An Enhanced Topology Optimization Approach Based on the Combined MMC and NURBS-Curve Boundaries

Rongzhen Zheng, Cheol Kim

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


An efficient topology optimization method is developed newly in this study by combining the Non-uniform rational B-spline (NURBS) curves and moving morphable components (MMC). The MMC-based topology optimization is an explicit and geometrical method that utilizes a set of morphable components to create basic blocks for optimization. Optimum topologies may be obtained by optimizing shapes, lengths, thicknesses, orientations and layout of these components. The combined method adopts a different way in the creation of morphable components that consist of NURBS curves. Various kinds of complicated curved components can be built with NURBS curves or surfaces. Here, the NURBS curve is applied for shaping the geometries of structural basic components, and the coordinates of control points become design variables for topology optimization. A MATLAB optimization code has been developed. Four numerical examples of a short cantilever, a MBB beam, a simply supported beam with two point loadings, and a vehicle lower chassis structure subjected to crash loadings are provided to prove that the combined topology optimization approach coupled with NURBS curves and basic morphable components can get optimum topologies with clear topological boundaries successfully. As results of comparison study with other approaches, we can obtain the same topologies and faster convergence rates for the three separate cases. The combined approach can improve the smoothness of the topological boundaries that are similar to the shape optimization results obtained by post-optimization after the density-based topology optimization.

Original languageEnglish
Pages (from-to)1529-1538
Number of pages10
JournalInternational Journal of Precision Engineering and Manufacturing
Issue number8
StatePublished - 1 Aug 2020


  • Clear boundary
  • FEM
  • Moving morphable component
  • NURBS curve
  • Topology optimization


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