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A variance-expected compliance model for structural optimization


Ivorra, Benjamin and Carrasco, Miguel and Manuel Ramos, Angel (2012) A variance-expected compliance model for structural optimization. Journal of optimization theory and applications, 152 (1). pp. 136-151. ISSN 0022-3239

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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.

Item Type:Article
Uncontrolled Keywords:structural optimization; truss modeling; variance-expected compliance model;stochastic programming
Subjects:Sciences > Mathematics > Operations research
ID Code:16161

Dorn, W., Gomory, R., Greenberg, M.: Automatic design of optimal structures. J. Mech. 3, 25–52(1964)

Ben-Tal, A., Nemirovski, A.: Robust truss topology design via semidefinite programming. SIAM J.Optim. 7(4), 991–1016 (1997)

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)

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)

Achtziger, W.: Multiple-load truss topology and sizing optimization: some properties of minimax compliance. J. Optim. Theory Appl. 98(2), 255–280 (1998)

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)

Ben-Tal, A., Bendsøe, M.P.: A new method for optimal truss topology design. SIAM J. Optim. 3(2),322–358 (1993)

Ben-Tal, A., Zibulevsky, M.: Penalty/barrier multiplier methods for convex programming problems.SIAM J. Optim. 7(2), 347–366 (1997)

Jarre, F., Koˇcvara, M., Zowe, J.: Optimal truss design by interior-point methods. SIAM J. Optim. 8(4),1084–1107 (1998)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)

Bendsøe, M.P., Sigmund, O.: Topology Optimization. Theory, Methods and Applications. Springer,Berlin (2003)

Eckhardt, H.: Kinematic Design of Machines and Mechanisms. McGraw-Hill, New York (1998)

Rockafellar, R.T.: Convex Analysis. Princeton Landmarks in Mathematics. Princeton University Press, Princeton (1997)

Mehrotra, S.: On the implementation of a primal-dual interior point method. SIAM J. Optim. 2(4),575–601 (1992)

Zhang, Y.: Solving large-scale linear programs by interior-point methods under theMATLAB environment.Technical Report TR96-01, Department of Mathematics and Statistics, University of Maryland,Baltimore County, Baltimore, MD, July 1995

Ivorra, B., Mohammadi, B., Ramos, A.M.: Optimization strategies in credit portfolio management. J.Glob. Optim. 43(2), 415–427 (2009)

Seber, G.A.F.: Linear Regression Analysis. Wiley, New York (1977)

Kanno, Y., Ohsaki, M.,Murota, K., Katoh, N.: Group symmetry in interior-point methods for semidefinite program. Optim. Eng. 2, 293–320 (2001)

Bai, Y., de Klerk, E., Pasechnik, D., Sotirov, R.: Exploiting group symmetry in truss topology optimization. Optim. Eng. 10(3), 331–349 (2009)

Ohsaki, M.: Optimization of geometrically non-linear symmetric systems with coincident critical points. Int. J. Numer. Methods Eng. 48, 1345–1357 (2000)

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)

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)

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)

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)

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)

Artzner, P., Delbaen, D., Eber, J.M., Heath, D.: Thinking coherently. Risk 10, 68–71 (1997)

Artzner, P., Delbaen, D., Eber, J.M., Heath, D.: Coherent measures of risk. Math. Finance 9, 203–228(1999)

Tukey, J.W.: Exploratory Data Analysis. Addison-Wesley, Reading (1977)

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)

Deposited On:11 Sep 2012 08:20
Last Modified:06 Feb 2014 10:39

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