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A variance-expected compliance model for structural optimization. (English) Zbl 1236.90086
Summary: The goal of this paper is to find robust structures for a given main load and its perturbations. In the first part, we show the mathematical formulation of an original variance-expected compliance model used for structural optimization. In the second part, we study the interest of this model on two 3D benchmark test cases and compare the obtained results with those given by an expected compliance model.

MSC:
90C15 Stochastic programming
Software:
LIPSOL
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[1] Dorn, W., Gomory, R., Greenberg, M.: Automatic design of optimal structures. J. Mech. 3, 25–52 (1964)
[2] Ben-Tal, A., Nemirovski, A.: Robust truss topology design via semidefinite programming. SIAM J. Optim. 7(4), 991–1016 (1997) · Zbl 0899.90133 · doi:10.1137/S1052623495291951
[3] Achtziger, W., Bendsøe, M., Ben-Tal, A., Zowe, J.: Equivalent displacement based formulations for maximum strength truss topology design. Impact Comput. Sci. Eng. 4(4), 315–345 (1992) · Zbl 0769.73054 · doi:10.1016/0899-8248(92)90005-S
[4] Achtziger, W.: Topology optimization of discrete structures: an introduction in view of computational and nonsmooth aspects. In: Rozvany, G.I.N. (ed.) Topology Optimization in Structural Mechanics, pp. 57–100. Springer, Vienna (1997) · Zbl 0885.73048
[5] Achtziger, W.: Multiple-load truss topology and sizing optimization: some properties of minimax compliance. J. Optim. Theory Appl. 98(2), 255–280 (1998) · Zbl 0915.73036 · doi:10.1023/A:1022637216104
[6] Alvarez, F., Carrasco, M.: Minimization of the expected compliance as an alternative approach to multiload truss optimization. Struct. Multidiscip. Optim. 29(6), 470–476 (2005) · Zbl 1243.74133 · doi:10.1007/s00158-004-0488-7
[7] Ben-Tal, A., Bendsøe, M.P.: A new method for optimal truss topology design. SIAM J. Optim. 3(2), 322–358 (1993) · Zbl 0780.90076 · doi:10.1137/0803015
[8] Ben-Tal, A., Zibulevsky, M.: Penalty/barrier multiplier methods for convex programming problems. SIAM J. Optim. 7(2), 347–366 (1997) · Zbl 0872.90068 · doi:10.1137/S1052623493259215
[9] Jarre, F., Kočvara, M., Zowe, J.: Optimal truss design by interior-point methods. SIAM J. Optim. 8(4), 1084–1107 (1998) · Zbl 0912.90231 · doi:10.1137/S1052623496297097
[10] Ivorra, B., Ramos, A.M., Mohammadi, B.: Semideterministic global optimization method: Application to a control problem of the burgers equation. J. Optim. Theory Appl. 135(3), 549–561 (2007) · Zbl 1146.90053 · doi:10.1007/s10957-007-9251-8
[11] Bendsøe, M.P., Sigmund, O.: Topology Optimization. Theory, Methods and Applications. Springer, Berlin (2003) · Zbl 1059.74001
[12] Eckhardt, H.: Kinematic Design of Machines and Mechanisms. McGraw-Hill, New York (1998)
[13] Rockafellar, R.T.: Convex Analysis. Princeton Landmarks in Mathematics. Princeton University Press, Princeton (1997)
[14] Mehrotra, S.: On the implementation of a primal-dual interior point method. SIAM J. Optim. 2(4), 575–601 (1992) · Zbl 0773.90047 · doi:10.1137/0802028
[15] Zhang, Y.: Solving large-scale linear programs by interior-point methods under the MATLAB environment. Technical Report TR96-01, Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, MD, July 1995
[16] Ivorra, B., Mohammadi, B., Ramos, A.M.: Optimization strategies in credit portfolio management. J. Glob. Optim. 43(2), 415–427 (2009) · Zbl 1169.90452 · doi:10.1007/s10898-007-9221-6
[17] Seber, G.A.F.: Linear Regression Analysis. Wiley, New York (1977) · Zbl 0354.62055
[18] Kanno, Y., Ohsaki, M., Murota, K., Katoh, N.: Group symmetry in interior-point methods for semidefinite program. Optim. Eng. 2, 293–320 (2001) · Zbl 1035.90056 · doi:10.1023/A:1015366416311
[19] Bai, Y., de Klerk, E., Pasechnik, D., Sotirov, R.: Exploiting group symmetry in truss topology optimization. Optim. Eng. 10(3), 331–349 (2009) · Zbl 1400.90242 · doi:10.1007/s11081-008-9050-6
[20] Ohsaki, M.: Optimization of geometrically non-linear symmetric systems with coincident critical points. Int. J. Numer. Methods Eng. 48, 1345–1357 (2000) · Zbl 0985.74053 · doi:10.1002/1097-0207(20000730)48:9<1345::AID-NME951>3.0.CO;2-O
[21] Carrasco, M.: Diseño óptimo de estructuras reticulares en elasticidad lineal vía teoría de la dualidad. Estudio teórico y numérico. Engineering Degree Thesis, Universidad de Chile (2003)
[22] Debiane, L., Ivorra, B., Mohammadi, B., Nicoud, F., Ern, A., Poinsot, T., Pitsch, H.: A low-complexity global optimization algorithm for temperature and pollution control in flames with complex chemistry. Int. J. Comput. Fluid Dyn., 20(2), 93–98 (2006) · Zbl 1184.76829 · doi:10.1080/10618560600771758
[23] Isebe, D., Azerad, P., Bouchette, F., Ivorra, B., Mohammadi, B.: Shape optimization of geotextile tubes for sandy beach protection. Int. J. Numer. Methods Eng. 74(8), 1262–1277 (2008) · Zbl 1159.74394 · doi:10.1002/nme.2209
[24] Ivorra, B., Mohammadi, B., Dumas, L., Durand, O., Redont, P.: Semi-deterministic vs. Genetic Algorithms for Global Optimization of Multichannel Optical Filters. Int. J. Comput. Eng. Sci. 2(3), 170–178 (2006) · doi:10.1504/IJCSE.2006.012769
[25] Ivorra, B., Mohammadi, B., Santiago, D.E., Hertzog, J.G.: Semi-deterministic and genetic algorithms for global optimization of microfluidic protein folding devices. Int. J. Numer. Methods Eng. 66(2), 319–333 (2006) · Zbl 1110.76311 · doi:10.1002/nme.1562
[26] Artzner, P., Delbaen, D., Eber, J.M., Heath, D.: Thinking coherently. Risk 10, 68–71 (1997)
[27] Artzner, P., Delbaen, D., Eber, J.M., Heath, D.: Coherent measures of risk. Math. Finance 9, 203–228 (1999) · Zbl 0980.91042 · doi:10.1111/1467-9965.00068
[28] Tukey, J.W.: Exploratory Data Analysis. Addison-Wesley, Reading (1977) · Zbl 0409.62003
[29] Carrasco, M., Ivorra, B., Lecaros, R., Ramos, A.M.: A variance-expected compliance approach for topology optimization. In: Hélder, R., Herskovits, J. (eds.) CD-ROM Proceedings of the ENGOPT 2010 Conference. Instituto Superior Técnico, Lisboa (2010) · Zbl 1327.74127
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