Structural stability and artificial buckling modes in topology optimization

Anna Dalklint, Mathias Wallin, Daniel A. Tortorelli

Research output: Contribution to journalArticlepeer-review


This paper demonstrates how a strain energy transition approach can be used to remove artificial buckling modes that often occur in stability constrained topology optimization problems. To simulate the structural response, a nonlinear large deformation hyperelastic simulation is performed, wherein the fundamental load path is traversed using Newton’s method and the critical buckling load levels are estimated by an eigenvalue analysis. The goal of the optimization is to minimize displacement, subject to constraints on the lowest critical buckling loads and maximum volume. The topology optimization problem is regularized via the Helmholtz PDE-filter and the method of moving asymptotes is used to update the design. The stability and sensitivity analyses are outlined in detail. The effectiveness of the energy transition scheme is demonstrated in numerical examples.

Original languageEnglish (US)
Pages (from-to)1751–1763
Number of pages13
JournalStructural and Multidisciplinary Optimization
Issue number4
StatePublished - Oct 2021


  • Artificial buckling modes
  • Eigenvalue problem
  • Energy transition
  • Nonlinear elasticity
  • Stability
  • Topology optimization

ASJC Scopus subject areas

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


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