A level set method for structural topology optimization. (English) Zbl 1083.74573

Summary: This paper presents a new approach to structural topology optimization. We represent the structural boundary by a level set model that is embedded in a scalar function of a higher dimension. Such level set models are flexible in handling complex topological changes and are concise in describing the boundary shape of the structure. Furthermore, a well-founded mathematical procedure leads to a numerical algorithm that describes a structural optimization as a sequence of motions of the implicit boundaries converging to an optimum solution and satisfying specified constraints. The result is a 3D topology optimization technique that demonstrates outstanding flexibility of handling topological changes, fidelity of boundary representation and degree of automation. We have implemented the algorithm with the use of several robust and efficient numerical techniques of level set methods. The benefit and the advantages of the proposed method are illustrated with several 2D examples that are widely used in the recent literature on topology optimization, especially in the homogenization-based methods.


74P15 Topological methods for optimization problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)


Full Text: DOI


[1] Rozvany, G.I.N., Structural design via optimality criteria, (1988), Kluwer Dordrecht · Zbl 1274.74383
[2] Bendsoe, M.P.; Kikuchi, N., Generating optimal topologies in structural design using a homogenisation method, Computer methods in applied mechanics and engineering, 71, 197-224, (1998)
[3] Suzuki, K.; Kikuchi, N., A homogenization method for shape and topology optimization, Computer methods in applied mechanics and engineering, 93, 291-381, (1991) · Zbl 0850.73195
[4] Diaz, A.R.; Bendoe, M.P., Shape optimization of structures for multiple loading conditions using a homogenization method, Structural optimization, 4, 17-22, (1992)
[5] Allaire, G.; Kohn, R.V., Topology optimization and optimal shape design using homogenization, (), 207-218
[6] Bendsoe, M.P.; Haber, R., The michell layout problem as a low volume fraction limit of the homogenization method for topology design: an asymoptotic study, Structural optimization, 6, 63-267, (1993)
[7] Allaire, G., The homogenization method for topology and shape optimization, (), 101-133 · Zbl 0885.73049
[8] Bendsoe, M.P., Optimization of structural topology, shape and material, (1997), Springer Berlin
[9] Bendsoe, M.P., Optimal shape design as a material distribution problem, Structural optimization, 1, 193-202, (1989)
[10] Mlejnek, H.P., Some aspects of the genesis of structures, Structural optimization, 5, 64-69, (1992)
[11] Bendsoe, M.P.; Sigmund, O., Material interpolations in topology optimization, Archive of applied mechanics, 69, 635-654, (1999) · Zbl 0957.74037
[12] Xie, Y.M.; Steven, G.P., A simple evolutionary procedure for structural optimization, Computers and structures, 49, 885-896, (1993)
[13] Chu, D.N.; Xie, Y.M.; Hira, A.; Steven, G.P., On various aspects of evolutionary structural optimization for problems with stiffness constraints, Finite elements in analysis and design, 24, 197-212, (1997) · Zbl 0914.73037
[14] Reynolds, D.; McConnachie, J.; Bettess, P.; Christie, W.C.; Bull, J.W., Reverse adaptivity–A new evolutionary tool for structural optimization, International journal of numerical methods in engineering, 45, 529-552, (1999) · Zbl 0949.74053
[15] Eschenauer, H.A.; Kobelev, H.A.; Schumacher, A., Bubble method for topology and shape optimization of structures, Structural optimization, 8, 142-151, (1994)
[16] Eschenauer, H.A.; Schumacher, A., Topology and shape optimization procedures using hole positioning criteria, (), 135-196 · Zbl 0885.73050
[17] Sethian, J.A.; Wiegmann, A., Structural boundary design via level set and immersed interface methods, Journal of computational physics, 163, 2, 489-528, (2000) · Zbl 0994.74082
[18] Sethian, J.A., Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science, (1999), Cambridge University Press · Zbl 0973.76003
[19] Osher, S.; Sethian, J.A., Front propagating with curvature-dependent speed: algorithms based on hamilton – jacobi formulations, Journal of computational physics, 79, 12-49, (1988) · Zbl 0659.65132
[20] Osher, S.; Fedkiw, R., Level set methods: an overview and some recent results, Journal of computational physics, 169, 475-502, (2001) · Zbl 0988.65093
[21] Breen, D.; Whitaker, R., A level set approach for the metamorphosis of solid models, IEEE transactions on visualization and computer graphics, 7, 2, 173-192, (2001)
[22] Rozvany, G., Aims, scope, methods, history and unified terminology of computer aided topology optimization in structural mechanics, Structural and multidisciplinary optimization, 21, 90-108, (2001)
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