A constrained non-linear system approach for the solution of an extended limit analysis problem

Authors

  • S. Tangaramvong,

    1. School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW 2052, Australia
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  • F. Tin-Loi

    Corresponding author
    1. School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW 2052, Australia
    • School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW 2052, Australia
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Abstract

A number of recent papers (see, e.g. (Int. J. Mech. Sci. 2007; 49:454–465; Eur. J. Mech. A/Solids 2008; 27:859–881; Eng. Struct. 2008; 30:664–674; Int. J. Mech. Sci. 2009; 51:179–191)) have shown that classical limit analysis can be extended to incorporate such important features as geometric non-linearity, softening and various so-called ductility constraints. The generic formulation takes the form of a challenging (nonconvex and nonsmooth) optimization problem referred to in the mathematical programming literature as a mathematical program with equilibrium constraints (MPEC). Similar to a classical limit analysis, the aim is to compute in a single step a bound (upper bound, in the case of the extended problem) to the maximum load. The solution algorithm so far proposed to solve the MPEC is to convert it into an iterative non-linear programming problem and attempts to process this using a standard non-linear optimizer. Motivated by the fact that no method is guaranteed to solve such MPECs and by the need to avoid the use of an optimization approach, which is unfamiliar to most practising engineers, we propose, in the present paper, a novel numerical scheme to solve the MPEC as a constrained non-linear system of equations. We illustrate the application of this approach using the simple class of elastoplastic softening skeletal structures for which certain ductility conditions are prescribed. Copyright © 2009 John Wiley & Sons, Ltd.

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