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Limit analysis in plasticity as a mathematical programming problem

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Abstract

We study an infinite dimensional mathematical programming problem, which arises naturally in solid mechanics. It concerns the moment of collapse, and the collapse state itself, of a plastic structure subjected to increasing loads. The duality between the «static» and «kinematic» theorems of limit analysis is well-known in discrete plasticity; we prove the same duality for a continuum including existence of the collapse fields for stresses and velocities as the primal and dual solutions. We then discuss the approximation of the infinite problem by a family of finite convex programming problems. Numerical results for classical problems in limit analysis where this discretization is based on finite elements will be published separately.

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Authors and Affiliations

  1. Mathematics Dept., University of Odense, DK-5230, Odense, Denmark

    E. Christiansen

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  1. E. Christiansen
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Additional information

This paper is based on parts of the author's Ph. D. thesis at MIT. I Should like to express my gratitude to my advisor, professor G. Strang, for drawing my attention to this problem and for his help and encouragement. The author was supported by the University of Aarhus, Denmark, during his work at MIT.

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Christiansen, E. Limit analysis in plasticity as a mathematical programming problem. Calcolo 17, 41–65 (1980). https://doi.org/10.1007/BF02575862

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  • DOI: https://doi.org/10.1007/BF02575862

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