A 120 lines code for isogeometric topology optimization and its extension to 3D in MATLAB
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866910909018931200 |
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| author | Xie, Xianda Ou, Zhihui Yang, Aodi Li, Xiaobing Wang, Shuting |
| author_facet | Xie, Xianda Ou, Zhihui Yang, Aodi Li, Xiaobing Wang, Shuting |
| contents | In this paper, a compact and efficient code implementation is presented for isogeometric topology optimization (ITO) approach. With the aid of Bėzier extraction technique, a derived explicit stiffness matrix computation formula is applied to all B-spline IGA elements with rectangular shape under linear elasticity assumption. Using the aforementioned explicit formula, the stiffness matrix calculation and updating of IGA are significantly simplified, which leads to the current ITO code implemented only in one main function without calling subroutines, such as IGA mesh generation and Gaussian quadrature. Both two-dimensional (2D) and three-dimensional (3D) cases are taken into consideration, which result into iga_top120 and iga_top3D257 MATLAB codes for 2D and 3D design problems. Numerical examples validate the effectiveness of our open-source codes, with several user-defined input parameters basically identical to those used in top88 and top3D. Therefore, iga_top120 and iga_top3D257 provide an effective entry for the code transforming from FEM-based TO into ITO. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08233 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A 120 lines code for isogeometric topology optimization and its extension to 3D in MATLAB Xie, Xianda Ou, Zhihui Yang, Aodi Li, Xiaobing Wang, Shuting Computational Engineering, Finance, and Science In this paper, a compact and efficient code implementation is presented for isogeometric topology optimization (ITO) approach. With the aid of Bėzier extraction technique, a derived explicit stiffness matrix computation formula is applied to all B-spline IGA elements with rectangular shape under linear elasticity assumption. Using the aforementioned explicit formula, the stiffness matrix calculation and updating of IGA are significantly simplified, which leads to the current ITO code implemented only in one main function without calling subroutines, such as IGA mesh generation and Gaussian quadrature. Both two-dimensional (2D) and three-dimensional (3D) cases are taken into consideration, which result into iga_top120 and iga_top3D257 MATLAB codes for 2D and 3D design problems. Numerical examples validate the effectiveness of our open-source codes, with several user-defined input parameters basically identical to those used in top88 and top3D. Therefore, iga_top120 and iga_top3D257 provide an effective entry for the code transforming from FEM-based TO into ITO. |
| title | A 120 lines code for isogeometric topology optimization and its extension to 3D in MATLAB |
| topic | Computational Engineering, Finance, and Science |
| url | https://arxiv.org/abs/2504.08233 |