Structural and Multidisciplinary Optimization

, Volume 56, Issue 3, pp 571–586 | Cite as

Topology optimization using the p-version of the finite element method

  • Tam H. NguyenEmail author
  • Chau H. Le
  • Jerome F. Hajjar


A multiresolution topology optimization approach is proposed using the p-version finite element method (p-version FEM). Traditional topology optimization, where a density design variable is assigned to each element, is suitable for low-order h-version FEM. However, it cannot take advantage of the higher accuracy of higher-order p-version FEM analysis for generating results with higher resolution. In contrast, the proposed method separates density variables and finite elements so that the resolution of the density field, which defines the structure, can be higher than that of the finite element mesh. Thus, the method can take full advantage of the higher accuracy of p-version FEM.


Topology optimization Finite element method Multiresolution Density method Density filter p-element 



This research was funded in part by the National Science Foundation under the Grant No. CMMI-1000666 and by Northeastern University. This support is gratefully acknowledged. The second author would like to thank the Vietnam National Foundation for Science and Technology Development (NAFOSTED) for the support under Grant No.107.02-2014.33.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Tam H. Nguyen
    • 1
    Email author
  • Chau H. Le
    • 2
  • Jerome F. Hajjar
    • 1
  1. 1.Department of Civil and Environmental EngineeringNortheastern UniversityBostonUSA
  2. 2.BM Research and Development Co. Ltd.HanoiVietnam

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