Performance of the Evolutionary Structural Optimization for Material with Elasto-Plastic Behavior

Document Type : Research Paper

Authors

ferdowsi university

Abstract

Topology optimization methods enable designers to find the best structural layout for required structural performances. Most papers in this area have been concerned with the optimization of structures with linear material. However, there are several structures involving nonlinear material.Evolutionary structural optimization (ESO) is based on the simple concept of systematically removing inefficient material from the structure after each finite element analysis, so that the resulting design is gradually evolved to an optimum. This method has been successfully applied to optimum material distribution problems for continuum structures and has been extended to a wide range of structural optimization problems.
This paper is concerned with optimization of elastic and elasto-plastic bodies, based on the von Misses stress criterion using two method.Several examples are presented to verify the proposed optimization methods. Results are compared for these two criteria and against elastic and elasto-plastic material and also with that of the adaptive method. It is concluded that for elastic and elasto-plastic bodies, the behavior of the both criteria is more or less the same and they can be used alternatively.

Keywords


[01] J. S. Arora,(2004), Introduction to optimum design (2nd Ed.), Elsevier
[02] O. M. Querin,(1997), Evolutionary Structural Optimisation: Stress Based Formulation and Implementation,
PhD Thesis, Department of Aeronautical Engineering, University of Sydney, Sydney, Australia
[03] O. Sigmund, K. Maute,(2013), “Topology optimization approaches”, Structural and Multidisciplinary
Optimization, Vol. 48, No. 6, pp. 1031-1055
[04] O. Sigmund, (2011), “On the usefulness of non-gradient approaches in topology optimization”, Structural
and Multidisciplinary Optimization, Vol. 43, No. 5, pp. 589-596
[05] M. Kociecki, H. Adeli,(2014), “Two-phase genetic algorithm for topology optimization of free-form steel
space-frame roof structures with complex curvatures”, Engineering Applications of Artificial
Intelligence, Vol. 32, No. 0, pp. 218-227
[06] M. J. Jakiela, C. Chapman, J. Duda, A. Adewuya, K. Saitou,(2000), “Continuum structural topology design
with genetic algorithms”, Computer Methods in Applied Mechanics and Engineering, Vol. 186, No.
2–4, pp. 339-356
[07] R. Balamurugan, C. Ramakrishnan, N. Swaminathan,(2011), “A two phase approach based on skeleton
convergence and geometric variables for topology optimization using genetic algorithm”, Structural
and multidisciplinary optimization, Vol. 43, No. 3, pp. 381-404
[08] R. Balamurugan, C. V. Ramakrishnan, N. Singh,(2008), “Performance evaluation of a two stage adaptive
genetic algorithm (TSAGA) in structural topology optimization”, Applied Soft Computing, Vol. 8,
No. 4, pp. 1607-1624
[09] G.-C. Luh, C.-H. Chueh,(2009), “Multi-modal topological optimization of structure using immune
algorithm”, Computer Methods in Applied Mechanics and Engineering, Vol. 193, No. 36–38, pp.
4035-4055
[10] G.-C. Luh, C.-Y. Lin,(2009), “Structural topology optimization using ant colony optimization algorithm”,
Applied Soft Computing, Vol. 9, No. 4, pp. 1343-1353
[11] A. Kaveh, B. Hassani, S. Shojaee, S. M. Tavakkoli,(2008), “Structural topology optimization using ant
colony methodology”, Engineering Structures, Vol. 30, pp. 2559–2565
[12] G.-C. Luh, C.-Y. Lin, Y.-S. Lin,(2011), “A binary particle swarm optimization for continuum structural
topology optimization”, Applied Soft Computing, Vol. 11, No. 2, pp. 2833-2844
[13] F. Kolahan, M. H. Abolbashari, S. Mohitzadeh,(2008), “Simulated Annealing Application for Structural
Optimization”, Internationla Journal of Mechanical Systems Science and Engineering, Vol. 1, No. 4,
pp. 186-189
[14] P. Y. Shim, S. Manoochehri,(1997), “Generating Optimal Configurations in Structural Design Using
Simultaed Annealing”, International Journal for Numerical Methods in Engineering, Vol. 40, No. 6,
pp. 1053-1069
پایان نامه ،)GESO( 15 [ لت ناج عیداللهی اودر ی،) 1389 (، بهینه سووازی ت املی سووازه ها با اسووتفاده از عملگرهای الگوریتم ینتیز [
کارشناسی ارشد، دانشگاه فردوسی مشهد
[16] G. Steven, Y. Xie,(1993), “Evolutionary structural optimization with FEA”, Computational mechanics, Vol.
1, pp. 27-34
[17] Y. M. Xie, G. P. Steven,(1992), “Shape and layout optimization via an evolutionary procedure”, Proceeding
of International Conference on Computational Engineering Scienc, Hong Kong, pp. 421
[18] Y. M. Xie, G. P. Steven,(1993), “A simple evolutionary procedure for structural optimization”, Computers
& Structures, Vol. 49, No. 5, pp. 885-896
[19] Y. M. Xie, G. P. Steven, (1997),Basic evolutionary structural optimization: Springer
[20] E. Hinton, J. Sienz,(1995), “Fully stressed topology design of structures using an evolutionary procedure”,
Engineering Computations, Vol. 12, pp. 229-244
[21] Y. M. Xie, G. P. Steven,(1994), “Optimal design of multiple load case structures using an evolutionary
procedure”, Engineering Computations, Vol. 11, No. 4, pp. 295 - 302
[22] Y. M. Xie, G. P. Steven,(1996), “Evolutionary structural optimization for dynamic problems”, Computers
and Structures, Vol. 58, No. 6, pp. 1067-1073
[23] A. Rispler, G. Steven,(1995), “Shape optimisation of metallic inserts in composite bolted joints”, Second
Pacific International Conference on Aerospace and Technology; Sixth Australian Aeronautical
Conference, Barton, A.C.T: Institution of Engineers, Australia, pp. 225-229
[24] G. P. Steven, O. M. Querin, Y. M. Xie,(1995), “Analysis of Aircraft Patch Repairs Using Evolutionary
Structural Optimisation”, International Aerospace Congress; Second Pacific International
Conference on Aerospace and Technology; Sixth Australian Aeronautical Conference. Barton,
A.C.T., Institution of Engineers, Australia, pp. 683-688
[25] D. Chu, Y. Xie, A. Hira, G. Steven,(1996), “Evolutionary structural optimization for problems with stiffness
constraints”, Finite Elements in Analysis and Design, Vol. 21, No. 4, pp. 239-251
[26] D. Manickarajah, Y. M. Xie, G. P. Steven,(1995), A simple method for the optimization of columns, frames
and plates against buckling, in Structural Stability and Design, A.A Balkema Publishers, Rotterdam,
pp. 175-180
[27] G. P. Steven, O. M. Querin, Y. M. Xie,(1995), “Multiple Constraint Environments for Evolutionary Structural
Optimisation”, Proceeding of the First World Congress on Structural and Multidisciplinary
Optimization, Goslar, Germany, May 28 - June 2., pp. 213-218
[28] C. Zhao, G. P. Steven, Y. M. Xie, “Evolutionary natural frequency optimization of thin plate bending
vibration problems”, Struct Multidisc Optim, Vol. 11, pp. 244-251
[29] C. B. Zhao, G. P. Steven, Y. M. Xie,(1997), “Evolutionary optimization of maximizing the difference
between two natural frequencies of a vibrating structure”, Structural Optimization, Vol. 13, pp. 148-
154
[30] O. M. Querin, G. P. Steven, Y. M. Xie,(1996), “Topology optimisation of structures with material and
geometric non-linearities”, Multidisciplinary Analysis Optimization Conferences in: 6th Symposium
on Multidisciplinary Analysis and Optimization, Eds.: American Institute of Aeronautics and
Astronautics
[31] X. Huang, Y. M. Xie,(2007), “Bidirectional Evolutionary Topology Optimization for Structures with
Geometrical and Material Nonlinearities”, AIAA JOURNAL, Vol. 45, No. 1, pp. 308-313
[32] X. Huang, Y. M. Xie, M. C. Burry,(2006), “A new algorithm for Bi-Directional Evolutionary Structural
Optimization”, JSME International Journal, Series C, Vol. 49, No. 4, pp. 1091-1099
[33] M. M. Neves, H. Rodrigues, J. M. Guedes,(1995), “Generalized topology design of structures with a buckling
load criterion”, Structural optimization, Vol. 10, No. 2, pp. 71-78
[34] J. E. Taylor, J. Logo,(1993), “Analysis and Design of Elastic/Softening Truss Structures Based on a Mixed-
Form Extremum Principle”, NATO ASI Series in: G. I. N. Rozvany, Optimization of Large
Structural Systems, Eds., pp. 683-695
[35] J. E. Taylor,(1993), “Truss Topology Design for Elastic/Softening Materials”, NATO ASI Series in: M.
Bendsøe, C. M تSoares, Eds., Topology Design of Structures, pp. 451-467
[36] K. Yuge, N. Kikuchi,(1995), “Optimization of a frame structure subjected to a plastic deformation”,
Structural optimization, Vol. 10, No. 3-4, pp. 197-208
[37] S. Huang,(1995), Continuum theory of plasticity: John Wiley & Sons ت
[38] Q. Li, G. P. Steven, Y. M. Xie,(2001), “A simple checkerboard suppression algorithm for evolutionary
structural optimization”, Struct Multidisc Optim, Vol. 22, pp. 230–239
[39]M تH. Abolbashari, M. Khajooei-Gharaei,(2011), “An improved evolutionary structural optimization method
for continuum structures of elastic and elasto-plastic bodies”, International Conference on
Mechanical and Aerospace Engineering (CMAE), India, New Delhi, pp. 435-439
[40] M. H. Abolbashari, M. Khajooei-Gharaei, H. R. Ghaffarianjam, M. R. Mahpeykar,(2010), “Topology
optimization of continuum structures with elasto-plastic behavior using evolutionary structural
optimization based on stress and stiffness criteria”, 6th Australasian Congress on Applied Mechanics,
ACAM 6, Perth, Australia
[41] ANSYS(R), Swanson Analysis System, Inc ت
[42] K. Maute, S. Schwarz, E. Ramm,(1998), “Adaptive topology optimization of elastoplastic structures”,
Structural Optimization, Vol. 15, pp. 81-91
[43] MATLAB,(2002), The MathWorks, Inc ت
[44] Q. Li, G. P. Steven, Y. M. Xie,(1999), “On equivalence between stress criterion and stiffness criterion in
evolutionary structural optimization”, Structural Optimization, Vol. 18, pp. 67-73