Stiffness optimization of non-linear elastic structures

Mathias Wallin, Niklas Ivarsson, Daniel Tortorelli

Research output: Contribution to journalArticlepeer-review


This paper revisits stiffness optimization of non-linear elastic structures. Due to the non-linearity, several possible stiffness measures can be identified and in this work conventional compliance, i.e. secant stiffness designs are compared to tangent stiffness designs. The optimization problem is solved by the method of moving asymptotes and the sensitivities are calculated using the adjoint method. For the tangent cost function it is shown that although the objective involves the third derivative of the strain energy an efficient formulation for calculating the sensitivity can be obtained. Loss of convergence due to large deformations in void regions is addressed by using a fictitious strain energy such that small strain linear elasticity is approached in the void regions. A well posed topology optimization problem is formulated by using restriction which is achieved via a Helmholtz type filter. The numerical examples provided show that for low load levels, the designs obtained from the different stiffness measures coincide whereas for large deformations significant differences are observed.

Original languageEnglish (US)
Pages (from-to)292-307
Number of pages16
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Mar 1 2018
Externally publishedYes


  • Finite strains
  • Non-linear elasticity
  • Stiffness optimization
  • Topology optimization

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications


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