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A temporal stable node-based smoothed finite element method for three-dimensional elasticity problems

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Abstract

A stabilized node-based smoothed finite element method (sNS-FEM) is formulated for three-dimensional (3-D) elastic-static analysis and free vibration analysis. In this method, shape functions are generated using finite element method by adopting four-node tetrahedron element. The smoothed Galerkin weak form is employed to create discretized system equations, and the node-based smoothing domains are used to perform the smoothing operation and the numerical integration. The stabilization term for 3-D problems is worked out, and then propose a strain energy based empirical rule to confirm the stabilization parameter in the formula. The accuracy and stability of the sNS-FEM solution are studied through detailed analyses of benchmark cases and actual elastic problems. In elastic-static analysis, it is found that sNS-FEM can provide higher accuracy in displacement and reach smoother stress results than the reference approaches do. And in free vibration analysis, the spurious non-zero energy modes can be eliminated effectively owing to the fact that sNS-FEM solution strengths the original relatively soft node-based smoothed finite element method (NS-FEM), and the natural frequency values provided by sNS-FEM are confirmed to be far more accurate than results given by traditional methods. Thus, the feasibility, accuracy and stability of sNS-FEM applied on 3-D solid are well represented and clarified.

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Acknowledgments

The support of Key Project of NSFC (61232014), National Science Foundation of China (11002053), China Postdoctoral Science Foundation (2013M531780), National Basic Research Program of China (2010CB328005), State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology (GZ1212) are gratefully acknowledged.

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Authors and Affiliations

  1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, People’s Republic of China

    H. Feng, X. Y. Cui, G. Y. Li & S. Z. Feng

  2. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024, People’s Republic of China

    X. Y. Cui

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  1. H. Feng
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  2. X. Y. Cui
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  3. G. Y. Li
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  4. S. Z. Feng
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Correspondence to G. Y. Li.

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Feng, H., Cui, X.Y., Li, G.Y. et al. A temporal stable node-based smoothed finite element method for three-dimensional elasticity problems. Comput Mech 53, 859–876 (2014). https://doi.org/10.1007/s00466-013-0936-6

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  • DOI: https://doi.org/10.1007/s00466-013-0936-6

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