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Deployment dynamics and topology optimization of a spinning inflatable structure

空间自旋充气结构展开动力学与拓扑优化设计

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Abstract

Inflatable space structures may undergo the vibration of a long duration because of their features of dynamic deployment, high flexibility, and low-frequency modes. In this paper, a topology optimization methodology is proposed to reduce the vibration of a spinning inflatable structure. As the first step, a variable-length shell element is developed in the framework of arbitrary Lagrange-Euler (ALE) and absolute nodal coordinate formulation (ANCF) to accurately model the deployment dynamics of the inflatable structure. With the help of two additional material coordinates, the shell element of ALE-ANCF has the ability to describe the large deformation, large overall motion, and variable length of an inflatable structure. The nonlinear elastic forces and additional inertial forces induced by the variable length are analytically derived. In the second step, a topology optimization procedure is presented for the dynamic response of an inflatable structure through the integration of the equivalent static loads (ESL) method and the density method. The ESL sets of the variable-length inflatable structure are defined to simplify the dynamic topology optimization into a static one, while the density-based topology optimization method is used to describe the topology of the inflatable structure made of two materials and solve the static optimization problem. In order to obtain more robust optimization results, sensitivity analysis, density filter, and projection techniques are also utilized. Afterwards, a benchmark example is presented to validate the ALE-ANCF modeling scheme. The deployment dynamics and corresponding topology optimization of a spinning inflatable structure are studied to show the effectiveness of the proposed topology optimization methodology.

摘要

空间充气结构因其具有可展开、大柔性, 以及低频模态等特性, 常常会产生难以消除的振动. 本文提出了一种空间自旋充气结构振动抑制的拓扑优化设计方法, 该方法首先采用任意拉格朗日-欧拉(ALE)描述的绝对节点坐标(ANCF)薄壳单元建立可展开空间充气结构的动力学模型. 通过引入两个物质坐标, 建立的ALE-ANCF薄壳单元可精确描述充气结构的大范围运动、大变形与变长度等特性. 本文还推导了该薄壳单元的非线性弹性力和由于变长度引起的附加惯性力的解析表达式. 此外, 综合利用等效静载荷法和变密度法, 本文提出了一种可展开空间充气结构动响应拓扑优化方法, 等效静载荷用以将动响应优化问题转化为静响应优化问题, 而变密度法用以描述双材料充气结构的拓扑并求解相应的静响应拓扑优化问题. 为了得到更加稳健的优化结果, 综合了灵敏度分析、密度过滤和密度映射等技巧. 最后, 通过一个基准算例验证了ALE-ANCF模型的正确性, 并研究了空间自旋充气结构的展开动力学与拓扑优化设计, 从而验证了该方法可以抑制可展开空间充气结构的振动.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12002153, 11827801, and 11832005), the Natural Science Foundation of Jiangsu Province (Grant No. BK20200434), and the Fundamental Research Funds for the Central Universities (Grant No. NS2021003).

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Authors and Affiliations

  1. State Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Jialiang Sun  (孙加亮), Dongping Jin  (金栋平) & Haiyan Hu  (胡海岩)

  2. MOE Key Laboratory of Dynamics and Control of Flight Vehicle, School of Aerospace Engineering, Beijing Institute of Technology, Beijing, 100081, China

    Haiyan Hu  (胡海岩)

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  1. Jialiang Sun  (孙加亮)
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  2. Dongping Jin  (金栋平)
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Correspondence to Haiyan Hu  (胡海岩).

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Author contributions

Jialiang Sun and Dongping Jin investigated the research. Jialiang Sun created the models, performed the simulation, processed the data and wrote the first draft of the manuscript. Dongping Jin and Haiyan Hu revised and edited the final version. Haiyan Hu acquired the financial support for the project leading to this publication and oversighted the research activity planning and execution.

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Sun, J., Jin, D. & Hu, H. Deployment dynamics and topology optimization of a spinning inflatable structure. Acta Mech. Sin. 38, 122100 (2022). https://doi.org/10.1007/s10409-022-22100-x

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