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Isogeometric Analysis and Shape Optimization of Holed Structures via the Patch Removing Technique

Daoyuan Yu, Shouyu Cai*, Wenya Fan, Lan Zhang*

School of Mechanics and Safety Engineering, Zhengzhou University, Zhengzhou, 450001, China

* Corresponding Authors: Shouyu Cai. Email: ; Lan Zhang. 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, 124(3), 787-806.


In this study, a patch removing based Isogeometric analysis (PR-IGA) method is proposed to conduct the holed structural analysis with only one parametric domain, in which there are also no trimmed elements. The theoretical foundation of this novel patch removing approach is that any holed structure can be obtained by removing sub-patches (i.e., the holes) from an intact base patch. Since the parametric domains of these patches are all meshed by rectangular grids, the elements in the resulted holed structural parametric domain could all be untrimmed rectangles under certain mapping conditions. To achieve the special condition, a systematic technique consisting of T-spline local refinement and control points substitution/adjustment is provided. Due to the intactness of parametric elements, the analysis procedure of holed structures based on the proposed PRIGA is quite simplified and efficient compared to traditional multi-patch and trimming schemes. Moreover, after the deduction of analytical sensitivities related to structural mass and mechanical responses, the PR-IGA is directly employed in the holed structural shape optimization to successfully eliminate the need for model transformation during modeling, analysis and optimization processes. Numerical examples involving analysis and shape optimization of complex holed structures are presented to demonstrate the effectiveness of the proposed method.


Cite This Article

Yu, D., Cai, S., Fan, W., Zhang, L. (2020). Isogeometric Analysis and Shape Optimization of Holed Structures via the Patch Removing Technique. CMES-Computer Modeling in Engineering & Sciences, 124(3), 787–806.

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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