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Mathematics > Optimization and Control

arXiv:2312.07889 (math)
[Submitted on 13 Dec 2023]

Title:Adaptive Isogeometric Topology Optimization of Shell Structures based on PHT-splines

Authors:Zepeng Wen, Qiong Pan, Xiaoya Zhai, Hongmei Kang, Falai Chen
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Abstract:This paper proposes an Adaptive Isogeometric Topology Optimization framework for shell structures based on PHT-splines (PHT-AITO). In this framework, the design domain, displacement, and density are represented by PHT-splines. Leveraging the local refinement capability of PHT-splines, mesh elements defining the density function are adaptively refined to achieve a suitable resolution at the interface between solid and void regions. This addresses the issue of excessive degrees of freedom resulting from global refinement. The refinement of the mesh elements is driven by their density. During the optimization of the density on a refined mesh, the initial value of the density is inherited from the optimization results on the previous mesh to accelerate the iteration process and maintain the stability of the optimized structure. Numerical experiments on various shell structures have verified the effectiveness of PHT-AITO. Compared with isogeometric topology optimization based on tensor-product splines, PHT-AITO can significantly reduce the degrees of freedom in the optimization problem, thereby improving computational efficiency.
Subjects: Optimization and Control (math.OC); Computational Engineering, Finance, and Science (cs.CE); Computational Geometry (cs.CG); Graphics (cs.GR)
Cite as: arXiv:2312.07889 [math.OC]
  (or arXiv:2312.07889v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2312.07889

Submission history

From: Zepeng Wen [view email]
[v1] Wed, 13 Dec 2023 04:23:44 UTC (9,239 KB)
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