### Abstract

This paper introduces a new implicit function based method for topology optimization that can: obtain solutions with smooth boundaries, be solved using standard mathematical programming methods and reduce the number of design variables. Using implicit functions for topology optimization is attractive because the solutions have clearly defined, smooth boundaries. Most current methods use the zero level-set of the implicit function to define the boundary. The implicit function is then modified during optimization to move the boundary location and connectivity. The new approach proposed in this paper abandons the zero level-set idea and instead uses a fixed signed-distance implicit function. The definition of the boundary from the fixed implicit function is then modified during optimization. This is achieved by using a cutting surface and defining the boundary as the intersection of the cutting surface and signed-distance function. The cutting surface is parameterized and the parameters become the design variables during optimization. Thus, the optimization problem can be solved using mathematical programming and the number of parameters used to define the cutting surface is less than the number of elements in the analysis mesh. The new method is demonstrated using minimization of compliance, minimization of volume and complaint mechanism problems. The results show that the method can obtain good solutions to well-known problems with smooth, clearly defined boundaries and that this can be achieved using significantly fewer design variables compared with element-based methods.

Original language | English |
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Title of host publication | ECCOMAS 2016 |

Subtitle of host publication | VII European Congress on Computational Methods in Applied Sciences and Engineering |

Editors | M. Papadrakakis, V. Papadopoulos, G. Stefanou, V. Plevris |

Publisher | Eccomas |

Pages | 3553-3565 |

Number of pages | 12 |

ISBN (Print) | 978-618-82844-0-1 |

Publication status | Published - 5 Jun 2016 |

Event | ECCOMAS Congress 2016: VII European Congress on Computational Methods in Applied Sciences and Engineering - Crete, Greece Duration: 5 Jun 2016 → 10 Jun 2016 https://www.eccomas2016.org |

### Conference

Conference | ECCOMAS Congress 2016 |
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Abbreviated title | ECCOMAS 2016 |

Country | Greece |

Period | 5/06/16 → 10/06/16 |

Internet address |

### Keywords

- Topology optimization
- implicit functions
- mathematical programming
- design space reduction

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## Cite this

Dunning, P. D. (2016). Topology optimisation with an implicit function and parameterized cutting surface. In M. Papadrakakis, V. Papadopoulos, G. Stefanou, & V. Plevris (Eds.),

*ECCOMAS 2016: VII European Congress on Computational Methods in Applied Sciences and Engineering*(pp. 3553-3565). Eccomas. https://www.eccomas2016.org/proceedings/pdf/7461.pdf