Journal of Central South University

, Volume 21, Issue 2, pp 558–566

A topology optimization method based on element independent nodal density

  • Ji-jun Yi (易继军)
  • Tao Zeng (曾韬)
  • Jian-hua Rong (荣见华)
  • Yan-mei Li (李艳梅)


A methodology for topology optimization based on element independent nodal density (EIND) is developed. Nodal densities are implemented as the design variables and interpolated onto element space to determine the density of any point with Shepard interpolation function. The influence of the diameter of interpolation is discussed which shows good robustness. The new approach is demonstrated on the minimum volume problem subjected to a displacement constraint. The rational approximation for material properties (RAMP) method and a dual programming optimization algorithm are used to penalize the intermediate density point to achieve nearly 0-1 solutions. Solutions are shown to meet stability, mesh dependence or non-checkerboard patterns of topology optimization without additional constraints. Finally, the computational efficiency is greatly improved by multithread parallel computing with OpenMP.

Key words

topology optimization element independent nodal density Shepard interpolation parallel computation 


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Copyright information

© Central South University Press and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Ji-jun Yi (易继军)
    • 1
    • 2
  • Tao Zeng (曾韬)
    • 1
  • Jian-hua Rong (荣见华)
    • 2
  • Yan-mei Li (李艳梅)
    • 3
  1. 1.School of Mechanical and Electrical EngineeringCentral South UniversityChangshaChina
  2. 2.School of Automobile and Mechanical EngineeringChangsha University of Science and TechnologyChangshaChina
  3. 3.Hunan Technical College of Water Resources and Hydro PowerChangshaChina

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