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A novel node-based smoothed finite element method with linear strain fields for static, free and forced vibration analyses of solids

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  • Li, Y.
  • Liu, G.R.

Abstract

This paper presents a novel node-based smoothed finite element method (NS-FEM) with a higher order strain field. It uses piecewise linear displacements on 3-node triangular elements, together with strain field which is also linear but over the node-based smoothed domains. This high-order strain NS-FEM is fundamentally different from the standard FEM that uses piecewise linear displacement and constants strain fields. In our high-order strain NS-FEM, the smoothed strains are expressed with complete order of polynomials which have coefficients, linear and high-order terms. This is also different from the smoothed strain used in the existing standard NS-FEM which is a constant obtained by a generalized smoothing technique. The unknown coefficients in assumed strain functions can be uniquely determined by linearly independent weight functions. This is because the smoothed strain and compatible strain within a local region are equal in an integral sense when weighted by continuous functions. We present, with proofs on convergence, two versions of high-order strain NS-FEMs which are termed as: NS-FEM-1 that uses 1st order smoothed strains and NS-FEM-2 that uses 2nd order smoothed strains. The new developed high-order strain NS-FEM is applied for static, free and forced vibration analyses of solids, and our numerical results support our theorems.

Suggested Citation

  • Li, Y. & Liu, G.R., 2019. "A novel node-based smoothed finite element method with linear strain fields for static, free and forced vibration analyses of solids," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 30-58.
    • Handle: RePEc:eee:apmaco:v:352:y:2019:i:c:p:30-58
    DOI: 10.1016/j.amc.2019.01.043
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    Cited by:

    1. Chai, Yingbin & Li, Wei & Liu, Zuyuan, 2022. "Analysis of transient wave propagation dynamics using the enriched finite element method with interpolation cover functions," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    2. Liu, Mingyang & Gao, Guangjun & Khoo, Boo Cheong & He, Zhenhu & Jiang, Chen, 2022. "A cell-based smoothed finite element model for non-Newtonian blood flow," Applied Mathematics and Computation, Elsevier, vol. 435(C).
    3. Meijun Zhou & Jiayu Qin & Zenan Huo & Fabio Giampaolo & Gang Mei, 2022. "epSFEM: A Julia-Based Software Package of Parallel Incremental Smoothed Finite Element Method (S-FEM) for Elastic-Plastic Problems," Mathematics, MDPI, vol. 10(12), pages 1-25, June.

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