Optimization‐based stability analysis of structures under unilateral constraints |
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Authors: | Yoshihiro Kanno Makoto Ohsaki |
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Affiliation: | 1. Department of Mathematical Informatics, University of Tokyo, Tokyo 113‐8656, Japan;2. Department of Architecture and Architectural Engineering, Graduate School of Engineering, Kyoto University, Nishikyo, Kyoto 615‐8540, Japan |
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Abstract: | This paper discusses an optimization‐based technique for determining the stability of a given equilibrium point of the unilaterally constrained structural system, which is subjected to the static load. We deal with the three problems in mechanics sharing the common mathematical properties: (i) structures containing no‐compression cables; (ii) frictionless contacts; and (iii) elastic–plastic trusses with non‐negative hardening. It is shown that the stability of a given equilibrium point of these structures can be determined by solving a maximization problem of a convex function over a convex set. On the basis of the difference of convex functions optimization, we propose an algorithm to solve the stability determination problem, at each iteration of which a second‐order cone programming problem is to be solved. The problems presented are solved for various structures to determine the stability of given equilibrium points. Copyright © 2008 John Wiley & Sons, Ltd. |
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Keywords: | frictionless contact unilateral constraint non‐smooth mechanics second‐order cone program stability analysis |
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