1998): Formulation and comparison of algorithms for frictional contact problems. - Int. J. Num. Meth. Eng., Vol. 42, pp. 145-173.
  • Demyanov V.F., Stavroulakis G.E., Polyakova L.N. and Panagiotopoulos P.D. (1996): Quasi differentiability and Nonsmooth Modeling in Mechanics, Engineering and Economics. - Dordrecht: Kluwer.
  • Ferris M.C. and Pang J.S. (1997): Engineering and economic applications of complementarity problems. - SIAM Rev., Vol. 39, pp. 669-713.
  • Gao D.Y., Ogden R.W. and Stavroulakis G.E. (Eds.)(2001): Nonsmooth Nonconvex Mechanics: Modeling, Analysis and Numerical Methods. - Dordrecht: Kluwer.
  • Herrmann L.R. (1978): Finite element analysis of contact problems. - ASCE J. Eng. Mech. Div., Vol. 104, pp. 1043-1057.
  • Hinge K.C. and Maniatty A.M. (1998): Model of steady rolling contact between layered rolls with thin media in the nip.- Eng. Comput., Vol. 15, No. 7, pp. 956-976.
  • Hlavacek I., Haslinger J., Necas J. and Lovisek J. (1988): Solution of Variational Inequalities in Mechanics. -Berlin: Springer.
  • Ionescu I.R. and Sofonea M. (1993): Functional and Numerical Methods in Viscoplasticity. - Oxford: Oxford University Press.
  • Kikuchi N. and Oden J.T. (1988): Contact Problems in Elasticity: A Study of Variational Ineualities and Finite Element Methods. - Philadelphia: SIAM.
  • Klarbring A. (1999): Contact, friction, discrete mechanical structures and mathematical programming, In: New Developments in Contact Problems (P. Wriggers and P. Panagiotopoulos, Eds.). - CISM Courses and Lectures No. 384, Wien: Springer, Ch. 2, pp. 55-100.
  • Leung A.Y.T., Guoqing Ch. and Wanji Ch.(1998): Smoothing Newton method for solving two- and three-dimensional frictional contact problems. - Int. J. Num. Meth. Eng., Vol. 41, pp. 1001-1027.
  • MARC (1996): Nonlinear Finite Element Analysis of Elastomer. -MARC Analysis Research Corp.
  • MARC (1997): Theory and User Information, Vol. A. - MARC Analysis Research Corporation.
  • Mijar A.R. and Arora J.S. (2000): Review of formulations for elastostatic frictional contact problems. - Struct. Multidiscipl. Optim., Vol. 20, pp. 167-189.
  • Mistakidis E.S. and Stavroulakis G.E. (1998): Nonconvex Optimization in Mechanics. Algorithms, Heuristics and Engineering Applications by the F.E.M.. - Dordrecht: Kluwer.
  • Moreau J.J., Panagiotopoulos P.D. and Strang G. (1988): Topics in Nonsmooth Mechanics. - Basel: Birkhauser.
  • Panagiotopoulos P.D. (1988): Inequality Problems in Mechanics and Applications. Convex and Nonconvex Energy Functions. - Basel: Birkhauser.
  • Panagiotopoulos P.D. (1993): Hemivariational Inequalities. - Berlin: Springer.
  • Rochdi M., Shillor M. and Sofonea M. (1998): Quasistatic viscoelastic contact with normal compliance and friction. -J. Elasticity, Vol. 51, No. 2, pp. 105-126.
  • Stavroulaki M.E., Stevenson A. and Bowron St. (2000): Finite element analysis of rubber coated rollers contact problem and the phenomena of friction. - Proc. 4-th Int.Coll. Computational Methods for Shell and Spatial Structures IASS-IACM 2000, Chania, Athens, Greece (on CD-ROM).
  • Stavroulakis G.E., Panagiotopoulos P.D. and Al-Fahed A.M. (1991): On the rigid body displacements and rotations inunilateral contact problems and applications. - Comp.Struct., Vol. 40, pp. 599-614.
  • Stavroulakis G.E. and Antes H. (2000): Nonlinear equation approach for inequality elastostatics. A 2-D BEM implementation. - Comp. Struct., Vol. 75, No. 6, pp. 631-646.
  • Yeoh O.H. (1995): Phenomenological theory of rubber elasticity, In: Comprehensive Polymer Science (S.L. Aggarwal, Ed.). - 2nd Suppl., Pergamon Press.
  • Yeoh O.H. (1997): Hyperelastic material models for finite element analysis of rubber. - J. Nat.Rubber Res., Vol. 12, No. 3, pp. 142-153.

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