Structural and Multidisciplinary Optimization

, Volume 50, Issue 4, pp 537–560 | Cite as

Element deformation scaling for robust geometrically nonlinear analyses in topology optimization



Geometrically nonlinear structural analyses in conventional density-based Topology Optimization (TO) may fail due to excessive deformation, concerning in particular compression in low stiffness parts (void) of the domain. This limits the application of TO in the field of realistic large deflection mechanisms, actuators and multi-stable structures.

This paper investigates the source of the instabilities that may be encountered using the conventional strategy to scale the stiffness of finite elements using the density (e.g. SIMP). Based on the findings, we propose a new design interpolation, called Element Deformation Scaling (EDS), to obtain more robust structural analyses for geometrically nonlinear TO. Instead of scaling the stiffness, EDS scales the local internal displacements, and therefore, the deformation, in a low-density finite element. This ensures that, even for extremely deformed finite elements, the internal displacements remain in the range of applicability of the material model and finite element description.

The effectiveness of the proposed method is compared with the conventional approach (e.g. SIMP) and the Element Connectivity Parameterization (ECP) method using several numerical experiments using path-following techniques. The proposed method, EDS, is demonstrated to lead to more robust structural analyses than the other approaches. However, EDS still has limitations. These limitations are discussed in detail.


Topology optimization Robust analyses Geometrical nonlinearities Material interpolation Design interpolation Element deformation scaling (EDS) 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • N. P. van Dijk
    • 1
  • M. Langelaar
    • 2
  • F. van Keulen
    • 2
  1. 1.Uppsala UniversityUppsalaSweden
  2. 2.Delft University of TechnologyCD DelftThe Netherlands

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