Abstract
This paper presents a compact Matlab implementation of the level-set method for topology optimization. The code can be used to minimize the compliance of a statically loaded structure. Simple code modifications to extend the code for different and multiple load cases are given. The code is inspired by a Matlab implementation of the solid isotropic material with penalization (SIMP) method for topology optimization (Sigmund, Struct Multidiscipl Optim 21:120–127, 2001). Including the finite element solver and comments, the code is 129 lines long. The code is intended for educational purposes, and in particular it could be used alongside the Matlab implementation of the SIMP method for topology optimization to demonstrate the similarities and differences between the two approaches.
References
Allaire G, Pantz O (2006) Structural optimization with FreeFem+ +. Struct Multidiscipl Optim 32:173–181
Allaire G, Jouve F, Toader A-M (2004) Structural optimization using sensitivity analysis and a level-set method. J Comput Phys 194:363–393
Allaire G, de Gournay F, Jouve F, Toader A-M (2005) Structural optimization using topological and shape sensitivity via a level set method. Control Cybern 34(1):59–80
Bendsøe MP, Sigmund O (2004) Topology optimization: theory, methods and applications, 2nd edn. Springer, Berlin
Burger M, Hackl B, Ring W (2004) Incorporating topological derivatives into level set methods. J Comput Phys 194:344–362
Challis VJ, Guest JK (2009) Level-set topology optimization of fluids in Stokes flow. Int J Numer Methods Eng 79:1284–1308
Challis VJ, Roberts AP, Wilkins AH (2008a) Design of three dimensional isotropic microstructures for maximized stiffness and conductivity. Int J Solids Struct 45:4130–4146
Challis VJ, Roberts AP, Wilkins AH (2008b) Fracture resistance via topology optimization. Struct Multidiscipl Optim 36:263–271
de Gournay F, Allaire G, Jouve F (2008) Shape and topology optimization of the robust compliance via the level set method. ESAIM COCV 14(1):43–70
Luo J, Luo Z, Chen L, Tong L, Wang MY (2008a) A semi-implicit level set method for structural shape and topology optimization. J Comput Phys 227:5561–5581
Luo J, Luo Z, Chen S, Tong L, Wang MY (2008b) A new level set method for systematic design of hinge-free compliant mechanisms. Comput Methods Appl Mech Eng 198:318–331
Osher S, Fedkiw R (2002) Level set methods and dynamic implicit surfaces. Applied mathematical sciences, vol 153. Springer, New York
Osher SJ, Santosa F (2001) Level set methods for optimization problems involving geometry and constraints I. Frequencies of a two-density inhomogeneous drum. J Comput Phys 171:272–288
Osher SJ, Sethian JA (1988) Fronts propagating with curvature dependent speed: algorithms based on the Hamilton–Jacobi formulation. J Comput Phys 79:12–49
Sethian JA (1999) Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision and materials science. Cambridge Monographs on Applied and Computational Mathematics, vol 3, 2nd edn. Cambridge University Press, Cambridge
Sethian JA, Wiegmann A (2000) Structural boundary design via level set and immersed interface methods. J Comput Phys 163(2):489–528
Sigmund O (2001) A 99 line topology optimization code written in Matlab. Struct Multidiscipl Optim 21:120–127
Wang MY, Wang X, Guo D (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192:227–246
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Challis, V.J. A discrete level-set topology optimization code written in Matlab. Struct Multidisc Optim 41, 453–464 (2010). https://doi.org/10.1007/s00158-009-0430-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00158-009-0430-0