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Isogeometric Shape Optimal Design of Elastic Structures under Design-dependent Loads

Seonho Cho1, Seung-Hyun Ha, Bonyong Koo, Minho Yoon, Seung-Ho Ahn

1 National Creative Research Initiatives Center for Isogeometric Optimal Design and Department of Naval Architecture and Ocean Engineering, Seoul National University, Kwanak-ro 599, Sillim- 9-dong, Kwanak-gu, Seoul 151-744, Korea, Tel: +82-2-880-7322, Fax: +82-2-888-9298, E-mail:

Structural Longevity 2011, 6(3), 109-114.


Using an isogeometric approach, a continuum-based shape optimization method is developed for elasticity problems. To obtain efficient and precise adjoint shape sensitivity, precise normal and curvature information should be taken into account in shape sensitivity expressions, especially for design-dependent problems. In this approach, the basis functions generated from NURBS are directly used to construct a geometrically exact model in response and shape sensitivity analyses. Refinements and design changes are easily implemented within the isogeometric framework. The isogeometric design sensitivity analysis provides more accurate sensitivity of complex geometries including higher order terms such as normal and curvature. Also, it vastly simplifies the design modification without communicating with the CAD geometry during optimization process. Since the NURBS basis functions are used in both isogeometric response and sensitivity analyses, design modifications are easily carried out by the adjustment of control points. We demonstrate some numerical examples, where the accuracy and efficiency of the isogeometric sensitivity are verified by the comparison with finite difference one. Also, some examples of design–dependent shape optimization are demonstrated to verify the applicability and effectiveness of the proposed method.


Cite This Article

Cho, S., Ha, S., Koo, B., Yoon, M., Ahn, S. (2011). Isogeometric Shape Optimal Design of Elastic Structures under Design-dependent Loads. Structural Longevity, 6(3), 109–114.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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