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ROBUST OPTIMIZATION USING REDUCED-ORDER MODELING FOR NON-LINEAR STATIC TRUSS SYSTEM

Motta, Renato de S.; Afonso, Silvana M. B.;

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In this work a design optimization tool to obtain robust optimum designs of trusses under nonlinear conditions is described and implemented. The robustness measures considered here are the expected value and standard deviation of the function involved in the optimization problem. To calculate such quantities, we employ two nonintrusive uncertainty propagation analysis techniques that exploit deterministic computer models: Monte Carlo (MC) method and Probabilistic Collocation Method (PCM). When using these robustness measures combined, the search of optimal design appears as a robust multi-objective optimization (RMO) problem. To overcome the time consuming problem inherent in a RMO problem a model reduction technique using the proper orthogonal decomposition (POD) method will be employed to provide fast outputs for nonlinear analysis of trusses. A structural sizing optimization (SSO) algorithm incorporating such procedure in the structural and sensitivity stochastic analyses will be used to obtain efficient optimal trusses design. Optimization studies will be conducted for trusses problems considering different loads level, exploring the material plasticity. Comparisons will be conducted with the SSO approach via traditional FEM and via POD.

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Palavras-chave: Robust Optimization, Multi-Objective Optimization, Proper Orthogonal Decomposition, Nonlinear Static Problem, Probabilistic Collocation Method,

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DOI: 10.5151/meceng-wccm2012-19472

Referências bibliográficas
  • [1] Schuller G.I., Jensen H.A., “Computational Methods in Optimization Considering Uncertainties - An Overview”. Computational Methods and Applications in Mechanical Engineering, 2008.
  • [2] Motta, R. S., Afonso, S.M.B, Lyra, P.R.M, “Structural Robust Optimization Considering Reduced-Basis Method”, Msc. Thesis (in Portuguese), Civil Engineering Department, UFPE, Recife-PE Brazil, 2009
  • [3] Ramamurthy D., “Smart Simulation Techniques For the Evaluation of Parametric Uncertainties on Black Box Systems”. Msc Thesis, Washington State University, 2005
  • [4] Collette, Y., Siarry, P., “Multiobjective Optimization: Principles and Case Studies”, Springer, 2004
  • [5] Motta, R. S., Afonso, S.M.B, Lyra, P.R.M, “A Modified NBI and NC Method For the Solution of N-Multiobjective Optimization Problems”. Structural and Multidisciplinary Optimization (Print), v. 1, p. 1-21, 2012
  • [6] Das, I.; Dennis, J.E., “Normal Boundary Intersection: A New Method for Generating Pareto Surface in Nonlinear Multicriteria Optimization Problems”, SIAM J Optimization, Vol. 8 No. 3, pp. 631-657, 1996
  • [7] Messac, A.; Mattson C.A., “Normal Constraint Method With Guarantee of Even Representation of Complete Pareto Frontier”, 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics Andamp; Material Conference, Palm Springs, CA, 2004
  • [8] Liang, Y.C., Lee, H.P., Lim, S.P., Lin, W.Z., Lee, K.H. and Wu, C.G., “Proper Orthogonal Decomposition and its Applications-Part I: Theory”, Journal of Sound and Vibration, 252(3), page 527-544, 2002
  • [9] Cardoso, M. A., “Development and Application of Reduced-Order Modeling Procedures For Reservoir Simulation”, Dissertation for the Degree of Doctor of Philosophy. Stanford University, 2009
  • [10] Crisfield, M. A., “Non-linear Finite Element Analysis of Solids and Structures - VOLUME 1: ESSENTIALS”, John Wiley Andamp; Sons Ltd, Chichester, England, 2000
  • [11] Afonso, S.M.B, Lyra, P.R.M, Albuquerque, T.M. M., R. S., Motta, “Structural Analysis and Optimization in the Framework of Reduced-Basis Method”. Structural and Multidisciplinary Optimization (Print) , Springer Berlin / Heidelberg, v. 40, p. 177-199, 2010.
  • [12] Burkardt , J., Gunzburger. M., Lee, H. C., “POD and CVT-based Reduced-Order Modeling of Navier-Stokes Flows”, Comput. Methods Appl. Mech. Engrg. 196, 337-355, 2006
  • [13] Sirovich, L., “Turbulence and the Dynamics of Coherent Structures, Part 1: Coherent Structures”, Quarterly of Applied Mathematics, Vol. 45, No. 3, pp. 561-571, 1987
  • [14] Tan, B. T., “Proper Orthogonal Decomposition Extensions and Their Applications in Steady Aerodynamics”, Master of Engineering in High Performance Computation for Engineered Systems (HPCES), Singapore-MIT Alliance, 2003
  • [15] Meyer, P. L., “Probabilidade: Aplicaes Estatstica”, 2nd edition, LTC, Rio de Janeiro, 1983
  • [16] Keane, A. J., Nair, P. B., “Computational Approaches for Aerospace Design: The Pursuit of Excellence”, John-Wiley and Sons. 602 p., 2005.
  • [17] Stoer J., Bulirsch R., “SIntroduction to Numerical Analysis - Second Edition”. Springer- Verlag, Heidelberg, Berlin. p. 150-166, 1991
  • [18] Arora J. S.; Messac, A.; Mullur, A. A., “Optimization of Structural and Mechanical System. Chapter 4 - Multiobjective Optimization: Concepts and Methods”. Jasbir S Arora, University of Iowa, USA, 2007
  • [19] Motta, R. S., Afonso, S. M. B., “Optimization of Trusses under Nonlinear Conditions Considering the Proper Orthogonal Decomposition Method”. In: XXXII CILAMCE - Iberian Latin American Congress on Computational Methods in Engineering, Ouro Preto, 2011.
Como citar:

Motta, Renato de S.; Afonso, Silvana M. B.; "ROBUST OPTIMIZATION USING REDUCED-ORDER MODELING FOR NON-LINEAR STATIC TRUSS SYSTEM", p. 3569-3580 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-19472

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