Geodesic
Chance constrained optimal beam design: Convex reformulation and probabilistic robust design
Kybernetika, Tome 54 (2018) no. 6, pp. 1201-1217.

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In this paper, we are concerned with a civil engineering application of optimization, namely the optimal design of a loaded beam. The developed optimization model includes ODE-type constraints and chance constraints. We use the finite element method (FEM) for the approximation of the ODE constraints. We derive a convex reformulation that transforms the problem into a linear one and find its analytic solution. Afterwards, we impose chance constraints on the stress and the deflection of the beam. These chance constraints are handled by a sampling method (Probabilistic Robust Design).
DOI : 10.14736/kyb-2018-6-1201
Classification : 49M25, 65C05, 90C15, 90C30
Keywords: optimal design; stochastic programming; chance constrained optimization; probabilistic robust design; geometric programming 
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     title = {Chance constrained optimal beam design: {Convex} reformulation and probabilistic robust design},
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     language = {en},
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Kůdela, Jakub; Popela, Pavel. Chance constrained optimal beam design: Convex reformulation and probabilistic robust design. Kybernetika, Tome 54 (2018) no. 6, pp. 1201-1217. doi : 10.14736/kyb-2018-6-1201. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-6-1201/

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