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

Y. Li and G.R. Liu

Applied Mathematics and Computation, 2019, vol. 352, issue C, 30-58

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.

Keywords: High-order NS-FEM; Strain field reconstruction; Node-based smoothing; Close-to-exact stiffness; Temporally stability (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:352:y:2019:i:c:p:30-58

DOI: 10.1016/j.amc.2019.01.043

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