Skip to main content
SpringerLink
Log in

Stability of elastic bodies with nonmonotone multivalued boundary conditions of the quasidifferential type

  • Published:
Journal of Elasticity Aims and scope Submit manuscript

Abstract

Necessary conditions for the stability of elastic bodies subjected to nonmonotone multivalued boundary conditions are derived. These conditions are assumed to be derived from nonconvex and nonsmooth, quasidifferentiable energy functions. A ‘difference convex’ approximation of the potential energy function is written based on an appropriate quasidifferential formulation. Under appropriate assumptions for the convex and the concave parts we prove the existence of at least one nontrivial solution to the nonlinear eigenvalue problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. P.D. Panagiotopoulos, Nonconvex energy functions. Hemivariational inequalities and substationary principles.Acta Mechanica 42 (1983) 160–183.

    Google Scholar 

  2. P.D. Panagiotopoulos,Inequality problems in mechanics and applications/Convex and nonconvex energy functionals. Birkhäuser Verlag, Boston/Basel/Stuttgart (1985); Russian translation by MIR Publishers, Moscow (1989).

    Google Scholar 

  3. J.J. Moreau and P.D. Panagiotopoulos (eds),Nonsmooth Mechanics and Applications. CISM Lect. Notes No. 302. Springer Verlag, Vienna/New York, (1988).

    Google Scholar 

  4. P.D. Panagiotopoulos,Hemivariational Inequalities. Applications in Mechanics and Engineering. Springer Verlag, New York, Berlin (1994).

    Google Scholar 

  5. V.F. Demyanov, On quasidifferential functionals.Soviet Math. Dokl. 21 (1980) 1: 14–17.

    Google Scholar 

  6. V.F. Demyanov and A.M. Rubinov,Quasidifferential Calculus. Optimization Software Inc., Publications Division, New York (1986).

    Google Scholar 

  7. V.F. Demyanov and L.C.W. Dixon (eds),Quasidifferential Calculus. Mathematical Programming Study 29. North-Holland, Amsterdam (1986).

    Google Scholar 

  8. D. Goeleven, Noncoercive variational problems: the recession approach. Fac. Univ. Notre Dame de la Paix, Namur, Research Report 95/01 (1995).

  9. P.D. Panagiotopoulos and G.E. Stavroulakis, The delamination effect in laminated von Karman plates under unilateral boundary conditions. A variational-hemivariational inequality approach.Journal of Elasticity 23 (1990) 69–96.

    Google Scholar 

  10. G.E. Stavroulakis, Analysis of structures with interfaces. Formulation and study of variational-hemivariational inequality problems. Ph.D. Dissertation, Aristotle University, Thessaloniki (1991).

  11. P.D. Panagiotopoulos and G.E. Stavroulakis, New type of variational principles based on the notion of quasidifferentiability.Acta Mechanica 94 (1992) 171–194.

    Google Scholar 

  12. D. Motreanu and P.D. Panagiotopoulos, Hysteresis: the eigenvalue problem for hemivariational inequalities. In: A. Visintin (ed.),Models of Hysteresis. Longman Scientific and Technical, J. Wiley Inc. pp. 102–117.

  13. B. Budiansky. Theory of buckling and post-buckling behaviour of elastic structures. In: Chia-Shun Yih (ed.),Advances in Applied Mechanics, Vol. 14. Academic Press, London (1974) pp. 1–65.

    Google Scholar 

  14. H. Brézis, Problèmes unilatéraux.J. Math. pures et appl. 51 (1972) 1–168.

    Google Scholar 

  15. V.F. Demyanov, G.E. Stavroulakis, L.N. Polyakova and P.D. Panagiotopoulos,Quasidifferentiability and nonsmooth modelling in engineering. Kluwer Academic Publishers Dordrecht (in press).

  16. P.D. Panagiotopoulos, Coercive and semicoercive hemivariational inequalities.Nonlinear Analysis. Theory Methods and Applications 16 (1991) 209–231.

    Google Scholar 

  17. G. Fichera, Problemi elastostatici con vincoli unilaterali: il problema di Signorini con ambigue condizioni al contorno.Mem. Accad. Naz. Lincei VIII 7 (1964) 91–140.

    Google Scholar 

  18. G. Fichera, Boundary value problems in elasticity with unilateral constraints. In: S. Flügge (ed.),Encyclopedia of Physics, Vol. VI a/2. Springer Verlag, Berlin (1972) pp. 391–424.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Technical Mechanics, Aachen, Germany

    G. E. Stavroulakis, D. Goeleven & P. D. Panagiotopoulos

  2. Institute of Mechanics, Department of Engineering Sciences, Technical University of Crete, GR-73100, Chania, Greece

    G. E. Stavroulakis

  3. Department of Mathematics, Faculty of Sciences, Facultés Universitaires N.D. de la Paix, B-5000, Namur, Belgium

    D. Goeleven

  4. Department of Civil Engineering, Institute of Steel Structures, School of Technology, Aristotle University, GR-54006, Thessaloniki, Greece

    P. D. Panagiotopoulos

Authors
  1. G. E. Stavroulakis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Goeleven
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. D. Panagiotopoulos
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stavroulakis, G.E., Goeleven, D. & Panagiotopoulos, P.D. Stability of elastic bodies with nonmonotone multivalued boundary conditions of the quasidifferential type. J Elasticity 41, 137–149 (1995). https://doi.org/10.1007/BF00042511

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00042511

Key words

Mathematics Subject Classifications (1991)

Search

Navigation