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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 61A New Methodology for an Optimal Shape Design

A New Methodology for an Optimal Shape Design

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Abstract:

The aim of this paper is to study the implementation of an efficient and reliable methodology for shape optimization problems where the objective function and constraints are not known explicitly and are dependent on the Finite Element Analysis (FEA). It is based on the Simultaneous Perturbation Stochastic Approximation (SPSA) method for solving unconstrained continuous optimization problems. We also propose Penalty SPSA (PSPSA) for solving constrained optimization problems, the constraints are handled using exterior point penalty functions within an algorithm that combines SPSA and exact penalty transformations. This paper presents a new structural optimization methodology that combines shape optimization, geometric modeling, FEA and PSPSA method to successfully optimize structural optimization problems. Several tests have been performed on some well known benchmark functions to demonstrate the robustness and high performance of the suggested methodology. In addition, an illustrative two-dimensional structural problem has been solved in a very efficient way. The numerical results demonstrate the robustness and high performance of the suggested methodology for structural optimization problems.

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Periodical:

Applied Mechanics and Materials (Volume 61)

Pages:

43-54

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.61.43

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Online since:

June 2011

Authors:

W. El Alem, A. El Hami, Rachid Ellaia

Keywords:

Finite Element Analysis (FEA), MATLAB, Simultaneous Perturbation Stochastic Approximation, Structural Optimisation

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© 2011 Trans Tech Publications Ltd. All Rights Reserved

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[1] W. Bangerth, H. Klie, V. Matossian, M. Parashar, and M.F. Wheeler: An Autonomic Reservoir Framework for the Stochastic Optimization of Well Placement, Cluster Computing Vol. 8 (2005), p.255–269.

DOI: 10.1007/s10586-005-4093-3

[2] H. J. C. Barbosa, A. C. C. Lemongeb, and C. C. H. Borges: A genetic algorithm encoding for cardinality constraints and automatic variable linking in structural optimization, Engineering Structures Vol. 30 (2008), pp.3708-3723.

DOI: 10.1016/j.engstruct.2008.06.014

[3] S. Bhatnagar: Adaptive Multivariate Three-Timescale Stochastic Approximation Algorithms for Simulation Based Optimization, ACM Transactions on Modelling and Computer Simulation Vol. 15 (2005), p.74–107.

DOI: 10.1145/1044322.1044326

[4] S. Bhatnagar, Michael C. Fu, Steven I. Marcus and I-J. Wang: Two-Timescale Simultaneous Perturbation Stochastic Approximation Using Deterministic Perturbation Sequences, ACM Transactions on Modelling and Computer Simulation Vol. 13 (2003).

DOI: 10.1145/858481.858486

[5] M. E. Botkin: Shape optimization of plate and shell structures, AIAA J Vol. 20 (1982), pp.268-273.

DOI: 10.2514/3.51074

[6] M. E. Botkin, and J. A. Bennett: Shape optimization of three dimensional folded plate structures, AIAA J Vol. 23 (1985), p.1804–1810.

DOI: 10.2514/3.9169

[7] C. A. Coello: Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art, Comput. Methods Appl. Mech. Engrg. Vol. 191 (2002), pp.1245-1287.

DOI: 10.1016/s0045-7825(01)00323-1

[8] X. Duan, and T. Sheppart: Shape optimization using FEA software: A V-shaped anvil as an example, Journal of Materials Processing Technology Vol. 120 (2002), pp.426-431.

DOI: 10.1016/s0924-0136(01)01200-6

[9] S. K. S. Fan, Y. C. Liang, and E. Zahara: A genetic algorithm and a particle swarm optimizer hybridized with Nelder-Mead simplex search, Computers and Industrial Engineering Vol. 50 (2006), pp.401-425.

DOI: 10.1016/j.cie.2005.01.022

[10] A. Georgieva, and I. Jordanov: Global optimization based on novel heuristics, low-discrepancy sequences and genetic algorithms, European Journal of Operational Research Vol. 196 (2009), p.413–422.

DOI: 10.1016/j.ejor.2008.03.019

[11] L. Gerencsér, G. Kozmann, and Z. Vágó: SPSA for Non-Smooth Optimization with Application in ECG Analysis, in: Proc. of IEEE Conf. on Decision and Control, IEEE, Tampa, (1998), pp.3907-3908.

DOI: 10.1109/cdc.1998.761839

[12] L. Gerencsér, G. Kozmann, Z. Vágó, and K. Haraszti: The Use of the SPSA Method in ECG Analysis, in: Proc. of IEEE Conf. of the American Control, Anchorage, AK, (2002), pp.2583-2588.

[13] W. Gong, Z. Cai, and L. Jiang: Enhancing the performance of differential evolution using orthogonal design method, Applied Mathematics and Computation Vol. 206 (2008), pp.56-69.

DOI: 10.1016/j.amc.2008.08.053

[14] L. Holzleitner, and K. G. Mahmoud: Structural shape optimization using MSC/NASTRAN and sequential quadratic programming, Comput Struct Vol. 70 (1999), pp.487-514.

DOI: 10.1016/s0045-7949(98)00179-5

[15] M. H. Imam: Three dimensional shape optimization, Int J Numer Meth Engng Vol. 18 (1982), pp.661-673.

DOI: 10.1002/nme.1620180504

[16] D.A. Johannsen, E.J. Wegman, J.L. Solka, C.E. and Priebe: Simultaneous Selection of Features and Metric for Optimal Nearest Neighbor Classification, Communications in Statistics–Theory and Methods Vol. 33 (2004), pp.2137-2157.

DOI: 10.1081/sta-200026587

[17] G. Kharmanda, A. El Hami and N. Olhoff: Global Reliability-Based Design Optimization, International Journal of Nonconvex Optimization and its Applications Vol. 74 (2003), pp.255-274.

DOI: 10.1007/978-1-4613-0251-3_14

[18] N. L. Kleinman, S.D. Hill, and V. A. Ilenda: SPSA/SIMMOD Optimization of Air Traffic Delay Cost, in: Proc. of IEEE Int. Conf. on American Control, IEEE, Albuquerque, (1997), pp.1121-1125.

DOI: 10.1109/acc.1997.609707

[19] L. Lamberti: An efficient simulated annealing algorithm for design optimization of truss structures, Computers and Structures Vol. 86 (2008), p.1936-(1953).

DOI: 10.1016/j.compstruc.2008.02.004

[20] D. C. Lee, and J. I. Lee: An integrated design for double-layered structures, Finite Elements in Analysis and Design Vol. 41 (2004), pp.133-146.

DOI: 10.1016/j.finel.2004.05.002

[21] K. S. Lee, and Z. W. Geem: A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice, Comput. Methods Appl. Mech. Engrg. Vol. 194 (2005), pp.3902-3933.

DOI: 10.1016/j.cma.2004.09.007

[22] D. G. Luenberger: Introduction to Linear and Nonlinear Programming, Addison Wesley, (1973).

[23] Y. Maeda: Real-Time Control and Learning Using Neuro-Controller via Simultaneous Perturbation for Flexible Arm System, ACM Transactions on Modelling and Computer Simulation Vol. 15 (2005), p.74–107.

DOI: 10.1109/acc.2002.1025174

[24] J.L. Maryak, and J.C. Spall: Simultaneous Perturbation Optimization for Efficient Image Restoration, IEEE Transactions on Aerospace and Electronic Systems Vol. 41 (2005), pp.356-361.

DOI: 10.1109/taes.2005.1413767

[25] A. Mohsine, G. Kharmanda and A. El Hami: Improved method as a robust toll for reliability based design optimization, International Journal of Structural and Multidisciplinary Optimization Vol. 32 (2006), pp.203-213.

DOI: 10.1007/s00158-006-0013-2

[26] M. Pourazady, and Z. Fu: An integrated approach to structural shape optimization, Comput. Struct. Vol. 60 (1996), pp.279-289.

[27] M. Redhe, and L. Nilsson: Optimization of the new Saab 9-3 exposed to impact load using a space mapping technique, Struct. Multidisc Optim. Vol. 27 (2004), pp.411-420.

DOI: 10.1007/s00158-004-0396-x

[28] J. C. Spall: Multivariate Stochastic Approximation using a Simultaneous Perturbation Gradient Approximation, IEEE transactions on automatic control Vol. 37 (1992), pp.332-341.

DOI: 10.1109/9.119632

[29] J. C. Spall: An Overview of the Simultaneous Perturbation Method for Efficient Optimization, Johns Hopkins APL Technical Digest Vol. 19 (1998), pp.482-492.

[30] P. Sadegh, and J.C. Spall: Optimal Random Perturbations for Stochastic Approximation Using a Simultaneous Perturbation Gradient Approximation, Proceedings of the American Control Conference (1997) Albuquerque, NM, 3582-3586.

DOI: 10.1109/acc.1997.609490

[31] W. Tang, L. Tong, and Y. Gu: Improved genetic algorithm for design optimization of truss structures with sizing, shape and topology variables, Int. J. Numer. Meth. Engng Vol. 62 (2005), pp.1737-1762.

DOI: 10.1002/nme.1244

[32] P. Tanskanen: The evolutionary structural optimization method: theoretical aspects, Comput. Methods Appl. Mech. Engrg. Vol. 191 (2002), pp.5485-5498.

DOI: 10.1016/s0045-7825(02)00464-4

[33] L. Wang, K. Chen, Y. S. Ong (Eds). Advances in Natural Computation. Part III, Springer Science & Business Publisher, Changsha, China, (2005).

[34] Z. Xinchao: A perturbed particle swarm algorithm for numerical optimization, Applied Soft Computing Vol. 10 (2010), pp.119-124.

DOI: 10.1016/j.asoc.2009.06.010