A novel twice-interpolation finite element method for solid mechanics problems

Formulation and numerical evaluation of a novel twice-interpolation finite element method （TFEM） is presented for solid mechanics problems. In this method, the trial function for Galerkin weak form is constructed through two stages of consecutive interpolation. The primary interpolation follows exac...

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Veröffentlicht in:Acta mechanica Sinica Jg. 26; H. 2; S. 265 - 278
Hauptverfasser: Zheng, C., Wu, S. C., Tang, X. H., Zhang, J. H.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer-Verlag 01.05.2010
Schlagworte:
Classical and Continuum Physics
Computational Intelligence
Construction
Convergence
Engineering
Engineering Fluid Dynamics
Finite element method
Galerkin
Interpolation
Mathematical analysis
Mathematical models
Research Paper
Solid mechanics
Theoretical and Applied Mechanics
固体力学
数值评价
有限元方法
有限元法
有限元程序
节点应力
Twice-interpolation finite element method
Stress smoothing
Volumetric locking
Mesh distortion
ISSN:0567-7718, 1614-3116
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Zusammenfassung:Formulation and numerical evaluation of a novel twice-interpolation finite element method （TFEM） is presented for solid mechanics problems. In this method, the trial function for Galerkin weak form is constructed through two stages of consecutive interpolation. The primary interpolation follows exactly the same procedure of standard FEM and is further reproduced according to both nodal values and averaged nodal gradients obtained from primary interpolation. The trial functions thus constructed have continuous nodal gradients and contain higher order polynomial without increasing total freedoms. Several benchmark examples and a real dam problem are used to examine the TFEM in terms of accuracy and convergence. Compared with standard FEM, TFEM can achieve significantly better accuracy and higher convergence rate, and the continuous nodal stress can be obtained without any smoothing operation. It is also found that TFEM is insensitive to the quality of the elemental mesh. In addition, the present TFEM can treat the incompressible material without any modification.
Bibliographie:Twice-interpolation finite element method·Stress smoothing · Volumetric locking · Mesh distortion
O34
O241.82
11-2063/O3
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SourceType-Scholarly Journals-1
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ISSN:0567-7718
1614-3116
DOI:10.1007/s10409-009-0265-3