Comparison of enriched meshless finite volume and element free Galerkin methods for the analysis of heterogeneous media

Davoudi-Kia, Abdullah; Fallah, N.

doi:10.1007/s00366-017-0573-3

Cited by 6 publications

(1 citation statement)

References 32 publications

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“…Whereas the Atluri and Shen [397] approach uses overlapping control volumes, the meshless finite volume method developed by Ebrahimnejad et al [414,415,417] employs non-overlapping control volumes. The method has been applied to 2-D elasticity with adaptive mesh refinement, and was later extended to problems with material discontinuities [419,420], to free vibration analysis of laminated composite plates [416,418], and to fractures in orthotropic media [421].…”

Section: Meshless Finite Volume Methodsmentioning

confidence: 99%

Thirty years of the finite volume method for solid mechanics

Cardiff,

Demirdžić

2018

Preprint

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Since early publications in the late 1980s and early 1990s, the finite volume method has been shown suitable for solid mechanics analyses. At present, there are several flavours of the method, including "cell-centred", "staggered", "vertex-centred", "periodic heterogenous microstructural", "Godunov-type", "matrix-free", "meshless", as well as others. This article gives an overview, historical perspective, comparison and critical analysis of the different approaches, including their relative strengths, weaknesses, similarities and dissimilarities, where a close comparison with the de facto standard for computational solid mechanics, the finite element method, is given. The article finishes with a look towards future research directions and steps required for finite volume solid mechanics to achieve widespread acceptance.

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