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Titolo:
Stochastic bilevel programming in structural optimization
Autore:
Christiansen, S; Patriksson, M; Wynter, L;
Indirizzi:
Ecole Polytech, Palaiseau, France Ecole Polytech Palaiseau FranceEcole Polytech, Palaiseau, France Chalmers Univ Technol, Dept Math, S-41296 Gothenburg, Sweden Chalmers UnivTechnol Gothenburg Sweden S-41296 41296 Gothenburg, Sweden Univ Versailles, PRISM, F-78000 Versailles, France Univ Versailles Versailles France F-78000 SM, F-78000 Versailles, France
Titolo Testata:
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
fascicolo: 5, volume: 21, anno: 2001,
pagine: 361 - 371
SICI:
1615-147X(200107)21:5<361:SBPISO>2.0.ZU;2-2
Fonte:
ISI
Lingua:
ENG
Soggetto:
UNILATERAL CONTACT; TRUSS TOPOLOGY; DESIGN; CONSTRAINTS;
Keywords:
topology optimization; mathematical program with equilibrium constraints (MPEC); contact conditions; average-case analysis; parallel algorithm;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Engineering, Computing & Technology
Citazioni:
32
Recensione:
Indirizzi per estratti:
Indirizzo: Christiansen, S Ecole Polytech, Palaiseau, France Ecole Polytech Palaiseau France tech, Palaiseau, France
Citazione:
S. Christiansen et al., "Stochastic bilevel programming in structural optimization", ST MULT OPT, 21(5), 2001, pp. 361-371

Abstract

We consider the mathematical modelling and solution of robust and cost-optimizing structural (topology) design problems. The setting is the optimal design of a linear-elastic structure, for example a truss topology, under unilateral frictionless contact, and under uncertainty in the data describingthe load conditions, the material properties, and the rigid foundation. The resulting stochastic bilevel optimization model finds a structural designthat responds the best to the given probability distribution in the data. This model is of special interest when a structural failure will lead to a reconstruction cost, rather than loss of life. For the mathematical model, we provide results on the existence of optimalsolutions which allow for zero lower design bounds. We establish that the optimal solution is continuous in the lower design bounds, a result which validates the use of small but positive values of them, and for such bounds we also establish the locally Lipschitz continuity and directional differentiability of the implicit upper-level objective function. We also provide aheuristic algorithm for the solution of the problem, which makes use of its differentiability properties and parallelization strategies across the scenarios. A small set of numerical experiments illustrates the behaviour of the stochastic solution compared to all average-case deterministic one, establishing ail increased robustness.

ASDD Area Sistemi Dipartimentali e Documentali, Università di Bologna, Catalogo delle riviste ed altri periodici
Documento generato il 05/04/20 alle ore 06:35:20