Publication: A variance-expected compliance approach for topology optimization
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In this paper we focus on the adaptation to topology optimization of a previous variance-expected compliance applied to truss design. The principal objective of such a model is to find robust structures for a given main load and its perturbations. In particular we are interested in avoiding high compliance values in cases of important perturbations. In the first part, we recall the varianceexpected formulation and main results in the case of truss structures. Then, we extend this model to topology optimization. Finally, we study the interest of this model on a 2D benchmark test.
 W. Achtziger (1997) Topology optimization of discrete structures: an introduction in view of computational and nonsmooth aspects. In Topology optimization in structural mechanics, volume 374 of CISM Courses and Lectures, pages 57–100. Springer, Vienna.  W. Achtziger, M. Bendsøe, A. Ben-Tal, and J. Zowe (1992) Equivalent displacement based formulations for maximum strength truss topology design. Impact Comput. Sci. Engrg., 4(4):315–345.  F. Alvarez and M. Carrasco (2005) Minimization of the expected compliance as an alternative approach to multiload truss optimization. Struct. Multidiscip. Optim., 29(6):470–476.  A. Ben-Tal and A. Nemirovski (1997) Robust truss topology design via semidefinite programming. SIAM J. Optim., 7(4):991–1016.  M. P. Bendsøe and O. Sigmund (2003) Topology optimization. Theory, methods and applications. Springer-Verlag, Berlin.  A. Ben-Tal and M. Zibulevsky (1997) Penalty/barrier multiplier methods for convex programming problems. SIAM J. Optim., 7(2):347–366.  M. Carrasco, B. Ivorra and A.M. Ramos (2010) A variance-expected compliance model for structural optimization. Submitted.  M. Carrasco, B. Ivorra, A.M. Ramos and F. Alvarez(2008) Validation of a new variance-expected compliance model for structural optimization. In Proceedings of the Congress EngOpt 2008. ISBN: 978857650156-5  P. Ciarlet (1988) Mathematical Elasticity, Vol. I, Three Dimensional Elasticity. North-Holland, Amsterdam.  S. Conti, H. Held, M. Pach, M. Rumpf and R. Schultz (2008) Shape optimization under uncertainty, a stochastic programming perspective. SIAM Journal on Optimization. 19(4):1610-1632  B. Ivorra, B. Mohammadi, and A.M. Ramos (2009) Optimization strategies in credit portfolio management. Journal Of Global Optimization 43(2):415–427  B. Ivorra, A.M. Ramos, and B. Mohammadi (2007) Semideterministic global optimization method: Application to a control problem of the burgers equation. Journal of Optimization Theory and Applications, 135(3):549–561.  L.D. Landau, E. M. Lifshitz (1986) Theory of Elasticity. Oxford, England: Butterworth Heinemann.  O. Sigmund (2001) A 99 line topology optimization code written in Matlab. Structural and Multidisciplinary Optimization, 21(2):120–127