Design parameterization for topology optimization by intersection of an implicit function

Research output: Contribution to journalArticle

8 Citations (Scopus)
5 Downloads (Pure)

Abstract

This paper introduces a new approach to topology optimization where the
structural boundary is defined by the intersection of an implicit signed-distance
function and a cutting surface. The cutting surface is discretized using finite
element shape-function polynomials and the nodal values become the design
variables during optimization. Thus, the design parameterization is separated
from the analysis discretization, which enables a reduction in the number
of design variables, compared with methods that use element-wise variables.
The proposed method can obtain solutions with smooth boundaries and the
parameterization allows solution by standard optimization methods. Several
2D and 3D examples are used to demonstrate the effectiveness of the method,
including minimization of compliance 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
Pages (from-to)993-1011
Number of pages19
JournalComputer Methods in Applied Mechanics and Engineering
Volume317
Early online date17 Jan 2017
DOIs
Publication statusPublished - 15 Apr 2017

Fingerprint

Shape optimization
Parameterization
parameterization
intersections
topology
optimization
shape functions
Polynomials
polynomials

Keywords

  • topology optimisation
  • implicit function
  • mathematical programming

Cite this

@article{cf85dd7e7ef4401093b160f1a3b1517b,
title = "Design parameterization for topology optimization by intersection of an implicit function",
abstract = "This paper introduces a new approach to topology optimization where thestructural boundary is defined by the intersection of an implicit signed-distancefunction and a cutting surface. The cutting surface is discretized using finiteelement shape-function polynomials and the nodal values become the designvariables during optimization. Thus, the design parameterization is separatedfrom the analysis discretization, which enables a reduction in the numberof design variables, compared with methods that use element-wise variables.The proposed method can obtain solutions with smooth boundaries and theparameterization allows solution by standard optimization methods. Several2D and 3D examples are used to demonstrate the effectiveness of the method,including minimization of compliance and complaint mechanism problems. Theresults 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.",
keywords = "topology optimisation, implicit function, mathematical programming",
author = "Dunning, {Peter D}",
note = "The author would like to thank Numerical Analysis Group at the Rutherford Appleton Laboratory for their FORTRAN HSL packages (HSL, a collection of Fortran codes for large-scale scientific computation. See http://www.hsl.rl.ac.uk/).",
year = "2017",
month = "4",
day = "15",
doi = "10.1016/j.cma.2017.01.008",
language = "English",
volume = "317",
pages = "993--1011",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",

}

TY - JOUR

T1 - Design parameterization for topology optimization by intersection of an implicit function

AU - Dunning, Peter D

N1 - The author would like to thank Numerical Analysis Group at the Rutherford Appleton Laboratory for their FORTRAN HSL packages (HSL, a collection of Fortran codes for large-scale scientific computation. See http://www.hsl.rl.ac.uk/).

PY - 2017/4/15

Y1 - 2017/4/15

N2 - This paper introduces a new approach to topology optimization where thestructural boundary is defined by the intersection of an implicit signed-distancefunction and a cutting surface. The cutting surface is discretized using finiteelement shape-function polynomials and the nodal values become the designvariables during optimization. Thus, the design parameterization is separatedfrom the analysis discretization, which enables a reduction in the numberof design variables, compared with methods that use element-wise variables.The proposed method can obtain solutions with smooth boundaries and theparameterization allows solution by standard optimization methods. Several2D and 3D examples are used to demonstrate the effectiveness of the method,including minimization of compliance and complaint mechanism problems. Theresults 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 approach to topology optimization where thestructural boundary is defined by the intersection of an implicit signed-distancefunction and a cutting surface. The cutting surface is discretized using finiteelement shape-function polynomials and the nodal values become the designvariables during optimization. Thus, the design parameterization is separatedfrom the analysis discretization, which enables a reduction in the numberof design variables, compared with methods that use element-wise variables.The proposed method can obtain solutions with smooth boundaries and theparameterization allows solution by standard optimization methods. Several2D and 3D examples are used to demonstrate the effectiveness of the method,including minimization of compliance and complaint mechanism problems. Theresults 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 - topology optimisation

KW - implicit function

KW - mathematical programming

U2 - 10.1016/j.cma.2017.01.008

DO - 10.1016/j.cma.2017.01.008

M3 - Article

VL - 317

SP - 993

EP - 1011

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

ER -