Skip to main content
SpringerLink
Log in

On the solution of structures involving elements with nonconvex energy potentials

  • Research Papers
  • Published:
Structural optimization Aims and scope Submit manuscript

Abstract

In this paper, a new method is proposed for the numerical treatment of problems involving elements with nonconvex energy potentials. Due to the nonconvexity, the problem may have more than one stable solution. The method is applied for the solution of structures with semirigid connections whose behaviour are described by means of a nonmonotone moment-rotation diagram. The method is based on the mathematical background of hemivariational inequalities which describe rigorously the introduced nonconvexities. Nmmerical examples demonstrate the properties and the applicability of the proposed numerical method.

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

  • Almusallam, T.H.; Richard, R.M. 1993: Steel frame analysis with flexible joints exhibiting a strain-softening behaviour.Comp. & Struct. 46, 55–65

    Google Scholar 

  • Clarke, F.H. 1983:Optimization and nonsmooth analysis. New York: J. Wiley

    Google Scholar 

  • Colson, A. (ed.) 1992: COST-C1.Proceedings of the first state of the art workshop. Ecole Nationale Superieure des Arts et Industries de Strasbourg

  • Demyanov, V.F.; Stavroulakis, G.E.; Polyakova, L.N.; Panagiotopoulos, P.H. 1996:Quasidifferentiability and nonsmooth modelling in mechanics, engineering and economics. Dordrecht: Kluwer

    Google Scholar 

  • Fletcher, R. 1990:Practical methods of optimization. Chichester: J. Wiley

    Google Scholar 

  • Mistakidis, E.S.; Panagiotopoulos, P.D. 1993: Numerical treatment of non-monotone (zig-zag) friction and adhesive contact problems with debonding. Approximation by monotone subproblems.Com. & Struct. 47, 33–46.

    Google Scholar 

  • Mistakidis, E.S.; Panagiotopoulos, P.D. 1994: On the approximation of nonmonotone mulitvalued problems by monotone subproblems.Comp. Meth. Appl. Mech. Eng. 114, 55–76

    Google Scholar 

  • Moreau, J.J.; Panagiotopoulos, P.D.; Strang, G., 1988:Topics in nonsmooth mechanics. Basel: Birkhäuser

    Google Scholar 

  • Naniewicz, Z.; Panagiotopoulos, P.D. 1995:Mathematical theory of hemivariational inequalities and applications. Marcel Dekker

  • Panagiotopoulos, P.D. 1983: Nonconvex energy functions. Hemivariational inequalities and substationary principles.Acta Mech. 42, 160–183

    Google Scholar 

  • Panagiotopoulos, P.D.; Baniotopoulos, C.C.; Avdelas, A.V. 1984: Certain propositions on the activation of yield modes in elastoplasticity and their applications to deterministic and stochastic problems.ZAMM 64, 491–501

    Google Scholar 

  • Panagiotopoulos, P.D. 1985:Inequality problems in mechanics and applications. Convex and nonconvex energy functions. Basel: Birkhäuser (Russian translation, Moscow: MIR, 1989)

    Google Scholar 

  • Panagiotopoulos, P.D. 1988: Nonconvex superpotentials and hemivariational inequalities. Quasidifferentiability in mechanics. In: Moreau, J.J., Panagiotopoulos, P.D. (eds.)nonsmooth mechanics and applications.CISM Lect.. Notes 302. Vienna: Springer

    Google Scholar 

  • Panagiotopoulos, P.D. 1991: Coercive and semicoercive hemivariational inequalities.Nonlinear Analysis 10, 209–231

    Google Scholar 

  • Panagiotopoulos, P.D. 1993:Hemivariational inequalities. Applications in mechanics and engineering. Berlin, Heidelberg, New York: Springer

    Google Scholar 

  • Pardalos, P.M.; Rosen, J.B. 1987:Constrained global optimization/algorithms and applications.Lecture Notes in Computer Science 268, Berlin: Springer

    Google Scholar 

  • Rockafellar, R.T. 1979:La théorie des sous-gradients et ses applications à l'optimization, functions convexes et non-convexes. Montreal: Les Presses de I Universite de Montreal

    Google Scholar 

  • Stavroulakis, G.E.; Polyakova, L.N. 1996: Nonsmooth and non-convex structural analysis algorithms based on difference convex optimization techniques.Struct. Optim. 12, 167–176

    Google Scholar 

  • Tzaferopoulos, M.A.; Panagiotopoulos, P.D. 1994: A numerical method for a class of hemivariational inequalities.Comput. Mech. 15, 223–248

    Google Scholar 

  • Tzaferopoulos, M.A.; Mistakidis, E.S.; Bisbos, C.D.; Panagiotopoulos, P.D.: Comparison of two methods for the solution of a class of nonconvex energy problems using convex minimization algorithms.Comp. & Struct. 57, 959–971

  • Wald, F. (ed.) 1994:COST-C1: Proceedings of the second state of the art workshop. Brussels: ECSP-EEC-EAEC

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Steel Structures, Aristotle University, GR-54006, Thessaloniki, Greece

    E. S. Mistakidis

Authors
  1. E. S. Mistakidis
    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

Mistakidis, E.S. On the solution of structures involving elements with nonconvex energy potentials. Structural Optimization 13, 182–190 (1997). https://doi.org/10.1007/BF01199238

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01199238

Keywords

Search

Navigation