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Smoothed Finite Element Methods (S-FEM): An Overview and Recent Developments

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Abstract

The smoothed finite element methods (S-FEM) are a family of methods formulated through carefully designed combinations of the standard FEM and some of the techniques from the meshfree methods. Studies have proven that S-FEM models behave softer than the FEM counterparts using the same mesh structure, often produce more accurate solutions, higher convergence rates, and much less sensitivity to mesh distortion. They work well with triangular or tetrahedral mesh that can be automatically generated, and hence are ideal for automated computations and adaptive analyses. Some S-FEM models can also produce upper bound solution for force driving problems, which is an excellent unique complementary feature to FEM. Because of these attractive properties, S-FEM has been applied to numerous problems in the disciplines of material mechanics, biomechanics, fracture mechanics, plates and shells, dynamics, acoustics, heat transfer and fluid–structure interactions. This paper reviews the developments and applications of the S-FEM in the past ten years. We hope this review can shed light on further theoretical development of S-FEM and more complex practical applications in future.

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Notes

  1. Some basic S-FEM source code can be found at www.ase.uc.edu/~liugr.

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Acknowledgements

This work is partially supported by US NSF Grant under the Award No. DMS-1214188.

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  1. Thayer School of Engineering, Dartmouth College, Hanover, NH, 03755, USA

    W. Zeng

  2. Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati, 2851 Woodside Dr., Cincinnati, OH, 45221, USA

    G. R. Liu

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Zeng, W., Liu, G.R. Smoothed Finite Element Methods (S-FEM): An Overview and Recent Developments. Arch Computat Methods Eng 25, 397–435 (2018). https://doi.org/10.1007/s11831-016-9202-3

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