A frequency error estimation for isogeometric analysis of Kirchhoff–Love cylindrical shells

Abstract

A frequency error estimation is presented for the isogeometric free vibration analysis of Kirchhoff–Love cylindrical shells using both quadratic and cubic basis functions. By analyzing the discrete isogeometric equations with the aid of harmonic wave assumption, the frequency error measures are rationally derived for the quadratic and cubic formulations for Kirchhoff–Love cylindrical shells. In particular, the governing relationship of the continuum frequency for Kirchhoff–Love cylindrical shells is naturally embedded into the frequency error measures without the need of explicit frequency expressions, which usually are not trivial for the shell problems. In accordance with these theoretical findings, the 2nd and 4th orders of frequency accuracy are attained for the isogeometric schemes using quadratic and cubic basis functions, respectively. Numerical results not only thoroughly verify the theoretical convergence rates of frequency solutions, but also manifest an excellent magnitude match between numerical and theoretical frequency errors for the isogeometric free vibration analysis of Kirchhoff–Love cylindrical shells.

Graphical abstract

Keywords

isogeometric analysis / Kirchhoff–Love cylindrical shell / free vibration / frequency error / convergence

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Acknowledgements

The support of this work by the National Natural Science Foundation of China (Grant Nos. 12072302 and 11772280) and the Natural Science Foundation of Fujian Province of China (No. 2021J02003) is gratefully acknowledged.

Electronic Supplementary Material

Supplementary material is available in the online version of this article at https://doi.org/10.1007/s11709-023-0006-x and is accessible for authorized users.

Conflict of Interest

The authors declare that they have no conflict of interest.

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