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Polyhedral elements using an edge-based smoothed finite element method for nonlinear elastic deformations of compressible and nearly incompressible materials

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Abstract

Polyhedral elements with an arbitrary number of nodes or non-planar faces, obtained with an edge-based smoothed finite element method, retain good geometric adaptability and accuracy in solution. This work is intended to extend the polyhedral elements to nonlinear elastic analysis with finite deformations. In order to overcome the volumetric locking problem, a smoothing domain-based selective smoothed finite element method scheme and a three-field-mixed cell-based smoothed finite element method with nodal cells were developed. Using several numerical examples, their performance and the accuracy of their solutions were examined, and their effectiveness for practical applications was demonstrated as well.

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Abbreviations

FEM:

Finite element method

S-FEM:

Smoothed finite element method

CS-FEM:

Cell-based smoothed finite element method

CS-FEM-FC:

Facial cell-based smoothed finite element method

CS-FEM-ND:

Nodal cell-based smoothed finite element method

NS-FEM:

Node-based smoothed finite element method

ES-FEM:

Edge-based smoothed finite element method

FS-FEM:

Face-based smoothed finite element method

ES/CS(EL)-FEM:

Smoothing domain-based selective edge/elemental cell-based smoothed finite element method

ES/NS-FEM:

Smoothing domain-based selective edge/node-based smoothed finite element method

MX CS-FEM-ND:

Nodal cell-based smoothed finite element method with three field mixed formulation

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Acknowledgements

The authors gratefully acknowledge the grant from the National Research Foundation of Korea (Grant No. K2015R1A2A1A15056263) in the course of this study. Kind suggestions and comments of Professor Dongwoo Sohn of the Department of Mechanical Engineering, Korea Maritime and Ocean University are sincerely appreciated.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon, 305-701, Republic of Korea

    Chan Lee, Hobeom Kim, Jungdo Kim & Seyoung Im

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  1. Chan Lee
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  2. Hobeom Kim
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  3. Jungdo Kim
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  4. Seyoung Im
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Correspondence to Seyoung Im.

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Lee, C., Kim, H., Kim, J. et al. Polyhedral elements using an edge-based smoothed finite element method for nonlinear elastic deformations of compressible and nearly incompressible materials. Comput Mech 60, 659–682 (2017). https://doi.org/10.1007/s00466-017-1433-0

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