Stress-based shape and topology optimization with the level set method

Renato Picelli, Scott Townsend, C. Brampton, Julian Norato, H. A. Kim

Research output: Contribution to journalArticlepeer-review

179 Citations (SciVal)

Abstract

This paper proposes a level set method to solve minimum stress and stress-constrained shape and topology optimization problems. The method solves a sub-optimization problem every iteration to obtain optimal boundary velocities. A p-norm stress functional is used to aggregate stresses in a single constraint. The shape sensitivity function is derived and a computational procedure based on a least squares interpolation approach is devised in order to compute sensitivities at the boundaries. Adaptive constraint scaling is used to enforce exact control of stress limits. Numerical results show that the method is able to solve the problem efficiently for single and multiple load cases obtaining solutions with smooth boundaries.

Original languageEnglish
Pages (from-to)1-23
JournalComputer Methods in Applied Mechanics and Engineering
Volume329
DOIs
Publication statusPublished - 1 Feb 2018

Funding

We thank the support of the European Office of Aerospace Research of the US Air Force Office of Scientific Research , grant number FA8655-13-1-3056 , and the Engineering and Physical Sciences Research Council , fellowship grants EP/M002322/2 for their supports. The authors would also like to thank Dr Ray Kolonay and Dr James Joo of the US Air Force Research Laboratory for their insights and discussions and 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/ ). Information on the data underpinning the results presented here, including how to access them, can be found in the Cardiff University data catalogue at http://doi.org/10.17035/d.2017.0041722993 .

Keywords

  • Level set method
  • Stress constraints
  • Stress minimization
  • Topology optimization

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications

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