Parallel Topology Optimization of Bi-Material Layout for Vibration Control in Plate Structures

Article Preview

Abstract:

This paper presents a parallel implementation process for the structural dynamic topology optimization problem. An energy flow analysis based topology optimization model is established for the objective of vibration control. The structural vibrations are excited by time-harmonic external mechanical loading with prescribed frequency and amplitude. Design variables are parameterized using Bi-material Solid Isotropic Material with Penalization (SIMP) models and Method of Moving Asymptotes (MMA) is applied for variable updating. A Parallel Finite Element (PFE) model is constructed by re-group the original finite element model. Each PFE will be computed by different processor, and then assembles together to get the global response. The efficiency and stability can be improved, which has been illustrated in the results discussion section in the end of the paper.

You might also be interested in these eBooks

Info:

Periodical:

Advanced Materials Research (Volumes 538-541)

Pages:

2586-2593

Citation:

Online since:

June 2012

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2012 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

[1] M.P. Bendsøe, N. Kikuchi, Generating optimal topologies in optimal design using a homogenization method, Comp. Meth. Appl. Mech. Engrg, vol. 71, p.197–224, 1988.

DOI: 10.1016/0045-7825(88)90086-2

Google Scholar

[2] M.P. Bendsøe, "Optimal shape design as a material distribution problem," Struct. Optim. Vol. 1, p.193–202, 1989.

Google Scholar

[3] G.I.N. Rozvany, A critical review of established methods of structural topology optimization, Structural and Multidisciplinary Optimization, vol. 37, p.217–237, 2009.

DOI: 10.1007/s00158-007-0217-0

Google Scholar

[4] Zhou M, Rozvany GIN (2001) On the validity of ESO type methods in topology optimization. Struct Multidisc Optim 21:80–83.

DOI: 10.1007/s001580050170

Google Scholar

[5] Sokolowski J, Zochowski A (1999) On the topological derivative in shape optimization. Siam J Control Optim 37:1251–1272

DOI: 10.1137/s0363012997323230

Google Scholar

[6] Wang MY, Wang XM, Guo DM (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192:227–246.

Google Scholar

[7] Allaire G, Jouve F, Toader AM (2004) Structural optimization using sensitivity analysis and a level-set method. J Comp Phys 104:363–393

DOI: 10.1016/j.jcp.2003.09.032

Google Scholar

[8] Hajela P, Lee E, Genetic algorithms in truss topology optimization. Int J Solids Struct 32:3341–3357, 1995.

DOI: 10.1016/0020-7683(94)00306-h

Google Scholar

[9] Sigmund O, A 99 line topology optimization code written in Matlab, Structural and Multidisciplinary Optimization, vol. 21(2), p.120–127, 2001.

DOI: 10.1007/s001580050176

Google Scholar

[10] Alberty J, Carstensen C, Funken S. Remarks around 50 lines of Matlab: short finite element implementation, Numerical Algorithms, vol. 20(2–3), p.117–137, 1999.

DOI: 10.1023/a:1019155918070

Google Scholar

[11] Alberty J, Carstensen C, Funken S, Klose R, Matlab implementation of the finite element method in elasticity, Computing vol. 69(3), p.239–263, 2002.

DOI: 10.1007/s00607-002-1459-8

Google Scholar

[12] Bendsøe M, Sigmund O, Topology Optimization. Theory, Methods and Applications, Springer, 2003.

Google Scholar

[13] Suresh K, A 199-line Matlab code for Pareto-optimal tracing in topology optimization, Structural and Multidisciplinary Optimization, Published online.

DOI: 10.1007/s00158-010-0534-6

Google Scholar

[14] Challis VJ, A discrete level-set topology optimization code written in Matlab, Structural and Multidisciplinary Optimization, vol. 41(3), p.453–464, 2010.

DOI: 10.1007/s00158-009-0430-0

Google Scholar

[15] Erik Andreassen, Anders Clausen, et al. Efficient topology optimization in MATLAB using 88 lines of code, Structural and Multidisciplinary Optimization, vol. 41(3), p.453–464, 2011.

DOI: 10.1007/s00158-010-0594-7

Google Scholar

[16] Yair Censor, Stavros A. ZeniosParallel Optimization- Theory, Algorithms, and Applications (Numerical Mathematics and Scientific Computation), Oxford University Press, USA, 1997.

Google Scholar

[17] Wang Jian, Xu Qiang, Chen Bingzhen et al. Parallel Optimization Scheme for Industrial Steam Cracking Process. Journal of Chemical Engineering of Japan, 36(1): 14-19, 2003.

DOI: 10.1252/jcej.36.14

Google Scholar

[18] Schutte JF, Reinbolt JA, Fregly BJ, Haftka RT, George AD. Parallel global optimization with particle swarm algorithm. International Journal for Numerical Methods in Engineering 2004; 61: 2296-2315.

DOI: 10.1002/nme.1149

Google Scholar

[19] Koh BI, Reinbolt JA, Fregly BJ, and George AD. Evaluation of parallel decomposition methods for biomechanical optimizations. Computer Methods in Biomechanics and Biomedical Engineering 2004; 7: 215-225.

DOI: 10.1080/10255840412331290398

Google Scholar

[20] Wu Changyou, Wang Fulin, Ju J inyan, A Multi-Point Parallel Optimization Method for Reducer Design. Mechanical Science and Technology for Aerospace Engineering, Vol. 18 No. 21, 2009.

Google Scholar

[21] Li Wen, Guo Li, Yuan Hongxing, Wei Yifang, Guan Hua, Parallel implementation and optimization of the sebvhos algorithm, Journal of Electronics, Vol. 28 Issue (3) :277-283, 2011.

DOI: 10.1007/s11767-011-0618-5

Google Scholar

[22] Nam Ho Kim, Jun Dong, Kyung Kook Choi, Energy flow analysis and design sensitivity of structural problems at high frequencies, Journal of sound and vibration, vol. 269, pp.213-250, 2004.

DOI: 10.1016/s0022-460x(03)00070-1

Google Scholar

[23] Seonho Cho, Chan-Young Park, et al. Topology design optimization of structures at high frequencies using power flow analysis, Journal of sound and vibration, vol. 298, pp.206-220, (2006)

DOI: 10.1016/j.jsv.2006.05.015

Google Scholar

[24] Seonho Cho, Seung-Hyun Ha, et al. Topological shape optimization of power flow problems at high frequencies using level set approach, International Journal of Solids and Structures 43172-192, (2006)

DOI: 10.1016/j.ijsolstr.2005.04.033

Google Scholar

[25] K. Svanberg, The method of moving asymptotes: a new method for structural optimization, International Journal for Numerical Method in Engineering, vol. 24, p.359–373, 1987.

DOI: 10.1002/nme.1620240207

Google Scholar

[26] Krister Svanberg. A class of globally convergent optimization methods based on conservative convex separable approximzations. SIAM Journal on Optimization, 12(2):555–573, 2002.

DOI: 10.1137/s1052623499362822

Google Scholar

[27] Sigmund O. Morphology-based black and white filters for topology optimization. Struct Multidisc Optim 33(4–5): 401–424, 2007.

DOI: 10.1007/s00158-006-0087-x

Google Scholar