Advertisement

Additional Topics

Stability, Economics, Flow Problems, Dynamic Problems
  • Vladimir F. Dem’yanov
  • Georgios E. Stavroulakis
  • Ludmila N. Polyakova
  • Panagiotis D. Panagiotopoulos
Chapter
  • 134 Downloads
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 10)

Abstract

Some additional problems are treated in this Chapter. They refer to quasidifferential modelling of various problems in engineering and economics and they are presented here as model problems before proceeding into the numerical treatment of the problems which is studied in the next Chapters. In particular the problems of the stability of structures with boundary conditions of quasidifferential type, of monotone and nonmonotone network flow problems, of rigid viscoplastic flow problems in cylindrical pipes with adhesion or nonmonotone friction and of time—dependent problems with QD—superpotentials in von Kármán plates and in thermoelasticity are treated.

Keywords

Weak Solution Variational Inequality Elastic Structure Solution Branch Additional Topic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Brezis H. (1972), Problemes unilateraux. J. Math, pures et appl, 51, 1–168.MathSciNetzbMATHGoogle Scholar
  2. 2.
    Budiansky B. (1974), Theory of buckling and post — buckling behaviour of elastic structures. In: Advances in Applied Mechanics, ed. Chia-Shun Yih, Academic Press, London, Vol. 14, 1–65.Google Scholar
  3. 3.
    Demyanov V.F. and Rubinov A.M. (1985), Quasidifferentiable Calculus, Optimization Software, New York.Google Scholar
  4. 4.
    Duvaut G. and Lions J.L. (1972), Les inequations en mechanique et en physique, Dunod, Paris.Google Scholar
  5. 5.
    Fichera G. (1964), Problemi elastostatici con vincoli unilaterali: il problema di Sig-norini con ambigue condizioni al contorno. Mem. Accad. Naz. Lincei, VIII, 7 91–140.Google Scholar
  6. 6.
    Fichera G. (1972), Boundary value problems in elasticity with unilateral constraints. In: Encyclopedia of Physics, (ed. by S. Fliigge) Vol VI a/2, Springer Verlag, Berlin.Google Scholar
  7. 7.
    Goeleven D. (1995), Noncoercive variational problems: the recession approach. Fac. Univ. Notre Dame de la Paix, Namur, Research Report 95/01, to appear in Journal of Global Optimization.Google Scholar
  8. 8.
    Goeleven D., Motreanu D. and Panagiotopoulos P.D. (1995), Multiple solutions for a class of eigenvalue problems in hemivariational inequalities. Metz Days 1995, Research Notes in Mathematics (to appear).Google Scholar
  9. 9.
    Moreau J.J. and Panagiotopoulos P.D. eds. (1988), Nonsmooth mechanics and applications. CISM Lect. Notes No. 302, Springer Verlag, Wien New York.zbMATHGoogle Scholar
  10. 10.
    Motreanu D. and Panagiotopoulos P.D. (1993), Hysteresis: the eigenvalue problem for hemivariational inequalities. In: Visintin A. (ed.): Models of Hysteresis. Longman Scientific and Technical, J. Wiley Inc.Google Scholar
  11. 11.
    Motreanu D. and Panagiotopoulos P.D. (1995), An eigenvalue problem for hemivariational inequalities involving a nonlinear compact operator. Set-Valued Analysis, 3, 155–166.MathSciNetGoogle Scholar
  12. 12.
    Panagiotopoulos P.D. (1982), On a method proposed by W. Prager for the nonlinear network flow problem. Ann. School of Technology, Aristotle University, Vol. Θ, Thessaloniki, 77–85.Google Scholar
  13. 13.
    Panagiotopoulos P.D. (1985), Inequality problems in mechanics and applications. Convex and nonconvex energy functions, Birkhauser Verlag, Basel — Boston — Stuttgart.CrossRefzbMATHGoogle Scholar
  14. 14.
    Panagiotopoulos P.D. (1991), Coercive and semicoercive hemivariational inequalities. Nonlinear Analysis. Theory Methods and Applications 16. 209–231.MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Panagiotopoulos P.D. and Stavroulakis G.E. (1992), New types of variational principles based on the notion of quasidifferentiability, Acta Mechanica 94, 171–194.MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Panagiotopoulos P.D. (1993), Hemivariational Inequalities. Applications in Mechanics and Engineering, Springer Verlag, Berlin — Heidelberg — New York.CrossRefzbMATHGoogle Scholar
  17. 17.
    Prager W. (1965), Problems on network flow. ZAMP, 16, 185.MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Stavroulakis G.E. and Tzaferopoulos M.Ap. (1994), A variational inequality approach to optimal plastic design of structures via the Prager-Rozvany theory. Structural Optimization, 7 (3), 160–169.CrossRefGoogle Scholar
  19. 19.
    Stavroulakis G.E. and Tzaferopoulos M.Ap. (1995), Optimal plastic design of structures with d.c. cost functions and optimality criteria methods. In: Structural and Multidisciplinary Optimization, Eds. N. Olhoff, G. Rozvany, Pergamon Press.Google Scholar
  20. 20.
    Stavroulakis G.E., Goeleven D. and Panagiotopoulos P.D. (1995), Stability of elastic bodies with nonmonotone multivalued boundary conditions of the quasidifferentiable type. Journal of Elasticity, 41 (2), 137–149.MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Tzaferopoulos M.Ap. and Stavroulakis G.E. (1995), Optimal structural design via optimality criteria as a nonsmooth mechanics problem. Computers and Structures, 55 (5), 761–772.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • Vladimir F. Dem’yanov
    • 1
  • Georgios E. Stavroulakis
    • 2
  • Ludmila N. Polyakova
    • 1
  • Panagiotis D. Panagiotopoulos
    • 3
    • 4
  1. 1.Department of MathematicsSt. Petersburg State UniversitySt. PetersburgRussia
  2. 2.Lehr- und Forschungsgebiet für Mechanik; Lehrstuhl C für MathematikRWTHAachenGermany
  3. 3.Department of Civil EngineeringAristotle UniversityThessalonikiGreece
  4. 4.Faculty of Mathematics and PhysicsRWTHAachenGermany

Personalised recommendations