Some advances in high-performance finite element methods

Purpose The purpose of this paper is to give a review on the newest developments of high-performance finite element methods (FEMs), and exhibit the recent contributions achieved by the authors’ group, especially showing some breakthroughs against inherent difficulties existing in the traditional FEM...

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Published inEngineering computations Vol. 36; no. 8; pp. 2811 - 2834
Main Authors Cen, Song, Wu, Cheng Jin, Li, Zhi, Shang, Yan, Li, Chenfeng
Format Journal Article
LanguageEnglish
Published Bradford Emerald Publishing Limited 15.10.2019
Emerald Group Publishing Limited
Subjects
Crack propagation
Elasticity
Exact solutions
Finite element method
Mathematical models
Mindlin plates
Propagation
Researchers
Stress concentration
Hybrid displacement-function (HDF)
Hybrid stress-function (HSF)
Fundamental analytical solutions
Improved unsymmetric finite element method
Mesh distortion
High-performance finite element methods
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Summary:Purpose The purpose of this paper is to give a review on the newest developments of high-performance finite element methods (FEMs), and exhibit the recent contributions achieved by the authors’ group, especially showing some breakthroughs against inherent difficulties existing in the traditional FEM for a long time. Design/methodology/approach Three kinds of new FEMs are emphasized and introduced, including the hybrid stress-function element method, the hybrid displacement-function element method for Mindlin–Reissner plate and the improved unsymmetric FEM. The distinguished feature of these three methods is that they all apply the fundamental analytical solutions of elasticity expressed in different coordinates as their trial functions. Findings The new FEMs show advantages from both analytical and numerical approaches. All the models exhibit outstanding capacity for resisting various severe mesh distortions, and even perform well when other models cannot work. Some difficulties in the history of FEM are also broken through, such as the limitations defined by MacNeal’s theorem and the edge-effect problems of Mindlin–Reissner plate. Originality/value These contributions possess high value for solving the difficulties in engineering computations, and promote the progress of FEM.
ISSN:0264-4401
1758-7077
DOI:10.1108/EC-10-2018-0479