Level set based robust shape and topology optimization under random field uncertainties |
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Authors: | Shikui Chen Wei Chen Sanghoon Lee |
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Affiliation: | (1) Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL, USA;(2) Korea Atomic Energy Research Institute, 1045 Daedeok-Daero, Yuseong-gu, Daejeon, Republic of Korea; |
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Abstract: | A robust shape and topology optimization (RSTO) approach with consideration of random field uncertainty in loading and material
properties is developed in this work. The proposed approach integrates the state-of-the-art level set methods for shape and
topology optimization and the latest research development in design under uncertainty. To characterize the high-dimensional
random-field uncertainty with a reduced set of random variables, the Karhunen–Loeve expansion is employed. The univariate
dimension-reduction (UDR) method combined with Gauss-type quadrature sampling is then employed for calculating statistical
moments of the design response. The combination of the above techniques greatly reduces the computational cost in evaluating
the statistical moments and enables a semi-analytical approach that evaluates the shape sensitivity of the statistical moments
using shape sensitivity at each quadrature node. The applications of our approach to structure and compliant mechanism designs
show that the proposed RSTO method can lead to designs with completely different topologies and superior robustness. |
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