Structural Engineering and Mechanics

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Complementarity and nonlinear structural analysis of skeletal structures

  • Tin-Loi, F. (School of Civil Engineering, University of New South Wales)
  • Published : 1997.09.25
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Abstract

This paper deals with the formulation and solution of a wide class of structures, in the presence of both geometric and material nonlinearities, as a particular mathematical programming problem. We first present key ideas for the nonholonomic (path dependent) rate formulation for a suitably discretized structural model before we develop its computationally advantageous stepwise holonomic (path independent) counterpart. A feature of the final mathematical programming problem, known as a nonlinear complementarity problem, is that the governing relations exhibit symmetry as a result of the introduction of so-called nonlinear "residuals". One advantage of this form is that it facilitates application of a particular iterative algorithm, in essence a predictor-corrector method, for the solution process. As an illustrative example, we specifically consider the simplest case of plane trusses and detail in particular the general methodology for establishing the static-kinematic relations in a dual format. Extension to other skeletal structures is conceptually transparent. Some numerical examples are presented to illustrate applicability of the procedure.

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