Robust topology optimization accounting for spatially varying manufacturing errors

M. Schevenels, Boyan Stefanov Lazarov, Ole Sigmund

    Research output: Contribution to journalJournal articleResearchpeer-review


    This paper presents a robust approach for the design of macro-, micro-, or nano-structures by means of topology optimization, accounting for spatially varying manufacturing errors. The focus is on structures produced by milling or etching; in this case over- or under-etching may cause parts of the structure to become thinner or thicker than intended. This type of error is modeled by means of a projection technique: a density filter is applied, followed by a Heaviside projection, using a low projection threshold to simulate under-etching and a high projection threshold to simulate over-etching. In order to simulate the spatial variation of the manufacturing error, the projection threshold is represented by a (non-Gaussian) random field. The random field is obtained as a memoryless transformation of an underlying Gaussian field, which is discretized by means of an EOLE expansion. The robust optimization problem is formulated in a probabilistic way: the objective function is defined as a weighted sum of the mean value and the standard deviation of the structural performance. The optimization problem is solved by means of a Monte Carlo method: in each iteration of the optimization scheme, a Monte Carlo simulation is performed, considering 100 random realizations of the manufacturing error. A more thorough Monte Carlo simulation with 10000 realizations is performed to verify the results obtained for the final design. The proposed methodology is successfully applied to two test problems: the design of a compliant mechanism and a heat conduction problem.
    Original languageEnglish
    JournalComputer Methods in Applied Mechanics and Engineering
    Issue number49-52
    Pages (from-to)3613-3627
    Publication statusPublished - 2011


    • Topology optimization
    • Robust design optimization
    • Monte Carlo method
    • Manufacturing errors


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