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**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.

### MSC:

74P15 | Topological methods for optimization problems in solid mechanics |

74S30 | Other numerical methods in solid mechanics (MSC2010) |

### Keywords:

implicit moving boundary### Software:

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\textit{M. Y. Wang} et al., Comput. Methods Appl. Mech. Eng. 192, No. 1--2, 227--246 (2003; Zbl 1083.74573)

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### References:

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