Abstract
In topology optimization filtering is a popular approach for preventing numerical instabilities. This short note shows that the well-known sensitivity filtering technique, that prevents checkerboards and ensures mesh-independent designs in density-based topology optimization, is equivalent to minimizing compliance for nonlocal elasticity problems known from continuum mechanics. Hence, the note resolves the long-standing quest for finding an explanation and physical motivation for the sensitivity filter.
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Acknowledgments
The authors would like to acknowledge constructive input to the manuscript provided by Professor Gregoire Allaire, Ecole Polytechnique, France and members of the TopOpt-group (www.topopt.dtu.dk).
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Grants: The first author appreciates the support from the Villum Foundation through the grant: “NextTop”. The second author acknowledges the support of the National Science Foundation under grant EFRI-1038305. The opinions and conclusions presented in this paper are those of the authors and do not necessarily reflect the views of the sponsoring organization. This work was performed during the first authors sabbatical leave at University of Colorado Boulder.
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Sigmund, O., Maute, K. Sensitivity filtering from a continuum mechanics perspective. Struct Multidisc Optim 46, 471–475 (2012). https://doi.org/10.1007/s00158-012-0814-4
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DOI: https://doi.org/10.1007/s00158-012-0814-4