Topological Optimal Material Design of Structures with Moved and Regularized Heaviside Function

  • Dongkyu Lee
  • Soomi ShinEmail author
Research paper


This study presents a new regularized penalty form to carry out material topology optimization of structures. In general, the regularization form of typical SIMP has been used to reduce material discontinuity of densities which describe boundaries of finite elements and finally provide numerical stability in sensitivity analysis of optimization procedures and the problem of 0–1 formulation. However, optimal solutions of the regularized SIMP depend on penalty parameters such as typical SIMP, since penalty relation of Young’s modulus and density of regularized SIMP is similar to that of typical SIMP in spite of regularization. In this paper, the penalty relationship between Young’s modulus and material density of typical SIMP becomes extended by multiplying it with a moved and regularized form of a material indication function, i.e., Heaviside function. The new penalization method does not depend on filter methods for free-checkerboards; therefore, computational savings can be obtained. Numerical examples demonstrate that the incorporation of moved and regularized Heaviside function in the SIMP leads to convergent solutions with clear boundaries between materials and no materials and without checkerboard patterns.


Structural topology optimization SIMP 0–1 formulation Material indication function Moved and regularized Heaviside function 



This research was supported by a grant (code# NRF-2017R1D1A1B03031350) from the National Research Foundation of Korea (NRF) funded by the Korea government.


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Copyright information

© Shiraz University 2018

Authors and Affiliations

  1. 1.Department of Architectural EngineeringSejong UniversitySeoulKorea
  2. 2.Research Institute of Industrial TechnologyPusan National UniversityBusanKorea

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