Achieving stress-constrained topological design via length scale control

Oded Amir, Boyan S. Lazarov

Research output: Contribution to journalArticlepeer-review


A new suite of computational procedures for stress-constrained continuum topology optimization is presented. In contrast to common approaches for imposing stress constraints, herein it is proposed to limit the maximum stress by controlling the length scale of the optimized design. Several procedures are formulated based on the treatment of the filter radius as a design variable. This enables to automatically manipulate the minimum length scale such that stresses are constrained to the allowable value, while the optimization is driven to minimizing compliance under a volume constraint – without any direct constraints on stresses. Numerical experiments are presented that incorporate the following : 1) Global control over the filter radius that leads to a uniform minimum length scale throughout the design; 2) Spatial variation of the filter radius that leads to local manipulation of the minimum length according to stress concentrations; and 3) Combinations of the two above. The optimized designs provide high-quality trade-offs between compliance, stress and volume. From a computational perspective, the proposed procedures are efficient and simple to implement: essentially, stress-constrained topology optimization is posed as a minimum compliance problem with additional treatment of the length scale.

Original languageEnglish
Pages (from-to)2053-2071
Number of pages19
JournalStructural and Multidisciplinary Optimization
Issue number5
StatePublished - 1 Nov 2018


  • Length scale
  • Stress constraints
  • Topology optimization

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Software
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Control and Optimization


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