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An hp-version adaptive finite element algorithm for eigensolutions of moderately thick circular cylindrical shells via error homogenisation and higher-order interpolation

Yongliang Wang (School of Mechanics and Civil Engineering, State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology, Beijing, China)
Jianhui Wang (School of Mechanics and Civil Engineering, China University of Mining and Technology, Beijing, China)

Engineering Computations

ISSN: 0264-4401

Article publication date: 13 December 2021

Issue publication date: 3 May 2022

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Abstract

Purpose

This study presents a novel hp-version adaptive finite element method (FEM) to investigate the high-precision eigensolutions of the free vibration of moderately thick circular cylindrical shells, involving the issues of variable geometrical factors, such as the thickness, circumferential wave number, radius and length.

Design/methodology/approach

An hp-version adaptive finite element (FE) algorithm is proposed for determining the eigensolutions of the free vibration of moderately thick circular cylindrical shells via error homogenisation and higher-order interpolation. This algorithm first develops the established h-version mesh refinement method for detecting the non-uniform distributed optimised meshes, where the error estimation and element subdivision approaches based on the superconvergent patch recovery displacement method are introduced to obtain high-precision solutions. The errors in the vibration mode solutions in the global space domain are homogenised and approximately the same. Subsequently, on the refined meshes, the algorithm uses higher-order shape functions for the interpolation of trial displacement functions to reduce the errors quickly, until the solution meets a pre-specified error tolerance condition. In this algorithm, the non-uniform mesh generation and higher-order interpolation of shape functions are suitable for addressing the problem of complex frequencies and modes caused by variable structural geometries.

Findings

Numerical results are presented for moderately thick circular cylindrical shells with different geometrical factors (circumferential wave number, thickness-to-radius ratio, thickness-to-length ratio) to demonstrate the effectiveness, accuracy and reliability of the proposed method. The hp-version refinement uses fewer optimised meshes than h-version mesh refinement, and only one-step interpolation of the higher-order shape function yields the eigensolutions satisfying the accuracy requirement.

Originality/value

The proposed combination of methodologies provides a complete hp-version adaptive FEM for analysing the free vibration of moderately thick circular cylindrical shells. This algorithm can be extended to general eigenproblems and geometric forms of structures to solve for the frequency and mode quickly and efficiently.

Keywords

Acknowledgements

The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (grants 41877275 and 51608301), Beijing Natural Science Foundation (grant L212016), Yue Qi Young Scholar Project Foundation of China University of Mining and Technology, Beijing (grant 2019QN14), Fundamental Research Funds for the Central Universities, Ministry of Education of China (grant 2019QL02), Teaching Reform and Research Projects of Undergraduate Education of China University of Mining and Technology, Beijing (grants J210613, J200709 and J190701) and the Open Fund of Tianjin Key Lab of Soft Soil Characteristics and Engineering Environment (grant 2017SCEEKL003).

Citation

Wang, Y. and Wang, J. (2022), "An hp-version adaptive finite element algorithm for eigensolutions of moderately thick circular cylindrical shells via error homogenisation and higher-order interpolation", Engineering Computations, Vol. 39 No. 5, pp. 1874-1901. https://doi.org/10.1108/EC-07-2021-0430

Publisher

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Emerald Publishing Limited

Copyright © 2021, Emerald Publishing Limited

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