Introducing the sequential linear programming level-set method for topology optimization

Peter D. Dunning; H. Alicia Kim

doi:10.1007/s00158-014-1174-z

Introducing the sequential linear programming level-set method for topology optimization

Peter D. Dunning^*, H. Alicia Kim

^*Corresponding author for this work

Engineering

University of Bath

Research output: Contribution to journal › Article › peer-review

93 Citations (Scopus)

11 Downloads (Pure)

Abstract

This paper introduces an approach to level-set topology optimization that can handle multiple constraints and simultaneously optimize non-level-set design variables. The key features of the new method are discretized boundary integrals to estimate function changes and the formulation of an optimization sub-problem to attain the velocity function. The sub-problem is solved using sequential linear programming (SLP) and the new method is called the SLP level-set method. The new approach is developed in the context of the Hamilton-Jacobi type level-set method, where shape derivatives are employed to optimize a structure represented by an implicit level-set function. This approach is sometimes referred to as the conventional level-set method. The SLP level-set method is demonstrated via a range of problems that include volume, compliance, eigenvalue and displacement constraints and simultaneous optimization of non-level-set design variables.

Original language	English
Pages (from-to)	631-643
Number of pages	13
Journal	Structural and multidisciplinary optimization
Volume	51
Early online date	30 Sept 2014
DOIs	https://doi.org/10.1007/s00158-014-1174-z
Publication status	Published - Mar 2015

Bibliographical note

The authors 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/). Dr H Alicia Kim
acknowledges the support from Engineering and Physical Sciences
Research Council, grant number EP/M002322/1

Keywords

Level-set method
Topology optimization
Constraints
Sequential linear programming
structural topology
sensitivity-analysis
shape optimization
design
FEM

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10.1007/s00158-014-1174-zLicence: CC BY

Introducing the sequential linear programming level-set method for topology optimization
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. http://creativecommons.org/licenses/by/4.0/
Final published version, 1.88 MBLicence: CC BY

Peter Dunning
- Engineering, Engineering - Lecturer
Person: Academic

Cite this

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title = "Introducing the sequential linear programming level-set method for topology optimization",

abstract = "This paper introduces an approach to level-set topology optimization that can handle multiple constraints and simultaneously optimize non-level-set design variables. The key features of the new method are discretized boundary integrals to estimate function changes and the formulation of an optimization sub-problem to attain the velocity function. The sub-problem is solved using sequential linear programming (SLP) and the new method is called the SLP level-set method. The new approach is developed in the context of the Hamilton-Jacobi type level-set method, where shape derivatives are employed to optimize a structure represented by an implicit level-set function. This approach is sometimes referred to as the conventional level-set method. The SLP level-set method is demonstrated via a range of problems that include volume, compliance, eigenvalue and displacement constraints and simultaneous optimization of non-level-set design variables.",

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AB - This paper introduces an approach to level-set topology optimization that can handle multiple constraints and simultaneously optimize non-level-set design variables. The key features of the new method are discretized boundary integrals to estimate function changes and the formulation of an optimization sub-problem to attain the velocity function. The sub-problem is solved using sequential linear programming (SLP) and the new method is called the SLP level-set method. The new approach is developed in the context of the Hamilton-Jacobi type level-set method, where shape derivatives are employed to optimize a structure represented by an implicit level-set function. This approach is sometimes referred to as the conventional level-set method. The SLP level-set method is demonstrated via a range of problems that include volume, compliance, eigenvalue and displacement constraints and simultaneous optimization of non-level-set design variables.

KW - Level-set method

KW - Topology optimization

KW - Constraints

KW - Sequential linear programming

KW - structural topology

KW - sensitivity-analysis

KW - shape optimization

KW - design

KW - FEM

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DO - 10.1007/s00158-014-1174-z

M3 - Article

SN - 1615-147X

VL - 51

SP - 631

EP - 643

JO - Structural and multidisciplinary optimization

JF - Structural and multidisciplinary optimization

ER -

Introducing the sequential linear programming level-set method for topology optimization

Abstract

Bibliographical note

Keywords

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