Journal article
Robust topology optimization accounting for spatially varying manufacturing errors
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.
Language: | English |
---|---|
Year: | 2011 |
Pages: | 3613-3627 |
ISSN: | 18792138 and 00457825 |
Types: | Journal article |
DOI: | 10.1016/j.cma.2011.08.006 |
ORCIDs: | Lazarov, Boyan Stefanov and Sigmund, Ole |