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Engineering with Computers
Published in: Engineering with Computers 1/2023

16-11-2022 | Original Article

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

Authors: Changkye Lee, Indra Vir Singh, Sundararajan Natarajan

Published in: Engineering with Computers | Issue 1/2023

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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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Footnotes
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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Metadata
Title
A cell-based smoothed finite-element method for gradient elasticity
Authors
Changkye Lee
Indra Vir Singh
Sundararajan Natarajan
Publication date
16-11-2022
Publisher
Springer London
Published in
Engineering with Computers / Issue 1/2023
Print ISSN: 0177-0667
Electronic ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-022-01734-2

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