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Lightweight Design of Shell Structures Using Adaptive Inner-Front Level Set Based Topology Optimization (AIFLS-TOP)

적응적 내부 경계 레벨셋 기반 위상최적화를 이용한 쉘 구조물의 경량화 설계

  • 박강수 (한국과학기술원 기계공학과) ;
  • 윤성기 (한국과학기술원 기계공학과)
  • Published : 2007.12.01

Abstract

In the present work, topology optimization method using adaptive inner-front level set method is presented. In the conventional level set based topology optimization method, there exists an incapability for inner-front creation during optimization process. In this regard, as a new attempt to avoid and to overcome the limitation, an inner-front creation algorithm is proposed. In the inner-front creation algorithm, the strain energy density of a structure along with volume constraint is considered. Especially, to facilitate the inner-front creation process during the optimization process, the inner-front creation map which corresponds to the discrete valued function of strain energy density is constructed. In the evolution of the level set function during the optimization process, the least-squares finite element method (LSFEM) is employed. As an application to shell structures, the lightweight design of doubly curved shell and segmented mirror is carried out.

Keywords

Topology Optimization;Level Set Method;Least-Squares Finite Element Method;Inner-Front Creation

References

  1. Setihan, J. A. and Wiegmann, A., 2000, 'Structural Boundary Design via Level Set and Immersed Interface Method,' Journal of Computational Physics, Vol. 163, No. 2, pp. 489-528 https://doi.org/10.1006/jcph.2000.6581
  2. Allaire, G, Jouve, F. and Toader A.M., 2004, 'Structural Optimization Using Sensitivity Analysis and a Level Set Method,' Journal of Computational Physics, Vol. 194, No.1, pp. 363-393 https://doi.org/10.1016/j.jcp.2003.09.032
  3. Wang, M. Y., Wang, X. M. and Guo D.M., 2003, 'A Level Set Method for Structural Topology Optimization,' Computer Methods in Applied Mechanics and Engineering , Vol. 192, No. 1-2, pp. 227-246 https://doi.org/10.1016/S0045-7825(02)00559-5
  4. Allaire, G, Jouve, F. and Toader A.M., 2004, 'Structural Optimization Using Topological and Shape Sensitivity via a Level Set Method,' Internal report, n. 555, CMAP, Ecole Polytechnique
  5. Wang, X. M., Mei, Y. and Wang, M.Y., 2004, 'Incorporating Topology Derivatives into Level Set Methods for Structural Topology Optimization,' Proceeding of 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, New York
  6. Osher, S. and Fedkiw, R., 2003, 'Level Set Methods and Dynamic Implicit Surfaces,' Springer-Verlag, Berlin
  7. Jiang, B.N., 1998, 'The Least-Squares Finite Element Method,' Springer-Verlag, Berlin
  8. Aubert, G. and Komprobst, P., 2001, 'Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations,' Springer-Verlag, Berlin
  9. Haug, E.H., Choi, K.K., and Komkov V., 1986, 'Design Sensitivity Analysis of Structural Systems,' Academic press, Orlando
  10. Nelson, J.E., 2000, 'Design Concepts for the California Extremely Large Telescope (CELT),' Proceedings of the SPIE - Telescope Structures, Enclosures, Controls, Assembly/Integration/Validation, and Commissioning, Munich, Germany
  11. Park Kang-Soo, Chang Su-Young, Lee Eung-Shik and Youn Sung-Kie, 'Topology Optimization of the Primary Mirror of a Multi-Spectral Camera,' Trans. of the KSME A, Vol. 26, No.6, pp. 1194-1202 https://doi.org/10.3795/KSME-A.2002.26.6.1194
  12. Park, K.S., Chang, S.Y., and Youn, S.K., 2003, 'Topology Optimization of the Primary Mirror of a Multi-Spectral Camera,' Structural and MultidiscipIinary Optimization, Vol. 25, No. 1, pp. 46-53 https://doi.org/10.1007/s00158-002-0271-6
  13. Park, K.S., Lee, J. H., and Youn, S.K., 2005, 'Lightweight Mirror Design Method Using Topology Optimization,' Optical Engineering, Vol. 44, No.5, pp. 053002-1-053002-6 https://doi.org/10.1117/1.1901685
  14. Osher, S. and Sethian, J.A., 1988, 'Front Propagating with Curvature Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations,' Journal of Computational Physics, Vol. 79, pp.12-49 https://doi.org/10.1016/0021-9991(88)90002-2

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