**43**, 1-2, pp. 279-312, 1995

### Some New Developments in Contact Pressure Optimization

Relatively few works have dealt with the optimization problems of bodies in contact. The present work is intended as a contribution to the determination of contact pressure distribution in the frame of linear elasticity. Solution of frictionless contact problems are investigated not only on the basis of minimum complementary energy principle, but also on the basis of minimum total potentional energy by the use of an augmented Lagrangian technique. The goal is to optimize the pressure distribution along the contact region. The minimum of maximal pressure is looked for by controlling the pressure distribution. The optimization problem can be handled by a so-called restricted linear programming problem. Effectiveness of the augmented Lagrangian technique has been proved by axisymmetric and plane stress type numerical examples, i.e., the pressure can be calculated directly, solution of the contact problem can be obtained by means of a relatively small penalty parameter, solution of the optimization problem can be found in a relatively easy way.

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#### References

J.I. TELEGA, Variational principles for mechanical contact problems [in Russian], Advances of Mech., 10, 2, 3-95, 1987.

I. PÁCZELT, Solution of elastic contact problems by the finite element displacement method, Acta Techn. Hung., 82, 3-4, 353-375, 1076.

S.K. CHAN and I.S. TUBA, A finite element method for contact problems of solid bodies. Part I, II, Int. J. Mech. Sci, 13, 615-625, 627-639, 1971.

T.R.J. HUGHES, R.L. TAYLOR et al., A finite element method for a class of contactimpact problems, Comput. Meths. Appl. Mech. Engng., 8, 249-276, 1976.

N. KIKUCHI and J.T. ODEN, Contact problems in elasticity: a study of variational inequalities and finite element methods, SIAM, Philadelphia. 1988.

J.C. SIMO and T.A. LAURSEN, An augmented Lagrangian treatment of contact problems involving friction, Comput. and Struct., 37, 319-331 , 1992.

I. PÁCZELT, Contact optimization problems, Advanced TEMPUS course on numerical methods in computer-aided optimal design, TEMPUS JEP 0045 Zakopane, May 11-15 (1992), Silesian Technical University of Gliwice, Poland, Lecture Notes, Volume 2, pp. 222-261, 1992.

I. PÁCZELT, Some remarks to the solution of quadratic programming problems, Publ. Techn. Univ. Heavy lndustry, Ser D., Natural Sci, 33, 137-156, 1979.

J. KALKER, Three-dimensional elastic bodies in rolling contact, Kluwer Academic Publisher, Dordrecht 1990.

T.F. CONRY and A. SEIREG, A mathematical programming method for design of elastic bodies in contact, Trans. ASME., J. Appl. Mech. Series E, 38, pp. 387-392, June 1971.

I. PÁCZELT and B. HERPAI, Some remarks on the solution contact problems of elastic shells, Arch. Budowy Maszyn, 24, 2, pp.117-202, 1977.

E.J. HAUG and B.M. KWAK, Contact stress minimization by contour design, Int. J. Num, Meth. Engng., 12, pp. 917-930, 1978.

N. KIKUCHI and J.E. TAYLOR, Shape optimization for unilateral elastic contact problems, Num. Meth. Coupl. Probl. Proc. Int. Conf. Swansea, pp. 430--441, 7-11 Sept 1981.

J. HASLINGER and P. NEITTAANMAKI, Finite element approximation for optimal shape design, John Wiley & Sons Ltd., London 1988.

I. PÁCZELT and T. SZABÓ, Optimal shape design for contact problems, Structural Optimization, 7, 1/2, pp. 66-75, 1994.

X. QIU, M.E. PLESHA and D.W. MEYER, Stiffness matrix integration rules for contact-friction finite elements, Computer Methods in Applied Mechanics and Engineering, 93, pp. 385-399, 1991.

I. PÁCZELT, Selected contact problems of elastic systems [in Polish], Mechanika Kontaktu Powierzchni, Z. MRÓZ [Ed.], Ossolineum, pp. 7-49, 1988.