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A non-classical model for circular cylindrical thin shells incorporating microstructure and surface energy effects

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Abstract

A non-classical model for circular cylindrical thin shells is developed by using a modified couple stress theory and a surface elasticity theory. The equations of motion and boundary conditions are simultaneously obtained by a variational formulation based on Hamilton’s principle, which provides a unified treatment of the microstructure and surface energy effects. The new non-classical shell model contains one material length scale parameter to capture the microstructure effect and three surface elastic constants to describe the surface energy effect. The current model includes the shell models considering the microstructure effect only or the surface energy effect alone as special cases. Also, the newly developed shell model reduces to the classical circular cylindrical Love–Kirchhoff thin shell model when both the microstructure and surface energy effects are suppressed. In addition, it recovers the non-classical model for Kirchhoff plates incorporating the microstructure and surface energy effects when the shell radius tends to infinity. To illustrate the new model, the static bending and free vibration problems of a simply supported closed circular cylindrical shell and of an open circular cylindrical shell with free edge boundary conditions are analytically solved by directly applying the model. For the static bending problem in each case, the numerical results show that the shell deflection predicted by the current model is smaller than that predicted by the classical model, and the difference is significant when the shell is very thin but diminishes as the shell thickness increases. For the free vibration problem in each case, it is found that the natural frequency predicted by the new model is higher than that predicted by its classical counterpart, and the difference is large only for very thin shells.

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Acknowledgements

GYZ gratefully acknowledges the support by the National Natural Science Foundation of China [Grant # 12002086] and the Fundamental Research Funds for the Central Universities [Grant # 2242020R10027]. The authors would like to thank Professor George Weng and one anonymous reviewer for their encouragement and helpful comments on an earlier version of the paper. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the U.S. Army.

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Authors and Affiliations

  1. Jiangsu Key Laboratory of Engineering Mechanics, School of Civil Engineering, Southeast University, Nanjing, 210096, Jiangsu, China

    G. Y. Zhang

  2. Department of Mechanical Engineering, Lyle School of Engineering, Southern Methodist University, Dallas, TX, 75275, USA

    X.-L. Gao

  3. US Army CCDC Armaments Center, Benét Laboratories, Watervliet, NY, 12189, USA

    A. G. Littlefield

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  1. G. Y. Zhang
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Correspondence to X.-L. Gao.

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Zhang, G.Y., Gao, XL. & Littlefield, A.G. A non-classical model for circular cylindrical thin shells incorporating microstructure and surface energy effects. Acta Mech 232, 2225–2248 (2021). https://doi.org/10.1007/s00707-020-02873-7

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  • DOI: https://doi.org/10.1007/s00707-020-02873-7

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