Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 200, Issue 49-52, Pages 3613-3627Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2011.08.006
Keywords
Topology optimization; Robust design optimization; Manufacturing errors; Monte Carlo method
Funding
- Center of Advanced User Support (CAUS)
- Danish Center of Scientific Computing (DCSC)
- Elite Research Prize from the Danish Minister of Research
- EUROHORCs/ESF
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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. (C) 2011 Elsevier B.V. All rights reserved.
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