A novel alpha finite element method (αFEM) for exact solution to mechanics problems using triangular and tetrahedral elements

By Guirong Liu, Trung Nguyen-Thoi, Khin Yong Lam. 2008

229 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/a89c6b36a22bf596b0df834313a5a2384fabfda1

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

A node-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates (2010, methodology): “Also, alpha finite element methods (αFEM) have been recently proposed have been recently proposed as an alternative to the NS-FEM and shown to significantly improve the results obtained by conventional and smoothed FEM techniques, at the cost of the introduction of a problem-dependent parameter α [5”
An n‐sided polygonal edge‐based smoothed finite element method (nES‐FEM) for solid mechanics (2010, methodology): “Hence, by combining NS-FEM and FEM with a scale factor ∈[0,1], a new method named as the alpha finite element method ( FEM) [27] is proposed to obtain nearly exact solutions in strain energy using triangular and tetrahedral elements.”
ADDITIONAL PROPERTIES OF THE NODE-BASED SMOOTHED FINITE ELEMENT METHOD (NS-FEM) FOR SOLID MECHANICS PROBLEMS (2009, methodology): “Hence, by combining the NS-FEM and FEM with a scale factor α ∈ [0, 1], a new method named as the alpha Finite Element Method (αFEM) [Liu et al. (2008)] is proposed to obtain nearly exact solutions in strain energy using triangular and tetrahedral elements.”
Free vibration analysis of cracked Mindlin plate using an extended cell-based smoothed discrete shear gap method (XCS-DSG3) (2014, unknown): “In the other front of the development of numerical methods, Liu and Nguyen Thoi Trung [22] have integrated the strain smoothing technique [23] into the FEM to create a series of smoothed FEM (SFEM) such as cell/element-based smoothed FEM (CS-FEM) [24-25], node-based smoothed FEM (NSFEM) [26-28], edg”
A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems (2009, methodology): “The model that gives an upper bound can be one of the following models: the stress equilibrium FEM model [1], the recovery of a statically admissible stress field from displacement FEM model [2–4], the hybrid equilibrium FEM model [5,6], the element-based smoothed finite element method (SFEM) model ”
An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids (2009, methodology): “[24] by combining a scale factor a 2 0; 1 1⁄2 with the NS-FEM and the FEM to give a so-called the alpha Finite Element Method (aFEM).”
An edge-based smoothed finite element method (ES-FEM) for analyzing three-dimensional acoustic problems (2009, methodology): “Introducing the gradient smoothing technique based on edges of elements [17] or faces of elements [19], the gradient component rN is replaced by the smoothed item rN, the smoothed Galerkin weak form for acoustic problem can be written as: Z”
Virtual and smoothed finite elements: A connection and its application to polygonal/polyhedral finite element methods (2015, methodology): “formulated a series of SFEM models: cell-based SFEM (CSFEM) [7], node-based SFEM [29], edge-based SFEM [30], face-based SFEM [31] and alpha-FEM [32].”
A theoretical study on the smoothed FEM (S‐FEM) models: Properties, accuracy and convergence rates (2010, background): “have formulated a series of smoothed FEM (S-FEM) models named as cell-based S-FEM (CS-FEM) [14–23], node-based S-FEM (NS-FEM) [24–26], edge-based S-FEM (ES-FEM) [27–32], face-based (FS-FEM) [33, 34] and alpha-FEM [35] that use linear interpolations.”
A face‐based smoothed finite element method (FS‐FEM) for 3D linear and geometrically non‐linear solid mechanics problems using 4‐node tetrahedral elements (2009, methodology): “[21] by combining a scale factor ∈[0,1] with the NS-FEM and the FEM to give a so-called the alpha Finite Element Method ( FEM).”