Eigenfrequency constrained topology optimization of finite strain hyperelastic structures

Research output: Contribution to journalArticle

Abstract

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.

Details

Authors
Organisations
External organisations
  • Lawrence Livermore National Laboratory
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Computational Mathematics
  • Applied Mechanics

Keywords

  • Degenerate eigenfrequencies, Eigenfrequency optimization, Element removal, Finite strain, Nonlinear hyperelasticity, Topology optimization
Original languageEnglish
Pages (from-to)2577-2594
Number of pages18
JournalStructural and Multidisciplinary Optimization
Volume61
Issue number6
Early online date2020 May 17
Publication statusPublished - 2020 Jun
Publication categoryResearch
Peer-reviewedYes