Open Access
Issue
Int. J. Simul. Multidisci. Des. Optim.
Volume 11, 2020
Article Number 3
Number of page(s) 10
DOI https://doi.org/10.1051/smdo/2019019
Published online 24 January 2020
  1. G.I.N. Rozvany, M. Zhou, T. Birker, Generalized shape optimization without homogenization, Struct. Optim. 4, 250–252 (1992) [CrossRef] [Google Scholar]
  2. G.I.N. Rozvany, M.P. Bendso̸E, U. Kirsch, Layout Optimization of Structures, Appl. Mech. Rev. 48, 41–119 (1995) [CrossRef] [Google Scholar]
  3. M.P. Bendsøe, N. Kikuchi, Generating optimal topologies in structural design using a homogenization method, Comput. Methods Appl. Mech. Eng. 71, 197–224 (1988) [CrossRef] [MathSciNet] [Google Scholar]
  4. J. Zhang, W.H. Zhang, J.H. Zhu, L. Xia, Integrated layout design of multi-component systems using XFEM and analytical sensitivity analysis, Comput. Methods Appl. Mech. Eng. 245–246, 75–89 (2012) [CrossRef] [Google Scholar]
  5. Y.M. Xie, Z.H. Zuo, X.D. Huang, J.H. Rong, Convergence of topological patterns of optimal periodic structures under multiple scales, Struct. Multidiscipl. Optim. 46, 41–50 (2012) [CrossRef] [Google Scholar]
  6. A. Takezawa, S. Nishiwaki, M. Kitamura, Shape and topology optimization based on the phase field method and sensitivity analysis, J. Comput. Phys. 229, 2697–2718 (2010) [CrossRef] [Google Scholar]
  7. T. Yamada, K. Izui, S. Nishiwaki, A. Takezawa, A topology optimization method based on the level set method incorporating a fictitious interface energy, Comput. Methods Appl. Mech. Eng. 199, 2876–2891 (2010) [CrossRef] [Google Scholar]
  8. S.J. Osher, F. Santosa, Level set methods for optimization problems involving geometry and constraints I. Frequencies of a two-density inhomogeneous drum, J. Comput. Phys. 171, 272–288 (2001) [CrossRef] [MathSciNet] [Google Scholar]
  9. J.A. Sethian, A. Wiegmann, Structural Boundary Design via Level Set and Immersed Interface Methods ☆, J. Comput. Phys. 163, 489–528 (2000) [CrossRef] [MathSciNet] [Google Scholar]
  10. M.Y. Wang, X.M. Wang, D.M. Guo, A level set method for structural topology optimization, Comput. Methods Appl. Mech. Eng. 192, 227–246 (2003) [CrossRef] [MathSciNet] [Google Scholar]
  11. M.Y. Wang, S. Zhou, Color level sets: a multi-phase method for structural topology optimization with multiple materials, Comput. Methods Appl. Mech. Eng. 193, 469–496 (2004) [CrossRef] [Google Scholar]
  12. G. Allaire, F. Jouve, A.M. Toader, Structural optimization using sensitivity analysis and a level-set method, J. Comput. Phys. 194, 363–393 (2004) [CrossRef] [Google Scholar]
  13. A.N. Christiansen, M. Nobel-Jørgensen, N. Aage, O. Sigmund, J.A. Bærentzen, Topology optimization using an explicit interface representation, Struct. Multidiscipl. Optim. 49, 387–399 (2013) [CrossRef] [Google Scholar]
  14. P. Wei, H. Ma, M.Y. Wang, The stiffness spreading method for layout optimization of truss structures, Struct. Multidiscip. Optim. 49, 667–682 (2014) [CrossRef] [Google Scholar]
  15. X. Guo, W. Zhang, W. Zhong, Doing topology optimization explicitly and geometrically—A new moving morphable components based framework, J. Appl. Mech. 81, 081009 (2014) [CrossRef] [Google Scholar]
  16. T.H. Nguyen, G.H. Paulino, J. Song, C.H. Le, A computational paradigm for multiresolution topology optimization (MTOP), Struct. Multidiscipl. Optim. 41, 525–539 (2009) [CrossRef] [Google Scholar]
  17. T.H. Nguyen, G.H. Paulino, J.H. Song, C.H. Le, Improving multiresolution topology optimization via multiple discretizations, Int. J. Numer. Methods Eng. 92, 507–530 (2012) [CrossRef] [Google Scholar]
  18. E.T. Filipov, J. Chun, G.H. Paulino, J. Song, Polygonal multiresolution topology optimization (PolyMTOP) for structural dynamics, Struct. Multidiscipl. Optim. 53, 673–694 (2015) [CrossRef] [Google Scholar]
  19. J. Park, A. Sutradhar, A multi-resolution method for 3D multi-material topology optimization, Comput. Methods Appl. Mech. Eng. 285, 571–586 (2015) [CrossRef] [Google Scholar]
  20. Q.X. Lieu, J. Lee, A multi-resolution approach for multi-material topology optimization based on isogeometric analysis, Comput. Methods Appl. Mech. Eng. 323, 272–302 (2017) [CrossRef] [Google Scholar]
  21. Y. Wang, Z. Kang, Q. He, An adaptive refinement approach for topology optimization based on separated density field description, Comput. Struct. 117, 10–22 (2013) [CrossRef] [Google Scholar]
  22. J.P. Groen, M. Langelaar, O. Sigmund, M. Ruess, Higher-order multi-resolution topology optimization using the finite cell method, Int. J. Numer. Methods Eng. 110, 903–920 (2017) [CrossRef] [Google Scholar]
  23. D. Schillinger, M. Ruess, The Finite Cell Method: A Review in the Context of Higher-Order Structural Analysis of CAD and Image-Based Geometric Models, Arch. Comput. Methods Eng. 22, 391–455 (2014) [CrossRef] [Google Scholar]
  24. D.K. Gupta, G.J. van der Veen, A.M. Aragon, M. Langelaar, F. van Keulen, Bounds for decoupled design and analysis discretizations in topology optimization, Int. J. Numer. Methods Eng. 111, 88–100 (2017) [CrossRef] [Google Scholar]
  25. R.L. Hardy, Multiquadric equations of topography and other irregular surfaces, J. Geophys. Res. 76, 1905–1915 (1971) [NASA ADS] [CrossRef] [Google Scholar]
  26. H. Wendland, Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree, Adv. Comput. Math. 4, 389–396 (1995) [CrossRef] [MathSciNet] [Google Scholar]
  27. X.H. Xie, M. Mirmehdi, Radial basis function based level set interpolation and evolution for deformable modelling, Image Vis. Comput. 29, 167–177 (2011) [Google Scholar]
  28. P. Wei, Z.Y. Li, X.P. Li, M.Y. Wang, An 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions, Struct. Multidiscipl. Optim. 58, 831–849 (2018) [CrossRef] [Google Scholar]
  29. S.Y. Wang, M.Y. Wang, Radial basis functions and level set method for structural topology optimization. Int. J. Numer. Methods Eng. 65, 2060–2090 (2006) [CrossRef] [Google Scholar]
  30. K.K. Choi, N.H. Kim, Structural Sensitivity Analysis and Optimization 1, Mech. Eng. 8, 189–194 (2006) [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.