2016
DOI: 10.1002/nme.5337
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F‐bar aided edge‐based smoothed finite element method using tetrahedral elements for finite deformation analysisof nearly incompressible solids

Abstract: Summary A new smoothed finite element method (S‐FEM) with tetrahedral elements for finite strain analysis of nearly incompressible solids is proposed. The proposed method is basically a combination of the F‐bar method and edge‐based S‐FEM with tetrahedral elements (ES‐FEM‐T4) and is named ‘F‐barES‐FEM‐T4’. F‐barES‐FEM‐T4 inherits the accuracy and shear locking‐free property of ES‐FEM‐T4. At the same time, it also inherits the volumetric locking‐free property of the F‐bar method. The isovolumetric part of the d… Show more

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Cited by 38 publications
(14 citation statements)
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“…Similar ideas were also explored by Pakravana and Krysl, 73 with mean energy stabilization mechanisms. Some connections also exist between these methods and the more recent work of Onishi et al 74 (iv) de Souza Neto et al [75][76][77][78] developed the F-bar strategy to stabilize nonlinear finite element computations on tetrahedra. (v) Very recently, Lew et al [79][80][81][82][83] proposed and proved stability for a discontinuous Galerkin method applicable to general grids (hence tetrahedral elements) in the static case.…”
Section: Overview Of Recent Work On Tetrahedral Finite Elementsmentioning
confidence: 99%
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“…Similar ideas were also explored by Pakravana and Krysl, 73 with mean energy stabilization mechanisms. Some connections also exist between these methods and the more recent work of Onishi et al 74 (iv) de Souza Neto et al [75][76][77][78] developed the F-bar strategy to stabilize nonlinear finite element computations on tetrahedra. (v) Very recently, Lew et al [79][80][81][82][83] proposed and proved stability for a discontinuous Galerkin method applicable to general grids (hence tetrahedral elements) in the static case.…”
Section: Overview Of Recent Work On Tetrahedral Finite Elementsmentioning
confidence: 99%
“…where F el and F p are the elastic and inelastic components of the deformation gradient, respectively, and the latter is associated to an intermediate plastic configuration/deformation. From (73), we can define the plastic right Cauchy-Green strain tensor as C = (F ) T F (74) and the elastic left Cauchy-Green strain tensor as…”
Section: Figurementioning
confidence: 99%
“…Compared with alternatives such as the stabilized nodal integration [14,19,21,29,38] and smoothed edges [23,37] and faces [33], no densitification occurs (cf. Fig.…”
Section: Resultsmentioning
confidence: 99%
“…with | | = 1 + 2 + 3 . In (37), e is the assembling operation, described by Hughes [25] with Ω e b being the reference configuration for element e. In terms of components, we have…”
Section: Stress-displacement Formulation For the Tetrahedronmentioning
confidence: 99%
“…Moreover, CS-FEM does not require the shape function derivatives or high generosity of program and is insensitive to mesh distortion because of the absence of isoparametric mapping. CS-FEM has been successfully extended into dynamical control of piezoelectric sensors and actuators, topological optimization of linear piezoelectric micromotor, and analysis of static behaviors, frequency, and defects of piezoelectric structures [33][34][35][36][37][38][39][40][41][42][43]. Due to its versatility, CS-FEM becomes a simple and effective numerical tool to solve numerous electric and mechanical physical problems.…”
Section: Introductionmentioning
confidence: 99%