Topology optimization with an implicit function and parameterized cutting surface

Peter D. Dunning*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

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 languageEnglish
Title of host publicationECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering
EditorsM. Papadrakakis, V. Papadopoulos, G. Stefanou, V. Plevris
PublisherNational Technical University of Athens
Pages3553-3564
Number of pages12
Volume2
ISBN (Electronic)9786188284401
Publication statusPublished - 2016
Event7th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS Congress 2016 - Crete, Greece
Duration: 5 Jun 201610 Jun 2016

Conference

Conference7th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS Congress 2016
CountryGreece
CityCrete
Period5/06/1610/06/16

Fingerprint

Implicit Function
Topology Optimization
Shape optimization
Zero set
Mathematical programming
Distance Function
Signed
Mathematical Programming
Level Set
Optimization
Compliance
Connectivity
Intersection
Mesh
Optimization Problem

Keywords

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

ASJC Scopus subject areas

  • Artificial Intelligence
  • Applied Mathematics

Cite this

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

ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering. ed. / M. Papadrakakis; V. Papadopoulos; G. Stefanou; V. Plevris. Vol. 2 National Technical University of Athens, 2016. p. 3553-3564.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Dunning, PD 2016, Topology optimization with an implicit function and parameterized cutting surface. in M Papadrakakis, V Papadopoulos, G Stefanou & V Plevris (eds), 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.
Dunning PD. Topology optimization with an implicit function and parameterized cutting surface. In Papadrakakis M, Papadopoulos V, Stefanou G, Plevris V, editors, ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering. Vol. 2. National Technical University of Athens. 2016. p. 3553-3564
Dunning, Peter D. / Topology optimization with an implicit function and parameterized cutting surface. ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering. editor / M. Papadrakakis ; V. Papadopoulos ; G. Stefanou ; V. Plevris. Vol. 2 National Technical University of Athens, 2016. pp. 3553-3564
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