Algorithms for point-wise state variable constraints in structural optimization |
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| Affiliation: | 1. Department of Management Control and Information Systems, School of Economics and Business, University of Chile, Av. Diagonal Paraguay 257, 8330015 Santiago, Chile;2. Institute of Computing Science, Poznań University of Technology, Street Piotrowo 2, 60-965 Poznań, Poland;3. Department of Statistics and Operations Research, University of Vienna, 1010 Wien, Austria;4. Department of Decision Sciences, Università Bocconi, Via Roentgen 1, 20139 Milano, Italy;5. Warwick Business School, University of Warwick, CV4 7AL, Coventry, UK;6. INESC TEC, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal;7. Faculty of Economics and Business, University of Groningen, PO Box 800, 9700 AV Groningen, Netherlandsn |
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| Abstract: | This paper presents algorithms to treat the point-wise state variable constraints in finite dimensional and distributed parameter structural optimization problems. The idea is to impose such constraints at all local maximum points, or over a small region around the maximum points. Therefore, methods for design sensitivity analysis to handle the constraints at some particular point for the distributed parameter problem are presented. The direct differentiation and adjoint variable methods are employed to derive the design sensitivity expressions. For the finite dimensional problem the new idea is easily carried out in optimization process. Simply supported and clamped beams are optimized using the new approach. These are modeled with nonuniform beam elements. Comparisons of finite dimensional and distributed parameter problems are also made. |
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