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T-Splines Based Isogeometric Topology Optimization with Arbitrarily Shaped Design Domains

Gang Zhao1,2, Jiaming Yang1, Wei Wang1,*, Yang Zhang1, Xiaoxiao Du1, Mayi Guo1
1 School of Mechanical Engineering and Automation, Beihang University, Beijing, 100191, China
2 Beijing Engineering Technological Research Center of High-Efficient & Green CNC Machining Process, Beijing, 100191, China
* Corresponding Author: Wei Wang. Email:
(This article belongs to this Special Issue: Recent Developments of Isogeometric Analysis and its Applications in Structural Optimization)

Computer Modeling in Engineering & Sciences 2020, 123(3), 1033-1059.

Received 29 January 2020; Accepted 19 March 2020; Issue published 28 May 2020


In this paper, a new isogeometric topology optimization (ITO) method is proposed by using T-splines based isogeometric analysis (IGA). The arbitrarily shaped design domains, directly obtained from CAD, are represented by a single T-spline surface which overcomes the topological limitations of Non-Uniform Rational B-Spline (NURBS). The coefficients correlated with control points are directly used as design variables. Therefore, the T-spline basis functions applied for geometry description and calculation of structural response are simultaneously introduced to represent the density distribution. Several numerical examples show that the proposed approach leads to a coherent workflow to handle design problems of complicated structures. The optimized results are free of checkerboard patterns without additional stabilization and filtering techniques due to the properties of T-splines, which also simplified the post-processing. In addition, through performing local refinement, we can easily achieve multiresolution optimization and infill optimization within the T-splines based framework. In general, the proposed method provides a possibility to design, analyze, and optimize engineering structures in a uniform model, which has the potential to improve design effi- ciency and reduce the cost of product development.


Topology optimization; isogeometric analysis; unstructured T-splines; Bézier extraction

Cite This Article

Zhao, G., Yang, J., Wang, W., Zhang, Y., Du, X. et al. (2020). T-Splines Based Isogeometric Topology Optimization with Arbitrarily Shaped Design Domains. CMES-Computer Modeling in Engineering & Sciences, 123(3), 1033–1059.


This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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