Abstract
Parametric level set method (PLSM) using interpolation method, such as radial basis function (RBF) interpolation, exposes high computational cost and poor stability when solving structural topology optimization (STO) problems with large-scale nodes. However, the quasi-interpolation method can approximate the level set function (LSF) and its generalized functions without solving any system of linear equations. With this good property, this paper utilizes multiquadric (MQ) quasi-interpolation to parameterize the LSF and innovatively introduces it into the STO problem. Moreover, the MQ quasi-interpolation is utilized to compute the element density, which makes the level set band method (LSBM) more rigorous. The proposed methods were compared with the PLSM based on compactly supported radial basis functions (CSRBFs). The results show that the approximation accuracy, computational efficiency and stability of the evolution process of the proposed methods are better than those of CSRBFs when the shape parameter takes a suitable small value.
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Acknowledgments
The authors gratefully acknowledge the financial support provided by the Science Foundation of Xi’ an Aeronautical Institute (Grant No. 2023KY1202) and the equipment support sponsored by the Big Data Laboratory of Xi’ an Aeronautical Institute.
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Chen-Dong Yang is currently a doctoral student of the School of Science, Chang’an University, Xi’an, China, and a lecturer of the School of Science, Aeronautical Institute, Xi’an, China. His research interests include optimum structural design and mathematical optimization.
Jian-Hu Feng is a Professor of the School of Science, Chang’an University, Xi’an, China. He received his Ph.D. in Aero Engine of Northwestern Polytechnical University Xi’an, China. His research interests include optimum structural design, computational fluid dynamics and high-performance computing technology for scientific and engineering problems.
Jiong Ren is a Lecturer of the School of Science, Aeronautical Institute, Xi’an, China. She received her Ph.D. in School of Aeronautics of Northwestern Polytechnical University Xi’an, China. Her research interests include optimum structural design, computational fluid dynamics and high-performance computing technology for scientific and engineering problems.
Ya-Dong Shen is a Lecturer in the School of Civil and Architectural Engineering, Nanyang Normal University, Nanyang, China. He received Ph.D. in School of Science, Chang’an University, Xi’an, China. His research interests include optimum structural design and foundation treatment.
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Yang, CD., Feng, JH., Ren, J. et al. MQ quasi-interpolation-based level set method for structural topology optimization. J Mech Sci Technol 38, 3521–3532 (2024). https://doi.org/10.1007/s12206-024-0625-8
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DOI: https://doi.org/10.1007/s12206-024-0625-8