Sensitivity filtering from the non-local perspective

Anton Evgrafov*, José C. Bellido

*Corresponding author for this work

    Research output: Contribution to journalJournal articleResearchpeer-review

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    We present a mathematical model of topology optimization for non-local linear diffusion equation. The model provides a rigorous and constructive answer to the challenge of interpreting sensitivity filtering as an internal feature of a specific continuum mechanics model, which has been raised in Sigmund and Maute (Struct Multidiscip Optim 46(4):471–475, 2012). Our model enjoys two very interesting properties. On the one hand, the governing non-local integral equations of this model approximate the well-known local generalized Laplace equation with diffusion coefficient obeying SIMP (Solid Isotropic Material with Penalization) law. On the other hand, the topology optimization problem admits optimal solutions for a range of penalization parameters of practical interest without the need for any external regularization techniques, something which is well known to be false in the case of topology optimization with SIMP for classical local description of continuum mechanics.
    Original languageEnglish
    JournalStructural and Multidisciplinary Optimization
    Issue number1
    Pages (from-to)401–404
    Publication statusPublished - 2019


    • Non-local optimal design
    • Existence of solutions
    • SIMP
    • Peridynamics


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