AN OVERVIEW ON TOPOLOGY OPTIMIZATION METHODS EMPLOYED IN STRUCTURAL ENGINEERING

Yıl 2019, , 159 - 175, 31.12.2019

Osman Yuksel

https://doi.org/10.34186/klujes.606666

Cited By: 5

Öz

Any mechanical performance measure of a structure is
strongly related with its topology. Size and shape optimization cannot give the
best structural performance, since these methods cannot change the
structure’s topology. Hence, topology optimization should be employed to obtain
the best performance. In this paper, a review of topology optimization is
provided. At first, the general topology optimization problem is defined. Then,
modern topology optimization methods are presented and discussed. 

Anahtar Kelimeler

topology optimization, structural optimization, optimum structural design, review

AN OVERVIEW ON TOPOLOGY OPTIMIZATION METHODS EMPLOYED IN STRUCTURAL ENGINEERING

Öz

Bir yapının gösterdiği mekanik performans, o
yapının topolojisi ile çok yakından alakalıdır. Boyut ve şekil eniyilemeleri
sonucunda, yapının topolojisinde bir değişiklik olmadığı için, en iyi
performans elde edilemez. Netice itibariyle, en iyi performansın elde
edilebilmesi için topoloji eniyilemesinden faydalanılması gerekmektedir. Bu
çalışmada, topoloji eniyilemesi yöntemleri hakkında bir derleme sunulmuştur.
İlk olarak, genel topolji eniyilemesi problemi tanıtılmış, ardından modern
topoloji eniyilemesi yöntemleri tartışılmıştır.

Anahtar Kelimeler

topoloji eniyilemesi, yapısal eniyileme, eniyilenmiş tasarım, derleme

Kaynakça

• [1] M. P. Bendsoe and O. Sigmund, Topology Optimization: Theory, Methods, and Applications, Berlin: Springer, 2004.
• [2] G. I. N. Rozvany, Topology Optimization In Structural Mechanics, Springer, 2014.
• [3] P. W. Christensen and A. Klarbring, An Introduction to Structural Optimization, Springer, 2009.
• [4] H. A. Eschenauer and N. Olhoff, "Topology optimization of continuum structures," Applied Mechanics Reviews, vol. 54, no. 4, pp. 331-390, 2001.
• [5] G. I. N. Rozvany, M. P. Bendsoe and U. Kirsch, "Layout optimization of structures," Applied Mechanics Reviews, vol. 48, no. 2, pp. 41-119, 1995.
• [6] O. Sigmund and K. Maute, "Topology optimization approaches," Structural and Multidisciplinary Optimization, vol. 48, no. 6, pp. 1031-1055, 2013.
• [7] O. Yüksel, "Shape and Topology Optimization of Inertial Amplification Induced Phononic Band Gap Structures," Boğaziçi University, Istanbul, 2018.
• [8] O. Yuksel and C. Yilmaz, "Size and topology optimization of inertial amplification induced phononic band gap structures," in Proceedings of the ASME International Mechanical Engineering Congress and Exposition, Tampa, Florida, USA, 2017.
• [9] O. Yuksel and C. Yilmaz, "Shape optimization of phononic band gap structures incorporating inertial amplification mechanisms," Journal of Sound and Vibration, vol. 355, pp. 232-245, 2015.
• [10] A. G. M. Michell, "LVIII. The limits of economy of material in frame-structures," The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, vol. 8, no. 47, pp. 589-597, 1904.
• [11] W. S. Hemp, Optimum Structures, Clarendon Press, 1973.
• [12] D. J. Munk, G. A. Vio and G. P. Steven, "Topology and shape optimization methods using evolutionary algorithms: a review," Structural and Multidisciplinary Optimization, vol. 52, no. 3, pp. 613-631, 2015.
• [13] U. Kirsch, Optimum Structural Design: Concepts, Methods, and Applications, McGraw-Hill Companies, 1981.
• [14] U. Kirsch, "Optimal topologies of structures," Applied Mechanics Reviews, vol. 42, no. 8, pp. 223-239, 1989.
• [15] G. I. N. Rozvany, "Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics," Structural and Multidisciplinary Optimization, vol. 21, no. 2, pp. 90-108, 2001.
• [16] J. D. Deaton and R. V. Grandhi, "A survey of structural and multidisciplinary continuum topology optimization: Post 2000," Structural and Multidisciplinary Optimization, vol. 49, no. 1, pp. 1-38, 2014.
• [17] B. Hassani and E. Hinton, "A review of homogenization and topology opimization II — Analytical and numerical solution of homogenization equations," Computers & Structures, vol. 69, no. 6, pp. 719-738, 1998.
• [18] B. Hassani and E. Hinton, "A review of homogenization and topology optimization I — Homogenization theory for media with periodic structure," Computers & Structures , vol. 69, no. 6, pp. 707-717, 1998.
• [19] M. P. Bendsoe and N. Kikuchi, "Generating optimal topologies in structural design using a homogenization method," Computer Methods in Applied Mechanics and Engineering, vol. 71, no. 2, pp. 197-224, 1988.
• [20] K. Suzuki and N. Kikuchi, "A homogenization method for shape and topology optimization," Computer Methods in Applied Mechanics and Engineering, vol. 93, no. 3, pp. 291-318, 1991.
• [21] B. Hassani and E. Hinton, Homogenization and Structural Topology Optimization, London: Springer-Verlag, 1999.
• [22] M. P. Bendsoe, "Optimal shape design as a material distribution problem," Structural Optimization, vol. 1, no. 4, pp. 193-202, 1989.
• [23] G. I. N. Rozvany, M. Zhou and T. Birker, "Generalized shape optimization without homogenization," Structural Optimization, vol. 4, no. 3, pp. 250-252, 1992.
• [24] M. Stolpe and K. Svanberg, "An alternative interpolation scheme for minimum compliance topology optimization," Structural and Multidisciplinary Optimization, vol. 22, no. 2, pp. 116-124, 2001.
• [25] K. Schittkowski, C. Zillober and R. Zotemantel, "Numerical comparison of nonlinear programming algorithms for structural optimization," Structural Optimization, vol. 7, no. 1-2, pp. 1-19, 1994.
• [26] O. Sigmund and J. Petersson, "Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima," Structural Optimization, vol. 16, no. 1, pp. 68-75, 1998.
• [27] O. Sigmund, "On the design of compliant mechanisms using topology optimization," Mechanics of Structures and Machines, vol. 25, no. 4, pp. 493-524, 1997.
• [28] B. Bourdin, "Filters in topology optimization," International Journal for Numerical Methods in Engineering, vol. 50, no. 9, pp. 2143-2158, 2001.
• [29] S. Xu, Y. Cai and G. Cheng, "Volume preserving nonlinear density filter based on heaviside functions," Structural and Multidisciplinary Optimization, vol. 41, no. 4, pp. 495-505, 2010.
• [30] O. Sigmund and K. Maute, "Sensitivity filtering from a continuum mechanics perspective," Structural and Multidisciplinary Optimization, vol. 46, no. 4, pp. 471-475, 2012.
• [31] O. Sigmund, "On the usefulness of non-gradient approaches in topology optimization," Structural and Multidisciplinary Optimization, vol. 43, no. 5, pp. 589-596, 2011.
• [32] X. Huang and M. Xie, Evolutionary Topology Optimization of Continuum Structures: Methods and Applications, John Wiley & Sons, 2010.
• [33] Y. M. Xie and G. P. Steven, "A simple evolutionary procedure for structural optimization," Computers & Structures, vol. 49, no. 5, pp. 885-896, 1993.
• [34] O. M. Querin, G. P. Steven and Y. M. Xie, "Evolutionary structural optimisation (ESO) using a bidirectional algorithm," Engineering Computations, vol. 15, no. 8, pp. 1031-1048, 1998.
• [35] G. I. N. Rozvany, "A critical review of established methods of structural topology optimization," Structural and Multidisciplinary Optimization, vol. 37, no. 3, pp. 217-237, 2009.
• [36] G. I. N. Rozvany, "Stress ratio and compliance based methods in topology optimization – a critical review," Structural and Multidisciplinary Optimization, vol. 21, no. 2, pp. 109-119, 2001.
• [37] M. Zhou and G. I. N. Rozvany, "On the validity of ESO type methods in topology optimization," Structural and Multidisciplinary Optimization, vol. 21, no. 1, pp. 80-83, 2001.
• [38] X. Huang and Y. M. Xie, "Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials," Computational Mechanics, vol. 43, no. 3, pp. 393-401, 2009.
• [39] X. Huang and Y. M. Xie, "A further review of ESO type methods for topology optimization," Structural and Multidisciplinary Optimization, vol. 41, no. 5, pp. 671-683, 2010.
• [40] J. A. Sethian, Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science, Cambridge University Press, 1999.
• [41] M. Y. Wang, X. Wang and D. Guo, "A level set method for structural topology optimization," Computer Methods in Applied Mechanics and Engineering, vol. 192, no. 1, pp. 227-246, 2003.
• [42] G. Allaire, F. Jouve and A. M. Toader, "Structural optimization using sensitivity analysis and a level-set method," Journal of Computational Physics, vol. 194, no. 1, pp. 363-393, 2004.
• [43] N. P. Van Dijk, K. Maute, M. Langelaar and F. Van Keulen, "Level-set methods for structural topology optimization: a review," Structural and Multidisciplinary Optimization, vol. 48, no. 3, pp. 437-472, 2013.