Bi-Complementarity and Duality: A Framework in Nonlinear Equilibria with Applications to the Contact Problem of Elastoplastic Beam Theory

Journal of Mathematical Analysis and Applications

Volumn 221, Issue 2, 1998, Pages 672-697

  Gao, David Yang ^a  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

Author keywords

Complementarity problems; duality; variational inequality; nonsmooth analysis; contact problem; beam theory

Indexed keywords

EID: 0000880013     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1998.5935     Document Type: Article

References (39)

1. Allen G. Variational inequalities, complementarity problems, and duality theorems. J. Math. Anal. Appl. 58:1977;1-10.
2. Aubin J. P. Applied Functional Analysis. 1979;Wiley, New York.
3. Chakrabarty J. Theory of Plasticity. 1987;McGraw-Hill, New York.
4. R. W. Cottle, Nonlinear Programs with Positively Bounded Jacobians, Department of Mathematics, University of California, Berkeley, 1964.
5. Cottle R. W., Pang J. S., Stone R. E. The Linear Complementarity Problems. 1992;Academic Press, New York.
6. Dem'yanov V. F., Stavroulakis G. E., Polyakova L. N., Panagiotopoulos P. D. Quasidifferentiability and Nonsmooth Modelling in Mechanics, Engineering and Economics. 1996;Kluwer, Dordrecht.
7. Duvaut G., Lions J. L. Inequalities in Mechanics and Physics. 1976;Springer-Verlag, Berlin.
8. Ekeland I., Temam R. Convex Analysis and Variational Problems. 1976;North-Holland, Amsterdam.
9. Ferris M. C., Pang J. S. Engineering and economic applications of complementarity problems. SIAM Rev. 39:1997;669-713.
10. Friedman A. Variational and Free Boundary Problems. 1993;Springer-Verlag, New York.
11. Gao D. Y. Panpenalty finite element programming for limit analysis. Comput. Struct. 28:1988;749-755.
12. Gao D. Y. Duality theory in nonlinear buckling analysis for von Karman equations. Stud. Appl. Math. 94:1995;423-444.
13. Gao D. Y. Nonlinear elastic beam theory with application in contact problems and variational approaches. Mech. Res. Comm. 23:1996;11-17.
14. Gao D. Y. Complementary finite-element method for finite deformation nonsmooth mechanics. J. Eng. Math. 30:1996;339-353.
15. Gao D. Y. Dual extremum principles in finite deformation theory with applications in post-buckling analysis of nonlinear beam model. Appl. Mech. Rev. ASME. 50:1997;S64-S71.
16. Gao D. Y., Russell D. L. An extended beam theory for smart materials applications. J. Appl. Math. Optim. 34:1996;279-298.
17. Gao D. Y., Strang G. Geometric nonlinearity: Potential energy, complementary energy, and the gap function. Quart. Appl. Math. XLVII:1989;487-504.
18. Gao D. Y., Strang G. Dual extremum principles in finite deformation elastoplastic analysis. Acta Appl. Math. 17:1989;257-267.
19. Glowinski R., Lions J. L., Trémolières R. Numerical Analysis of Variational Inequalities. 1981;North-Holland, Amsterdam.
20. Haslinger J., Panagiotopoulos P. D. The reciprocal variational approach to the Signorini problem with friction, approximation results. Proc. Roy Soc. Edinburgh Sect. A. 98:1984;365-383.
21. Hlavacek I., Haslinger J., Necas J., Lovisek J. Solution of Variational Inequalities in Mechanics. 1982;Springer-Verlag, New York.
22. Isac G. Complementarity Problems. Lecture Notes in Mathematics. 1992;Springer-Verlag, New York.
23. Karamardian S. Generalized complementarity problems. J. Optim. Theory Appl. 6:1971;161-168.
24. Kikuchi N., Oden J. T. Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods. 1988;SIAM, Philadelphia.
25. Kinderlehrer D., Stampacchia G. An Introduction to Variational Inequalities and Their Applications. 1980;Academic Press, New York.
26. Klarbring A., Mikelic A., Shillor M. Duality applied to contact problems with friction. Appl. Math. Optim. 22:1990;211-226.
27. Lovísek J. Duality in the obstacle and unilateral problem for the biharmonic operator. Aplikace Matematiky. 26:1981;291-303.
28. Luo Z. Q., Pang J. S., Ralph D. Mathematical Programs with Equilibrium Constraints. 1996;Cambridge University Press, Cambridge.
29. Mosco U. Dual variational inequalities. J. Math. Anal. Appl. 40:1972;202-206.
30. Oden J. T., Reddy J. N. Variational Methods in Theoretical Mechanics. 1976;Springer-Verlag, Berlin.
31. Panagiotopoulos P. D. Inequality Problems in Mechanics and Applications. 1985;Birkhäuser, Boston.
32. Panagiotopoulos P. D. Hemivariational Inequalities, Applications in Mechanics and Engineering. 1993;Springer-Verlag, Berlin.
33. Pang J. S. Complementarity problems. Horst R., Padalos P. Handbook in Global Optimization. 1994;Kluwer, Boston.
34. Reddy B. D. Mixed variational inequalities arising in elastoplasticity. Nonlinear Anal. 19:1992;1071-1089.
35. Rockafellar R. T. Duality and stability in extremum problems involving convex functions. Pacific J. Math. 21:1967;167-187.
36. Rodrigues J. F. Obstacle Problems in Mathematical Physics. 1987;Elsevier, Amsterdam.
37. Strang G. Introduction to Applied Mathematics. 1986;Wellesley-Cambridge Press, Wellesley.
38. E. Tonti, 1972, A mathematical model for physical theories, I, II, Rend. Accad. Lincei, LII, 1972, 133, 139, 350, 356.
39. S. T. Yau, D. Y. Gao, 1992, Obstacle problem for von Karman equations, Adv. Appl. Math. 13, 1992, 123, 141.