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A level-set-based topology and shape optimization method for continuum structure under geometric constraints

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Abstract

Recent advances in level-set-based shape and topology optimization rely on free-form implicit representations to support boundary deformations and topological changes. In practice, a continuum structure is usually designed to meet parametric shape optimization, which is formulated directly in terms of meaningful geometric design variables, but usually does not support free-form boundary and topological changes. In order to solve the disadvantage of traditional step-type structural optimization, a unified optimization method which can fulfill the structural topology, shape, and sizing optimization at the same time is presented. The unified structural optimization model is described by a parameterized level set function that applies compactly supported radial basis functions (CS-RBFs) with favorable smoothness and accuracy for interpolation. The expansion coefficients of the interpolation function are treated as the design variables, which reflect the structural performance impacts of the topology, shape, and geometric constraints. Accordingly, the original topological shape optimization problem under geometric constraint is fully transformed into a simple parameter optimization problem; in other words, the optimization contains the expansion coefficients of the interpolation function in terms of limited design variables. This parameterization transforms the difficult shape and topology optimization problems with geometric constraints into a relatively straightforward parameterized problem to which many gradient-based optimization techniques can be applied. More specifically, the extended finite element method (XFEM) is adopted to improve the accuracy of boundary resolution. At last, combined with the optimality criteria method, several numerical examples are presented to demonstrate the applicability and potential of the presented method.

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Acknowledgments

The research work sponsored in part by the Natural Science Foundation of China (Grants: 50975107), the National Key Technologies R & D Program of China (Grants: 2010ZX04001-032), the Open Research Fund Program of the State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body (Grants: 31115020), and also by the Guangdong Province High-Tech Zone Development Guiding Program (Grants: 2011B010700081).

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Authors and Affiliations

  1. The State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, People’s Republic of China

    Tao Liu, Bin Li & Liang Gao

  2. School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, People’s Republic of China

    Shuting Wang

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  1. Tao Liu
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  2. Shuting Wang
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Correspondence to Shuting Wang.

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Liu, T., Wang, S., Li, B. et al. A level-set-based topology and shape optimization method for continuum structure under geometric constraints. Struct Multidisc Optim 50, 253–273 (2014). https://doi.org/10.1007/s00158-014-1045-7

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  • DOI: https://doi.org/10.1007/s00158-014-1045-7

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