DOI QR코드

DOI QR Code

Optimal shape design of contact systems

  • Mahmoud, F.F. (Department of Mechanical Engineering, Zagazig University) ;
  • El-Shafei, A.G. (Department of Mechanical Engineering, Zagazig University) ;
  • Al-Saeed, M.M. (Department of Mechanical Engineering, Zagazig University)
  • 투고 : 2004.12.08
  • 심사 : 2006.05.16
  • 발행 : 2006.09.30

초록

Many applications in mechanical design involve elastic bodies coming into contact under the action of the applied load. The distribution of the contact pressure throughout the contact interface plays an important role in the performance of the contact system. In many applications, it is desirable to minimize the maximum contact pressure or to have an approximately uniform contact pressure distribution. Such requirements can be attained through a proper design of the initial surfaces of the contacting bodies. This problem involves a combination of two disciplines, contact mechanics and shape optimization. Therefore, the objective of the present paper is to develop an integrated procedure capable of evaluating the optimal shape of contacting bodies. The adaptive incremental convex programming method is adopted to solve the contact problem, while the augmented Lagrange multiplier method is used to control the shape optimization procedure. Further, to accommodate the manufacturing requirements, surface parameterization is considered. The proposed procedure is applied to a couple of problems, with different geometry and boundary conditions, to demonstrate the efficiency and versatility of the proposed procedure.

키워드

참고문헌

  1. Arora, J.S. (1989), Introduction to Optimum Design, McGraw-Hill, New York
  2. Arora, J.S. (1990), 'Computational design optimization: A review and future directions', Struct. Safety, 7, 131-148 https://doi.org/10.1016/0167-4730(90)90063-U
  3. Arora, J.S. and Haug, E.J. (1979), 'Methods of design sensitivity analysis in structural optimization', AIAA, 17, 970-973 https://doi.org/10.2514/3.61260
  4. Arora, J.S., Chahande, A.I. and Paeng, J.K. (1991), 'Multiplier methods for engineering optimization', Int. J. Numer. Methods Eng., 32, 1485-1525 https://doi.org/10.1002/nme.1620320706
  5. Barboza, J., Fourment, L. and Chenot, J.L. (2002), 'Contact algorithm for 3D multi-bodies problems: Application to forming of multi-materials parts and tool deflection', 5th World Congress on Computational Mechanics, WCCMV, Vienna, Austria, July 7-12
  6. Belegundu, A.D. and Arora, J.S. (1985), 'A study of mathematical programming methods for structural optimization, Part I: Theory, Part II: Numerical aspects', Int. J. Numer. Methods Eng., 21, 1583-1624 https://doi.org/10.1002/nme.1620210904
  7. Beremlijski, P., Haslinger, J., Kocvara, M. and Outrata, J. (2002), 'Shape optimization in contact problems with Coulomb friction', J. Optim., 13(2), 561-587
  8. Berisekas, D.P. (1976), 'On penalty and multiplier methods for constrained minimization', SIAM J. Control Optim., 14, 216-235 https://doi.org/10.1137/0314017
  9. Campos, L.T., Oden, J.T. and Kikuchi, N. (1982), 'A numerical analysis of a class of contact problems with friction in elastostatics', Comp. Meth. App. Mech. Eng., 34, 821-845 https://doi.org/10.1016/0045-7825(82)90090-1
  10. Chapra, S.C. and Canale, Raymond P. (1989), Numerical Method for Engineers, 2nd ed., McGraw-Hill, New York
  11. Cheney, W. and Kincaid, D. (1985), Numerical Mathematics and Computing, 2nd ed., Brooks/Cole, Monterey, CA
  12. Coope, I.D. and Fletcher, R. (1980), 'Some numerical experience with a globally convergent algorithm for nonlinearly constrained optimization', J. Optim. Theory Appl., 32, 1-16 https://doi.org/10.1007/BF00934840
  13. Dundurs, J. (1975), 'Properties of elastic bodies in contact', The Mechanics of Contact Between Deformable Bodies, (Kalker, J.J. and de Pater, A.D., Eds.), Delft Univ. Press
  14. El-Shafei, A.G. (2004), 'Solution of nonlinear frictional contact problems of multibody with application to multileaf springs', J. Eng. & Appl. Sci., Faculty of Eng., Cairo Univ., 51(2), 309-328
  15. El-Shafei, A.G. and Mahmoud, F.F. (1999), 'Nonlinear analysis of thermoelastic frictional contact problems', Proc. of the IASTED Int. Conf. Artificial Intelligence and Soft Computing, Honolulu, Hawaii, USA, August 9-12
  16. Fletcher, R. (1975), 'An ideal penalty function for constrained optimization', J. Ins. Math. Optim., 15, 319-342
  17. Fletcher, R. (1987), Practical Methods of Optimization, 2nded., Wiley, New York
  18. Francavilla, A. and Zeinkiewicz, O.C. (1975), 'A note on numerical computation of elastic contact problems', Int. J. Numer. Methods Eng., 9, 913-924 https://doi.org/10.1002/nme.1620090410
  19. Haslinger, J. and Neittaanmaki, P. (1988), Finite Element Approximation for Optimal Shape Design: Theory and Applications, John Wiley & Sons
  20. Hassan, M.M. and Mahmoud, F.F. (2002), 'A generalized adaptive incremental approach for solving inequality problemss of convex nature', J. Eng. & Appl. Sci., Faculty of Eng., Cairo Univ., 49, 627-645
  21. Haug, E.J. and Arora, J.S. (1979), Applied Optimal Design, John Wiley and Sons, New York
  22. Haug, E.J. and Kwak, B.M. (1978), 'Contact stress minimization by contour design', Int. J. Numer. Methods Eng., 12, 917-930 https://doi.org/10.1002/nme.1620120604
  23. Herskovits, J., Leontiev, A., Dias, G. and Santos, G. (1998), 'An interior point algorithm for optimal design of unilateral constrained mechanical systems', in 'Computational Mechanics, New Trends and Applications', Idelsohn, S., Onate, E. and Dvorkin, E. (Eds.), CIMNE, Barcelona, Spain
  24. Hilding, D., Klarbring, A. and Petterson, J. (1999), 'Optimization of structures in unilateral contact', J. Appl. Mech. Rev., ASME, 52(4), 139-160 https://doi.org/10.1115/1.3098931
  25. Johnson, K.L. (1985), Contact Mechanics, Cambridge Univ. Press, Cambridge
  26. Kim, N.H., Choi, K.K. and Botkin, M.E. (2003), 'Numerical methods for shape optimization using meshfree method', Struct. Multidisc. Optim., 24, 418-429 https://doi.org/10.1007/s00158-002-0255-6
  27. Kim, N.H., Choi, K.K. and Chen, S.C. (2000), 'Shape design sensitivity analysis and optimization of elastoplasticity with frictional contact', AIAA, 38(9)
  28. Kim, N.H., Park, Y.H. and Choi, K.K. (2001), 'Optimization of hyper-elastic structure with multibody contact using continuum-based shape design sensitivity analysis', Struct. Multidisc. Optim., 21, 196-208 https://doi.org/10.1007/s001580050184
  29. Kyung, K., Choi, K., Yo, Kiyoung, Kim, N.H. and Botkin, M.E. (2003), 'Design sensitivity analysis of nonlinear shell structure with frictionless contact', Proc. of DETC'03, ASME 2003 Design Engineering Technical Conf., Chicago, Illinois, USA, Sep. 2-6
  30. Mahmoud, F.F., Al-Saffar, A.K. and Hassan, K.A. (1993), 'An adaptive incremental approach for the solution of convex programming models', Math. & Camp. in Simul., 35, 501-508 https://doi.org/10.1016/0378-4754(93)90068-6
  31. Mahmoud, F.F., Ali-Eldin, S.S., Hassan, M.M. and Emam, S.A. (1998), 'An incremental mathematical programming model for solving multi-phase frictional contact problems', Comput. Struct., 68, 567-581 https://doi.org/10.1016/S0045-7949(98)00093-5
  32. Mahmoud, F.F., EI-.Sharkawy, A.A. and Hassan, K.M. (1989), 'Contour design for contact stress minimization by interior penalty method', Appl. Math. & Mod., 13, 596-600 https://doi.org/10.1016/0307-904X(89)90206-0
  33. Mahmoud, F.F., Salamon, N.J. and Pawlak, T.P. (1986), 'Simulaion of structural elements in receding/advancing contact', Comput. Struct., 22(4), 629-635 https://doi.org/10.1016/0045-7949(86)90015-5
  34. Paczelt, I. and Mros, Z. (2004), 'Contact optimization problems associated with the wear process', XXI ICTAM, Warsaw, Poland, Aug. 15-21
  35. Powell, M.J.D. (1969), A Method for Nonlinear Constraints in Minimization Problems, in R. Fletcher (Ed.), Optimization Academic Press, New York
  36. Zhong, W.X. and Sun, S.M. (1989), 'A parametric quadratic programming approach to elastic contact problems with friction', Comput. Struct., 32(1), 37-43 https://doi.org/10.1016/0045-7949(89)90066-7