### 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 Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering |

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

Publisher | National Technical University of Athens |

Pages | 3553-3564 |

Number of pages | 12 |

Volume | 2 |

ISBN (Electronic) | 9786188284401 |

Publication status | Published - 2016 |

Event | 7th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS Congress 2016 - Crete, Greece Duration: 5 Jun 2016 → 10 Jun 2016 |

### Conference

Conference | 7th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS Congress 2016 |
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Country | Greece |

City | Crete |

Period | 5/06/16 → 10/06/16 |

### Fingerprint

### Keywords

- Design space reduction
- Implicit functions
- Mathematical programming
- Topology optimization

### ASJC Scopus subject areas

- Artificial Intelligence
- Applied Mathematics

### Cite this

*ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering*(Vol. 2, pp. 3553-3564). National Technical University of Athens.

**Topology optimization with an implicit function and parameterized cutting surface.** / Dunning, Peter D.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering.*vol. 2, National Technical University of Athens, pp. 3553-3564, 7th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS Congress 2016, Crete, Greece, 5/06/16.

}

TY - GEN

T1 - Topology optimization with an implicit function and parameterized cutting surface

AU - Dunning, Peter D.

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Design space reduction

KW - Implicit functions

KW - Mathematical programming

KW - Topology optimization

UR - http://www.scopus.com/inward/record.url?scp=84995480000&partnerID=8YFLogxK

M3 - Conference contribution

VL - 2

SP - 3553

EP - 3564

BT - ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering

A2 - Papadrakakis, M.

A2 - Papadopoulos, V.

A2 - Stefanou, G.

A2 - Plevris, V.

PB - National Technical University of Athens

ER -