Eigenfrequency constrained topology optimization of finite strain hyperelastic structures

Anna Dalklint, Mathias Wallin, Daniel A. Tortorelli

Research output: Contribution to journalArticlepeer-review


This paper incorporates hyperelastic materials, nonlinear kinematics, and preloads in eigenfrequency constrained density–based topology optimization. The formulation allows for initial finite deformations and subsequent small harmonic oscillations. The optimization problem is solved by the method of moving asymptotes, and the gradients are calculated using the adjoint method. Both simple and degenerate eigenfrequencies are considered in the sensitivity analysis. A well-posed topology optimization problem is formulated by filtering the volume fraction field. Numerical issues associated with excessive distortion and spurious eigenmodes in void regions are reduced by removing low volume fraction elements. The optimization objective is to maximize stiffness subject to a lower bound on the fundamental eigenfrequency. Numerical examples show that the eigenfrequencies drastically change with the load magnitude, and that the optimization is able to produce designs with the desired fundamental eigenfrequency.

Original languageEnglish (US)
Pages (from-to)2577-2594
Number of pages18
JournalStructural and Multidisciplinary Optimization
Issue number6
StatePublished - Jun 1 2020
Externally publishedYes


  • Degenerate eigenfrequencies
  • Eigenfrequency optimization
  • Element removal
  • Finite strain
  • Nonlinear hyperelasticity
  • Topology optimization

ASJC Scopus subject areas

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

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