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Nonlinear dynamic stability analysis of imperfect architected cellular sandwich plate under impact loading

冲击载荷下含缺陷蜂窝夹层板的非线性动态稳定性分析

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Abstract

Architected cellular structures are designed by tessellating unit cells in a periodic fashion. The optimisation of the cellular structures ensures their compatibility with engineering applications in which mechanical properties are highly customised to meet a specific requirement while preserving considerable lightweight. The present paper aims to explore the dynamic buckling behaviour of the imperfect sandwich plate with an architected cellular core. The homogeneous method is adopted to obtain the effective material properties of the cellular core with various unit cell configurations. Different impact loading cases, namely, the sinusoidal, exponential, rectangular, and damping impulses, have been simulated. Meanwhile, two common types of boundary restraints (i.e., simply supported and clamped) are embraced in the investigation. The governing equation system is built based on the first-order shear deformation plate theory with the Von Karman nonlinearity and then resolved by the Galerkin and the fourth-order Runge-Kutta methods. Volmir criterion is employed to determine the critical dynamic buckling load. Several validations are made before conducting systematic numerical experiments. The correlations between the dynamic buckling load of the sandwich model and a number of crucial factors, such as the geometry and relative density of the cell unit, the initial imperfection and boundary conditions of the sandwich plate, elastic foundation coefficients, and damping, are discussed. In addition, the load-to-weight ratio is shown, which will aid in determining the optimal unit cell design and relative density for light-weighting a specific technical component.

摘要

蜂窝结构具有周期性拓扑分布的特征. 定制蜂窝结构可在满足特定工程要求的机械性能的同时保持其轻重量的优点. 本文旨在 探索在冲击荷载作用下, 具有不同晶格结构的含缺陷蜂窝夹层板的动态屈曲行为. 本文采用均质法来获得不同晶格结构配置的蜂窝芯 层的有效材料特性, 并采用正弦波、指数、矩形和阻尼脉冲来模拟不同的冲击载荷情况. 同时, 研究中考虑了两种常见的边界约束类 型, 即简单支撑和夹持边界. 基于冯·卡门非线性理论和一阶剪切变形板理论建立控制方程, 然后使用Galerkin方法和四阶Runge-Kutta 方法进行求解, 并进一步使用Volmir准则来确定结构的临界动态屈曲载荷. 本文讨论了晶格结构形状、蜂窝芯相对密度、初始几何缺 陷、边界条件、弹性基础系数和结构阻尼对夹层板模型的动态屈曲载荷的影响. 此外, 文章还给出了研究模型的载荷-重量比, 有助于 确定最佳晶格单元设计和蜂窝结构相对密度, 可服务于工程中特定技术构件的轻量化.

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Acknowledgements

The work was supported by an Australian Government Research Training Program Scholarship and Australian Research Council Projects (Grant Nos. IH210100048, IH150100006, IH200100010, and DP210101353).

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Authors and Affiliations

  1. Centre for Infrastructure Engineering and Safety (CIES), School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW, 2052, Australia

    Qingya Li  (李清雅), Weizhe Tian  (田伟哲) & Wei Gao  (高伟)

  2. School of Civil and Environmental Engineering, University of Technology Sydney, Sydney, NSW, Australia

    Di Wu  (吴迪)

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  1. Qingya Li  (李清雅)
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  2. Weizhe Tian  (田伟哲)
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  3. Di Wu  (吴迪)
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  4. Wei Gao  (高伟)
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Contributions

Qingya Li and Weizhe Tian proposed the presented idea in discussions with Di Wu and Wei Gao. Qingya Li developed the theoretical formula derivation and performed the numerical computations on the manuscript. Weizhe Tian and Di Wu verified the numerical results by comparing the current results with published literature. Qingya Li, Weizhe Tian, Di Wu, and Wei Gao contributed to interpreting the results. Qingya Li and Weizhe Tian took the lead in writing the manuscript. Di Wu and Wei Gao supervised the development of the work. Qingya Li, Weizhe Tian, Di Wu, and Wei Gao revised and edited the final version.

Corresponding authors

Correspondence to Di Wu  (吴迪) or Wei Gao  (高伟).

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Li, Q., Tian, W., Wu, D. et al. Nonlinear dynamic stability analysis of imperfect architected cellular sandwich plate under impact loading. Acta Mech. Sin. 39, 722333 (2023). https://doi.org/10.1007/s10409-022-22333-x

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