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Layout optimization of continuum structures embedded with movable components and holes simultaneously

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A Correction to this article was published on 26 February 2020

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Abstract

In this paper, the layout optimization problem of continuum structures embedded with movable components and holes simultaneously is solved for the first time. We propose a new methodology for the embedding problem under SIMP-based computational framework, where the positions and orientations of embedded components and holes and the topology of connecting structure are optimized concurrently to maximize the overall stiffness. To this end, the parameterized topology description function, combining the Kreisselmeier-Steinhauser (KS) function, is used to construct the geometric shapes of embedded components and holes. The material density defining the topology of connecting structure and the geometric parameters used to describe the location and orientation of embedded components and holes are considered as design variables of the optimization problem. To unite these two seemingly different representations into a single computational framework, we first project the embedded components and holes into two density fields on a fixed grid using a smoothed Heaviside function, then introduce a new SIMP-motivated material interpolation scheme invoked at the finite element level for material parameterization. The material parameterization scheme supports full analytical sensitivities, which can greatly improve the accuracy and efficiency of sensitivity analysis, and make it suitable for use with efficient gradient-based algorithms. Finally, the effectiveness of the proposed method is illustrated by several numerical examples.

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  • 26 February 2020

    The original version of this article unfortunately contained a mistake. The Figure 11 in the original article should be replaced by the following figure.

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Acknowledgments

These supports are gratefully acknowledged. The authors are also grateful to Prof. Krister Svanberg for providing the matlab MMA code, and the anonymous reviewers for their insightful suggestions and comments on the early version of this paper.

Funding

This work is supported by the National Natural Science Foundation of China (Grant Nos. 11872140, 11872017) and the Fundamental Research Funds for the Central Universities (Grant Nos. JZ2019HGBZ0127, PA2019GDPK0039, and PA2019GDQT0016).

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Authors and Affiliations

  1. School of Civil Engineering, Hefei University of Technology, Hefei, 230009, China

    Xuan Wang

  2. Anhui Key Laboratory of Civil Engineering Structures and Materials, Hefei University of Technology, Hefei, 230009, China

    Xuan Wang

  3. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116023, China

    Ping Hu & Zhan Kang

Authors
  1. Xuan Wang
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  2. Ping Hu
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  3. Zhan Kang
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Correspondence to Ping Hu.

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Wang, X., Hu, P. & Kang, Z. Layout optimization of continuum structures embedded with movable components and holes simultaneously. Struct Multidisc Optim 61, 555–573 (2020). https://doi.org/10.1007/s00158-019-02378-5

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