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H-DGTP—a Heaviside-function based directional growth topology parameterization for design optimization of stiffener layout and height of thin-walled structures

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Abstract

Plates with ribs or stiffeners (stiffened plates) have been widely used as primary or secondary load bearing structures. Such structures could be fabricated by casting – a conventional yet important manufacturing process, their load bearing capacities are strongly dependent on the layout and sizes of the stiffeners. Thus it is necessary to establish specific topology optimization model and algorithm to obtain optimum layout, sizes and shapes of the stiffeners with casting constraints being considered. In this paper, we propose a new Heaviside-function based directional growth topology parameterization (H-DGTP) of the casting constraints for simultaneously optimizing the layout and height of the stiffeners. By using the new explicit parameterization, we can obtain a clear stiffener layout with optimized height. The differentiability of the parameterization is obtained by the use of a smooth approximation of the Heaviside function. In order to be applicable to a non-uniform mesh, a base surface is introduced and the minimum length of a stiffener can be controlled. Several numerical examples are presented to show the validity of this method.

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Acknowledgments

The authors gratefully acknowledge the financial support to this work by the National Basic Research Program of China (Grant No. 2011CB610304), the National Natural Science Foundation of China (Grant Nos. 11172052 and 11332004), the 111 Project (B14013) and the Fundamental Research Funds for the Central Universities of China (2342013DUT13RC(3)28).

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024, China

    Shutian Liu, Quhao Li, Wenjiong Chen, Rui Hu & Liyong Tong

  2. School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW, 2006, Australia

    Liyong Tong

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  1. Shutian Liu
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  2. Quhao Li
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  3. Wenjiong Chen
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  4. Rui Hu
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  5. Liyong Tong
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Correspondence to Shutian Liu.

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Liu, S., Li, Q., Chen, W. et al. H-DGTP—a Heaviside-function based directional growth topology parameterization for design optimization of stiffener layout and height of thin-walled structures. Struct Multidisc Optim 52, 903–913 (2015). https://doi.org/10.1007/s00158-015-1281-5

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