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Optimization‐based stability analysis of structures under unilateral constraints
Author(s) -
Kanno Yoshihiro,
Ohsaki Makoto
Publication year - 2008
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2401
Subject(s) - truss , stability (learning theory) , mathematical optimization , regular polygon , mathematics , maximization , optimization problem , convex optimization , convex analysis , computer science , structural engineering , geometry , engineering , machine learning
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.