EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 21 / No 4 (October-December 2015) ESAIM: COCV, 21 4 (2015) 901-923 References
Free Access
Issue
ESAIM: COCV
Volume 21, Number 4, October-December 2015
Page(s) 901 - 923
DOI https://doi.org/10.1051/cocv/2014049
Published online 20 May 2015
  1. G. Allaire, Shape Optimization by the Homogenization Method. Vol. 146 of Appl. Math. Sci. Springer-Verlag, New York (2002). [Google Scholar]
  2. M. Allen and K. Maute, Reliability-based shape optimization of structures undergoing fluid-structure interaction phenomena. Comput. Methods Appl. Mech. Engrg. 194 (2005) 3472–3495. [Google Scholar]
  3. F. Alvarez and M. Carrasco, Minimization of the expected compliance as an alternative approach to multiload truss optimization. Struct. Multidisc. Optim. 29 (2005) 470–476. [CrossRef] [Google Scholar]
  4. A. Asadpoure, M. Tootkaboni and J.K. Guest, Robust topology optimization of structures with uncertainties in stiffness: application to truss structures. Comput. Struct. 89 (2011) 1131–1141. [CrossRef] [Google Scholar]
  5. I. Babuška, F. Novile and R. Tempone, A Stochastic collocation method for elliptic partial differential equations with random input data. SIAM Rev. 52 (2010) 317–355. [CrossRef] [MathSciNet] [Google Scholar]
  6. M.P. Bensøe and O. Sigmund, Topology Optimization: Theory, Methods and Applications. Springer-Verlag, Berlin (2003). [Google Scholar]
  7. H.-G. Beyer and B. Sendhoff, Robust optimization â a comprehensive survey. Comput. Methods Appl. Mech. Engrg. 196 (2007) 3190–3218. [Google Scholar]
  8. S.I. Birbil, S.C. Fang, J.B.G. Frenk and S. Zhang, Recursive approximation of the high dimensional max function. Oper. Res. Lett. 33 (2005) 450–458. [CrossRef] [MathSciNet] [Google Scholar]
  9. D. Buccur and G. Buttazzo, Variational Methods in Shape Optimization Problems. Progr. Non Lin. Differ. Eq. Appl. Birkhäuser Boston, Inc., Boston, MA (2005). [Google Scholar]
  10. G. Buttazzo, N. Varchon and H. Zoubairi, Optimal measures for elliptic problems. Ann. Mat. Pura Appl. 185 (2006) 207–221. [CrossRef] [MathSciNet] [Google Scholar]
  11. G. Buttazzo and F. Maestre, Optimal shape for elliptic problems with random perturbations. Discrete Contin. Dyn. Syst. 31 (2011) 1115–1128. [CrossRef] [MathSciNet] [Google Scholar]
  12. G.C. Calafiore and F. Dabbene, Optimization under uncertainty with applications to design of truss structures. Struct. Multidisc. Optim. 35 (2008) 189–200. [Google Scholar]
  13. J. Casado-Díaz, C. Castro, M. Luna-Laynez and E. Zuazua, Numerical approximation of a one-dimensional elliptic optimal design problem. Multiscale Model. Simul. 9 (2011) 1181–1216. [CrossRef] [MathSciNet] [Google Scholar]
  14. S. Chen, W. Chen and S. Lee, Level set based robust shape and topology optimization under random field uncertainties. Struct. Multidisc. Optim. 41 (2010) 507–524. [CrossRef] [Google Scholar]
  15. A. Cherkaev, Variational Methods for Structural Optimization. Vol. 140 of Appl. Math. Sci. Springer-Verlag, New York (2000). [Google Scholar]
  16. A. Cherkaev and E. Cherkaeva, Principal compliance and robust optimal design. J. Elasticity 72 (2003) 71–98. [CrossRef] [MathSciNet] [Google Scholar]
  17. J. Cohon, Multiobjective Programming and Planning. Dover Publications (2004). [Google Scholar]
  18. S. Conti, H. Held, M. Pach, M. Rumpf and R. Schultz, Shape optimization under uncertainty – A stochastic programming approach. SIAM J. Optim. 19 (2009) 1610–1632. [CrossRef] [Google Scholar]
  19. S. Conti, H. Held, M. Pach, M. Rumpf and R. Schultz, Risk Averse Shape Optimization. SIAM J. Control Optim. 49 (2011) 927–947. [CrossRef] [MathSciNet] [Google Scholar]
  20. M. Davis, Production of Conditional Simulations via the LU Triangular Decomposition of the Covariance Matrix. J. Math. Geol. 19 (1987) 91–98. [Google Scholar]
  21. F. de Gournay, G. Allaire and F. Jouve, Shape and topology optimization of the robust compliance via the level set method. ESAIM:COCV 14 (2008) 43–70. [Google Scholar]
  22. X. Guo, W. Zhang and L. Zhang, Robust structural topology optimization considering boundary uncertainties. Comput. Methods Appl. Mech. Engrg. 253 (2013) 356–368. [CrossRef] [MathSciNet] [Google Scholar]
  23. E. de Rocquigny, N. Devictor, S. Tarantola. Uncertainty in Industrial Practice: A Guide to Quantitative Uncertainty Management. John Wiley (2008). [Google Scholar]
  24. I. Doltsinis and Z. Kang, Robust design of structures using optimization methods. Comput. Methods Appl. Mech. Engrg. 193 (2004) 2221–2237. [CrossRef] [Google Scholar]
  25. P.D. Dunning and H.A. Kim, Robust Topology Optimization: Minimization of Expected and Variance of Compliance. AIAA J. 51 (2013) 2656–2664. [CrossRef] [Google Scholar]
  26. I. Enevoldsen and J.D. Sørensen, Reliability-based optimization in structural engineering. Struct. Safety 15 (1994) 169–196. [CrossRef] [Google Scholar]
  27. B. Geihe, M. Lenz, M. Rumpf and R. Schultz, Risk averse elastic shape optimization with parametrized fine scale geometry. Math. Program. 141 (2013) 1–2. [CrossRef] [MathSciNet] [Google Scholar]
  28. W. Hager, Runge–Kutta methods in optimal control and the transformed adjoint system. Numer. Math. 87 (2000) 247–282. [Google Scholar]
  29. A. Henrot and H. Maillot, Optimization of the shape and the location of the actuators in an internal control problem. Bolletino U.M.I. 8 (2001) 737–757. [Google Scholar]
  30. A. Henrot and M. Pierre, Variation et optimization de formes. Math. Appl. Springer (2005). [Google Scholar]
  31. D.W. Kim and B.M. Kwak, Reliability-based shape optimization of two-dimensional elastic problems using BEM. Comput. Struct. 60 (1996) 743–750. [CrossRef] [Google Scholar]
  32. M. Loève, Probability Theory. I, 4th edition. Vol. 45 of Grad. Texts Math. Springer-Verlag, New York (1977). [Google Scholar]
  33. M. Loève, Probability Theory. II, 4th edition. Vol. 46 of Grad. Texts Math. Springer-Verlag, New York (1978). [Google Scholar]
  34. R.T. Marler and J.S. Arora, Survey of multi-objective optimization methods for engineering. Struct. Multidisc. Optim. 26 (2004) 369–395. [CrossRef] [Google Scholar]
  35. G.I. Schuëller and H.A. Jensen, Computational methods in optimization considering uncertainties – An overview. Comput. Methods Appl. Mech. Engrg. 198 (2008) 2–13. [Google Scholar]
  36. A. Shapiro, D. Dentcheva and A. Ruszczynski, Lectures on Stochastic Programming. Modelling and Theory. MPS-SIAM Series on Optimization (2009). [Google Scholar]
  37. C. Shikui and C. Wei, A new level-set based approach to shape and topology optimization under geometric uncertainty. Struct. Multidisc. Optim. 44 (2011) 1–18. [CrossRef] [Google Scholar]
  38. S.A. Smolyak, Quadrature and interpolation formulas for tensor products of certain classes of functions. Doklady Akademii Nauk SSSR 4 (1963) 240–243. [Google Scholar]
  39. J. Sokolowski and J.P. Zolésio, Introduction to Shape Optimization: Shape Sensitivity Analysis. Vol. 16 of Springer Series Comput. Math. Springer-Verlag, Berlin (1992). [Google Scholar]
  40. K. Svanberg, The method of moving asymptotes – a new method for structural optimization. Int. J. Numer. Methods Engrg. 24 (1987) 359–373. [Google Scholar]
  41. K. Svanberg, A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM J. Optim. 12 (2002) 555–573. [CrossRef] [Google Scholar]
  42. N. Varchon, Optimal measures for nonlinear cost functionals. Appl. Math. Optim. 54 (2006) 205–221. [CrossRef] [MathSciNet] [Google Scholar]
  43. N. Wiener, The homogeneous chaos. Amer. J. Math. 60 (1938) 897–936. [Google Scholar]
  44. E. Zuazua, Propagation, Observation, Control and Numerical Approximation of Waves approximated by finite difference method. SIAM Rev. 47 (2005) 197–243. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.