Adaptive finite element analysis of free vibration of elastic membranes via element energy projection technique
ISSN: 0264-4401
Article publication date: 29 March 2021
Issue publication date: 22 September 2021
Abstract
Purpose
A general strategy is developed for adaptive finite element (FE) analysis of free vibration of elastic membranes based on the element energy projection (EEP) technique.
Design/methodology/approach
By linearizing the free vibration problem of elastic membranes into a series of linear equivalent problems, reliable a posteriori point-wise error estimator is constructed via EEP super-convergent technique. Hierarchical local mesh refinement is incorporated to better deal with tough problems.
Findings
Several classical examples were analyzed, confirming the effectiveness of the EEP-based error estimation and overall adaptive procedure equipped with a local mesh refinement scheme. The computational results show that the adaptively-generated meshes reasonably catch the difficulties inherent in the problems and the procedure yields both eigenvalues with required accuracy and mode functions satisfying user-preset error tolerance in maximum norm.
Originality/value
By reasonable linearization, the linear-problem-based EEP technique is successfully transferred to two-dimensional eigenproblems with local mesh refinement incorporated to effectively and flexibly deal with singularity problems. The corresponding adaptive strategy can produce both eigenvalues with required accuracy and mode functions satisfying user-preset error tolerance in maximum norm and thus can be expected to apply to other types of eigenproblems.
Keywords
Citation
Sun, H. and Yuan, S. (2021), "Adaptive finite element analysis of free vibration of elastic membranes via element energy projection technique", Engineering Computations, Vol. 38 No. 9, pp. 3492-3516. https://doi.org/10.1108/EC-09-2020-0511
Publisher
:Emerald Publishing Limited
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