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Topology optimization of hyperelastic bodies including non-zero prescribed displacements

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Abstract

Stiffness topology optimization is usually based on a state problem of linear elasticity, and there seems to be little discussion on what is the limit for such a small rotation-displacement assumption. We show that even for gross rotations that are in all practical aspects small (<3 deg), topology optimization based on a large deformation theory might generate different design concepts compared to what is obtained when small displacement linear elasticity is used. Furthermore, in large rotations, the choice of stiffness objective (potential energy or compliance), can be crucial for the optimal design concept. The paper considers topology optimization of hyperelastic bodies subjected simultaneously to external forces and prescribed non-zero displacements. In that respect it generalizes a recent contribution of ours to large deformations, but we note that the objectives of potential energy and compliance are no longer equivalent in the non-linear case. We use seven different hyperelastic strain energy functions and find that the numerical performance of the Kirchhoff–St.Venant model is in general significantly worse than the performance of the other six models, which are all modifications of this classical law that are equivalent in the limit of infinitesimal strains, but do not contain the well-known collapse in compression. Numerical results are presented for two different problem settings.

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Notes

  1. For the nested formulation, the last term disappears and the Lagrangian becomes the potential energy.

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Acknowledgement

This project was financed by Swedish Foundation for Strategic Research through the ProViking programme.

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Authors and Affiliations

  1. Mechanics, Department of Management and Engineering, The Institute of Technology, Linköping University, 581 83, Linköping, Sweden

    Anders Klarbring

  2. Department of Mechanical Engineering, Jönköping University, 551 11, Jönköping, Sweden

    Niclas Strömberg

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  1. Anders Klarbring
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  2. Niclas Strömberg
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Correspondence to Niclas Strömberg.

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Klarbring, A., Strömberg, N. Topology optimization of hyperelastic bodies including non-zero prescribed displacements. Struct Multidisc Optim 47, 37–48 (2013). https://doi.org/10.1007/s00158-012-0819-z

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  • DOI: https://doi.org/10.1007/s00158-012-0819-z

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