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A cell-based smoothed finite-element method for gradient elasticity

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Abstract

In this paper, the cell-based smoothed finite-element method (CS-FEM) is proposed for solving boundary value problems of gradient elasticity in two and three dimensions. The salient features of the CS-FEM are: it does not require an explicit form of the shape functions and alleviates the need for iso-parametric mapping. The main idea is to sub-divide the element into simplicial sub-cells and to use a constant smoothing function in each cell to compute the gradients. This new gradient is then used to compute the bilinear/linear form. The robustness of the method is demonstrated with problems involving smooth and singular solutions in both two and three dimensions. Numerical results show that the proposed framework is able to yield accurate results. The influence of the internal length scale on the stress concentration is studied systematically for a case of a plate with a hole and a plate with an edge crack in two and three dimensions.

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Notes

  1. Note that, although the aforementioned non-homogeneous Dirichlet BCs are derived from the finite elasticity approximation, we simply employ them as prescribed displacements boundary conditions for this test.

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Acknowledgements

Changkye Lee would like to thank the support by Basic Science Research Program through the National Research Foundation (NRF) funded by Korea Ministry of Education (No. 2016R1A6A1A0312812).

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Authors and Affiliations

  1. University Core Research Center for Disaster-free & Safe Ocean City Construction, Dong-A University, Busan, 49315, South Korea

    Changkye Lee

  2. Department of Mechanical Engineering, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, 247667, India

    Indra Vir Singh

  3. Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, Tamil Nadu, 600036, India

    Sundararajan Natarajan

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  1. Changkye Lee
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  2. Indra Vir Singh
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  3. Sundararajan Natarajan
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Correspondence to Sundararajan Natarajan.

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Lee, C., Singh, I.V. & Natarajan, S. A cell-based smoothed finite-element method for gradient elasticity. Engineering with Computers 39, 925–942 (2023). https://doi.org/10.1007/s00366-022-01734-2

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