Unilateral contact applications using FEM software

M. Stavroulaki; G. Stavroulakis

International Journal of Applied Mathematics and Computer Science (2002)

  • Volume: 12, Issue: 1, page 115-125
  • ISSN: 1641-876X

Abstract

top
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.

How to cite

top

Stavroulaki, M., and Stavroulakis, G.. "Unilateral contact applications using FEM software." International Journal of Applied Mathematics and Computer Science 12.1 (2002): 115-125. <http://eudml.org/doc/207563>.

@article{Stavroulaki2002,
abstract = {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.},
author = {Stavroulaki, M., Stavroulakis, G.},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {nonsmooth analysis; constrained optimization; contact problems; general purpose FEM program MARC; inequality constrained optimization; variational inequalities; unilateral contact; rubber-coated roller contact problem; masonry wall},
language = {eng},
number = {1},
pages = {115-125},
title = {Unilateral contact applications using FEM software},
url = {http://eudml.org/doc/207563},
volume = {12},
year = {2002},
}

TY - JOUR
AU - Stavroulaki, M.
AU - Stavroulakis, G.
TI - Unilateral contact applications using FEM software
JO - International Journal of Applied Mathematics and Computer Science
PY - 2002
VL - 12
IS - 1
SP - 115
EP - 125
AB - 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.
LA - eng
KW - nonsmooth analysis; constrained optimization; contact problems; general purpose FEM program MARC; inequality constrained optimization; variational inequalities; unilateral contact; rubber-coated roller contact problem; masonry wall
UR - http://eudml.org/doc/207563
ER -

References

top
  1. 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. Zbl1013.65069
  2. Antes H. and Panagiotopoulos P.D. (1992): The Boundary Integral Approach to Static and Dynamic Contact Problems. Equality and Inequality Methods. - Basel: Birkhauser. Zbl0764.73002
  3. Bathe K.J. (1996): Finite Element Procedures. -New Jersey: Prentice-Hall. Zbl0994.74001
  4. Batra R.C. (1980): Rubber covered rolls. The nonlinear elastic problem. - J. Appl. Mech., Vol. 47, pp. 82-86. Zbl0436.73020
  5. Bertsekas D.P. (1996): Constrained optimization and Lagrange multiplier methods. - Athena Scientific Press, MA. Zbl0572.90067
  6. 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. Zbl0604.73116
  7. 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. Zbl0917.73063
  8. 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. 
  9. Ferris M.C. and Pang J.S. (1997): Engineering and economic applications of complementarity problems. - SIAM Rev., Vol. 39, pp. 669-713. Zbl0891.90158
  10. Gao D.Y., Ogden R.W. and Stavroulakis G.E. (Eds.)(2001): Nonsmooth Nonconvex Mechanics: Modeling, Analysis and Numerical Methods. - Dordrecht: Kluwer. Zbl0959.00041
  11. Herrmann L.R. (1978): Finite element analysis of contact problems. - ASCE J. Eng. Mech. Div., Vol. 104, pp. 1043-1057. 
  12. 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. Zbl0943.74065
  13. Hlavacek I., Haslinger J., Necas J. and Lovisek J. (1988): Solution of Variational Inequalities in Mechanics. -Berlin: Springer. Zbl0654.73019
  14. Ionescu I.R. and Sofonea M. (1993): Functional and Numerical Methods in Viscoplasticity. - Oxford: Oxford University Press. Zbl0787.73005
  15. Kikuchi N. and Oden J.T. (1988): Contact Problems in Elasticity: A Study of Variational Ineualities and Finite Element Methods. - Philadelphia: SIAM. Zbl0685.73002
  16. 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. Zbl0941.74037
  17. 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. Zbl0905.73079
  18. MARC (1996): Nonlinear Finite Element Analysis of Elastomer. -MARC Analysis Research Corp. 
  19. MARC (1997): Theory and User Information, Vol. A. - MARC Analysis Research Corporation. 
  20. Mijar A.R. and Arora J.S. (2000): Review of formulations for elastostatic frictional contact problems. - Struct. Multidiscipl. Optim., Vol. 20, pp. 167-189. Zbl1031.74002
  21. Mistakidis E.S. and Stavroulakis G.E. (1998): Nonconvex Optimization in Mechanics. Algorithms, Heuristics and Engineering Applications by the F.E.M.. - Dordrecht: Kluwer. Zbl0918.73002
  22. Moreau J.J., Panagiotopoulos P.D. and Strang G. (1988): Topics in Nonsmooth Mechanics. - Basel: Birkhauser. Zbl0646.00014
  23. Panagiotopoulos P.D. (1988): Inequality Problems in Mechanics and Applications. Convex and Nonconvex Energy Functions. - Basel: Birkhauser. 
  24. Panagiotopoulos P.D. (1993): Hemivariational Inequalities. - Berlin: Springer. 
  25. 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. Zbl0921.73231
  26. 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). 
  27. 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. Zbl0746.73022
  28. 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. 
  29. Yeoh O.H. (1995): Phenomenological theory of rubber elasticity, In: Comprehensive Polymer Science (S.L. Aggarwal, Ed.). - 2nd Suppl., Pergamon Press. 
  30. Yeoh O.H. (1997): Hyperelastic material models for finite element analysis of rubber. - J. Nat.Rubber Res., Vol. 12, No. 3, pp. 142-153. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.