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The Time-Dependent Von Kármán Shell Equation as a Limit of Three-Dimensional Nonlinear Elasticity

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Abstract

The asymptotic behaviour of solutions of three-dimensional nonlinear elastodynamics in a thin shell is considered, as the thickness h of the shell tends to zero. Given the appropriate scalings of the applied force and of the initial data in terms of h, it’s verified that three-dimesional solutions of the nonlinear elastodynamic equations converge to solutions of the time-dependent von KMorármMorán equations or dynamic linear equations for shell of arbitrary geometry.

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Authors and Affiliations

  1. Department of Mathematical Science, Tsinghua University, Bei**g, 100084, China

    Yizhao Qin

  2. Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Bei**g, 100190, China

    Peng-Fei Yao

  3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Bei**g, 100049, China

    Peng-Fei Yao

Authors
  1. Yizhao Qin
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  2. Peng-Fei Yao
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Corresponding authors

Correspondence to Yizhao Qin or Peng-Fei Yao.

Additional information

This research was supported by the National Science Foundation of China under Grant Nos. 61473126 and 61573342, and Key Research Program of Frontier Sciences, CAS, under Grant No. QYZDJ-SSW-SYS011.

This paper was recommended for publication by Editor HU **aoming.

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Qin, Y., Yao, PF. The Time-Dependent Von Kármán Shell Equation as a Limit of Three-Dimensional Nonlinear Elasticity. J Syst Sci Complex 34, 465–482 (2021). https://doi.org/10.1007/s11424-020-9146-4

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  • DOI: https://doi.org/10.1007/s11424-020-9146-4

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