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Keywords: robust topology optimization, uncertain-but-bounded parameters, uncertain load magnitude and direction, expected compliance, worst compliance.

Summary

Uncertainty is an important consideration in topology optimization to produce robust and reliable solutions. In a recent paper, Dunning et al. introduced a new probabilistic approach for robust topology optimization to minimize the volume-constrained expected compliance with uncertainty in the loading magnitude and applied direction, where uncertainties are assumed normally distributed and statistically independent. The model presented was formulated as a statistical model which after some manipulation was replaced by an equivalent multiple load problem in the function of the number of perturbed loads. Our opinion is that the presented parametric statistical approach is far from engineering practice, because in the most applications the desired results are ones that achieve minimal maximal compliance which is a rigorous nonparametric measure of robustness. To demonstrate the differences between the minimal maximal and the conventional expected compliance models two examples with load perturbations are presented. We show that the parametric expected compliance as the preferred measure of robustness is unable to characterize the compliance variability so it has to be replaced with the easy-to-understand maximal (minimal) compliance and the range which are generally applicable nonparametric measures of robustness. In comparison, in the applied nonparametric approach developed by Csébfalvi the load perturbations are handled as "uncertain-but-bounded" parameters. The result is a robust volume-constrained compliance-minimal design which is invariant to the feasible load perturbations. The proposed robust optimization algorithm is a worst compliance searching model, which can be formulated as a small quadratic programming problem with linearized constraints and box constraints. In the model, the robustness criterion was borrowed from Kocvara which defines the optimal robust solution as the minimum of the maximal compliance on the set of load perturbations.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 108 PROCEEDINGS OF THE FIFTEENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: J. Kruis, Y. Tsompanakis and B.H.V. Topping Paper 189 Critical Examination of Volume-Constrained Topology Optimization for Uncertain Load Magnitude and Direction A. Csébfalvi¹ and J. Lógó² ¹University of Pécs, Hungary ²Budapest University of Technology and Economics, Hungary doi:10.4203/ccp.108.189 purchase the full-text of this paper Full Bibliographic Reference for this paper , "Critical Examination of Volume-Constrained Topology Optimization for Uncertain Load Magnitude and Direction", in J. Kruis, Y. Tsompanakis, B.H.V. Topping, (Editors), "Proceedings of the Fifteenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 189, 2015. doi:10.4203/ccp.108.189 Keywords: robust topology optimization, uncertain-but-bounded parameters, uncertain load magnitude and direction, expected compliance, worst compliance. Summary Uncertainty is an important consideration in topology optimization to produce robust and reliable solutions. In a recent paper, Dunning et al. introduced a new probabilistic approach for robust topology optimization to minimize the volume-constrained expected compliance with uncertainty in the loading magnitude and applied direction, where uncertainties are assumed normally distributed and statistically independent. The model presented was formulated as a statistical model which after some manipulation was replaced by an equivalent multiple load problem in the function of the number of perturbed loads. Our opinion is that the presented parametric statistical approach is far from engineering practice, because in the most applications the desired results are ones that achieve minimal maximal compliance which is a rigorous nonparametric measure of robustness. To demonstrate the differences between the minimal maximal and the conventional expected compliance models two examples with load perturbations are presented. We show that the parametric expected compliance as the preferred measure of robustness is unable to characterize the compliance variability so it has to be replaced with the easy-to-understand maximal (minimal) compliance and the range which are generally applicable nonparametric measures of robustness. In comparison, in the applied nonparametric approach developed by Csébfalvi the load perturbations are handled as "uncertain-but-bounded" parameters. The result is a robust volume-constrained compliance-minimal design which is invariant to the feasible load perturbations. The proposed robust optimization algorithm is a worst compliance searching model, which can be formulated as a small quadratic programming problem with linearized constraints and box constraints. In the model, the robustness criterion was borrowed from Kocvara which defines the optimal robust solution as the minimum of the maximal compliance on the set of load perturbations. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £75 +P&P)
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