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Stress constrained compliance minimization by means of the small amplitude homogenization method

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Abstract

Under the assumption of small contrast between the elasticity tensors of two materials, we derive an algorithm based on an approximate relaxation of a problem that minimizes the compliance under a constraint on stress. Numerical results are presented for the short cantilever problem, where we see that, for a 1 to 2 contrast in Young moduli, and when compared with a configuration that only minimizes compliance, one can get up to a 46 % reduction in peak stress, while compliance increases by only 1 %. The basis of the method is the small amplitude homogenization technique derived by Allaire and Gutiérrez, which relies on the use of H-measures introduced by Tartar to study the quadratic interaction of weakly convergent sequences of functions.

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Acknowledgments

The authors would like to acknowledge partial funding provided by the Regular FONDECYT grant N°1090334 and the helpful remarks of the reviewers.

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Authors and Affiliations

  1. Department of Structural and Geotechnical Engineering, Pontificia Universidad Católica de Chile, casilla 306 correo 22, Santiago, Chile

    Sergio Gutiérrez & Esteban Zegpi

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  1. Sergio Gutiérrez
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  2. Esteban Zegpi
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Correspondence to Sergio Gutiérrez.

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Gutiérrez, S., Zegpi, E. Stress constrained compliance minimization by means of the small amplitude homogenization method. Struct Multidisc Optim 49, 1025–1036 (2014). https://doi.org/10.1007/s00158-013-1040-4

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  • DOI: https://doi.org/10.1007/s00158-013-1040-4

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