Shape Design Optimization Using Isogeometric Analysis

등기하 해석법을 이용한 형상 최적설계

  • 하승현 (서울대학교 조선해양공학과) ;
  • 조선호 (서울대학교 조선해양공학과 및 RIMSE)
  • Published : 2008.06.30


In this paper, a shape design optimization method for linearly elastic problems is developed using isogeometric approach. In many design optimization problems for practical engineering models, initial raw data usually come from a CAD modeler. Then, designers should convert the CAD data into finite element mesh data since most of conventional design optimization tools are based on finite element analysis. During this conversion, there are some numerical errors due to geometric approximation, which causes accuracy problems in response as well as design sensitivity analyses. As a remedy for this phenomenon, the isogeometric analysis method can be one of the promising approaches for the shape design optimization. The main idea of isogeometric approach is that the basis functions used in analysis is exactly the same as the ones representing the geometry. This geometrically exact model can be used in the shape sensitivity analysis and design optimization as well. Therefore the shape design sensitivity with high accuracy can be obtained, which is very essential for a gradient-based optimization. Through numerical examples, it is verified that the shape design optimization based on an isogeometic approach works well.


  1. 조선호, 정현승, 양영순 (2002) 기하학적 비선형 구조물의 설계민감도 해석 및 위상 최적설계, 한국전산구조공학회 02 봄 학술발표회 논문집, pp.335-342
  2. 하승현, 조선호 (2007) 등기하 해석법을 이용한 설계민감도 해석, 한국전산구조공학회논문집, 20(3), pp.339-345
  3. Arora, J.S., Lee, T.H., Cardoso, J.B. (1992) Structural shape design sensitivity analysis: Relationship between material derivative and control volume approaches, AIAA Journal, 30(6), pp.1638-1648
  4. Azegami, H., Kaizu, S., Shimoda, M., Katamine, E. (1997) Irregularity of shape optimization problems and an improvement technique, Computer Aided Optimization Design of Structures, V, pp.309-326
  5. Braibant, V., Fluery, C. (1984) Shape optimal design using B-splines, Computer Methods in Applied Mechanics and Engineering, 44, pp.247-267
  6. Cho, M., Roh, H.Y. (2003) Development of geometrically exact new shell elements based on general curvilinear coordinates, International Journal for Numerical Methods in Engineering, 56(1), pp.81-115
  7. Cho, S., Ha, S.H. (2007) Shape design optimization of geometrically nonlinear structures using isogeometric analysis, 9th United States National Congress on Computational Mechanics, San Francisco, California, U.S.A., July 22-26
  8. Choi, K.K., Chang, K.H. (1994) A study of design velocity field computation for shape optimal design, Finite Elements in Analysis and Design, 15, pp. 317-341
  9. Choi, K.K., Duan, W. (2000) Design sensitivity analysis and shape optimization of structural components with hyperelastic material, Computer Methods in Applied Mechanics and Engineering, 187, pp.219-243
  10. Choi, K.K., Kim, N.H. (2004) Structural Sensitivity Analysis and Optimization: Volume 1, Linear Systems & Volume 2, Nonlinear Systems and Applications, Springer, New York, NY
  11. Cottrell, J.A., Hughes, T.J.R., Reali, A. (2007) Studies of refinement and continuity in isogeometric structural analysis. Computer Methods in Applied Mechanics and Engineering, 196, pp.4160-4183
  12. Cottrell, J.A., Reali, A., Bazilevs, Y., Hughes, T.J.R. (2006) Isogeometric analysis of structural vibrations, Computer Methods in Applied Mechanics and Engineering, 195, pp.5257-5296
  13. Farin, G. (2002), Curves and Surfaces for CAGD: A Practical Guide, Academic Press
  14. Ha, S.H., Cho, S. (2007) Shape design optimization of structural problems based on isogeometric approach, 7th World Congress on Structural and Multidisciplinary Optimization, COEX Seoul, Korea, May 21-25
  15. Hughes, T.J.R., Cottrell, J.A., Bazilevs, Y. (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Computer Methods in Applied Mechanics and Engineering, 194, pp.4135-4195
  16. Lindby, T., Santos, J.L.T. (1997) 2-D and 3-D shape optimization using mesh velocities to integrate analytical sensitivities with associative CAD, Structural Optimization, 13, pp.213-222
  17. Piegl, L., Tiller, W. (1997) The NURBS Book (Monographs in Visual Communication), second ed., Springer-Verlag, New York
  18. Rogers, D.F. (2001) An Introduction to NURBS With Historical Perspective. Academic Press, San Diego, CA
  19. Roh, H.Y., Cho, M. (2004) The application of geometrically exact shell elements to B-spline surfaces, Computer Methods in Applied Mechanics and Engineering, 193, pp.2261-2299
  20. Roh, H.Y., Cho, M. (2005) Integration of geometric design and mechanical analysis using B-spline functions on surface, International Journal for Numerical Methods in Engineering, 62(14), pp. 1927-1949