Nonlinear analysis of semirigid frames: a parametric complementarity approach

F. Tin-Loi, V. Vimonsatit

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)


The nonlinear elastoplastic analysis of plane frames with semirigid connections is performed using a mathematical programming approach. A Lagrangian formulation suitable for any order analysis is first derived for a suitably discretized structural system through the three basic relations of statics, kinematics, and the elastoplastic constitutive law. Particular features of this formulation include the preservation of static-kinematic duality through the concept of fictitious forces and deformations, the use of a powerful class of piecewise linearized constitutive laws to model plasticity conditions in general and semirigidity in particular, and an exact governing description for the two-dimensional case which can be specialized to any order of geometrical nonlinearity. Specific consideration is then given to a simple, essentially second-order case since it can model sufficiently accurately the behaviour of most real frames. Whilst the particular mathematical programming problem takes the form of a parametric nonlinear complementarity problem involving reversible or holonomic laws, the proposed numerical algorithm which is based on an iterative adaptation of the Wolfe-Markowitz method can accommodate irreversible or nonholonomic phenomena. The scheme can trace a complete skeleton equilibrium path beyond any critical point by capturing only events involving hinge activation or unloading. Numerical examples are presented to illustrate and validate the accuracy of the approach.
Original languageEnglish
Pages (from-to)115-124
Number of pages10
JournalEngineering Structures
Issue number2
Publication statusPublished - Feb 1996
Externally publishedYes


  • elastoplastic analysis
  • mathematical programming
  • plasticity
  • semirigid connections


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