APPLICATION OF CONVEX ANALYSIS CONCEPTS TO THE NUMERICAL SOLUTION OF ELASTIC-PLASTIC PROBLEMS BY USING AN INTERNAL VARIABLE APPROACH |
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Authors: | ALFONSO NAPPI |
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Affiliation: | Department of Structural Engineering , Politecnico di Milano , Piazza L. da Vinci, 32, Milan, 1-20133, Italy |
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Abstract: | Stepwise holonomic elastic-plastic problems are considered both at the material level and at the structural level by using an internal variable formulation (in which a free energy and a dissipation function ptay a central role). Under convenient hypotheses concerning the material behaviour, some extremal properties are proved, which imply that the elastic-plastic response can be determined by solving non-linear (mostly unconstrained) programs. The paper also discusses the links with extremum theorems previously demonstrated by other authors on the basis of a different approach, which explicitly consider yield surfaces and sometimes plastic multipliers, leading lo non-linear constrained optimization problems. Finally, limit analysis and shakedown problems are briefly discussed within the context of the same internal variable formulation. |
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Keywords: | Internal variables plasticity convex analysis extremal properties |
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