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Topology optimization for minimum weight with compliance and simplified nominal stress constraints for fatigue resistance

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Abstract

This work investigates a simplified approach to cope with the optimization of preliminary design of structures under local fatigue constraints along with a global enforcement on the overall compliance. The problem aims at the minimization of the weight of linear elastic structures under given loads and boundary conditions. The expected stiffness of the optimal structure is provided by the global constraint, whereas a set of local stress–based constraints ask for a structure to be fatigue resistant. A modified Goodman fatigue strength comparison is implemented through the same formalism to address pressure–dependent failure in materials as in Drucker–Prager strength criterion. As a simplification, the Sines approach is used to define the equivalent mean and alternating stresses to address the fatigue resistance for an infinite life time. Sines computation is based on the equivalent mean and alternate stress depending on the invariants of the stress tensor and its deviatoric part, respectively. The so–called singularity phenomenon is overcome by the implementation of a suitable qp-relaxation of the equivalent stress measures. Numerical examples are presented to illustrate the features of the achieved optimal layouts and of the proposed algorithm.

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Notes

  1. 1 \(\mathbf {M}^{0}_{e}= \mathbf {T_{e}^{0,T}}\mathbf {V}\mathbf {{T_{e}^{0}}}\) with \(\mathbf {V}= \left (\begin {array}{ccc} 1 & -1/2 & 0 \\ -1/2 & 1 & 0\\ 0& 0 & 3 \end {array}\right )\).

  2. 2 \(\mathbf {H}^{0}_{e}=\left (\begin {array}{l}1\\1\\0 \end {array}\right )\mathbf {{T_{e}^{0}}}\).

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Acknowledgments

Part of the work has been done when the first author was spending a research period at Politecnico di Milano. This author would like to acknowledge the Belgian National Fund for Scientific research (FRIA) for its financial support.

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Authors and Affiliations

  1. Department of Aerospace and Mechanical Engineering, University of Liège, 4000, Liège, Belgium

    Maxime Collet & Pierre Duysinx

  2. Department of Civil and Environmental Engineering, Politecnico di Milano, I20133, Milano, Italy

    Matteo Bruggi

Authors
  1. Maxime Collet
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  2. Matteo Bruggi
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  3. Pierre Duysinx
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Correspondence to Maxime Collet.

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Collet, M., Bruggi, M. & Duysinx, P. Topology optimization for minimum weight with compliance and simplified nominal stress constraints for fatigue resistance. Struct Multidisc Optim 55, 839–855 (2017). https://doi.org/10.1007/s00158-016-1510-6

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  • DOI: https://doi.org/10.1007/s00158-016-1510-6

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