Polyhedral elements using an edge-based smoothed finite element method for nonlinear elastic deformations of compressible and nearly incompressible materials

Lee, Chan; Kim, Hobeom; Kim, Jungdo; Im, Seyoung

doi:10.1007/s00466-017-1433-0

Cited by 14 publications

(6 citation statements)

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“…[ 15 ] and Lee et al. [ 38 ], the last one has been taken as a reference for the analysis of the following study case. The internal radius of the torus is r i = 8 m, the external radius is r O = 10 m for a resulting radius of the circular section of r int = 1 m. The uniform vertical pressure is applied to a specific span of the external surface considering a double span of in the plane x-y and y-z, as shown in Figure 11(a) and (b) .…”

Section: Numerical Resultsmentioning

confidence: 99%

Unified three-dimensional finite elements for large strain analysis of compressible and nearly incompressible solids

Pagani,

Chiaia,

Filippi

et al. 2023

Mechanics of Advanced Materials and Structures

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This work proposes a displacement-based finite element model for large strain analysis of isotropic compressible and nearly-incompressible hyperelastic materials. Constitutive law is written in terms of invariants of the right Cauchy-Green tensor; coupled and decoupled formulations of strain energy functions are presented, whereas a penalty function is used to impose an incompressibility constraint. Based on a total Lagrangian formulation, the nonlinear governing equations are thus obtained by employing the principle of virtual displacements. Analytic expression of both internal forces vector and tangent matrix of linear and high-order hexahedral finite elements are derived by adopting a three-dimensional formalism based on the Carrera Unified Formulation. Popular benchmark problems in hyperelasticity are analyzed to establish the capabilities of the present implementation of fully-nonlinear solid elements in the case of compressible and nearly-incompressible beams, cylindrical shells, and curved structures.

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Section: Numerical Resultsmentioning

confidence: 99%

Unified three-dimensional finite elements for large strain analysis of compressible and nearly incompressible solids

Pagani,

Chiaia,

Filippi

et al. 2023

Mechanics of Advanced Materials and Structures

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show abstract

“…and Îi = I i /N. (22) By using the normalized index, a weighted average of the error indicator is given by…”

Section: The Procedures For Improving Edge-based Finite Element Solut...mentioning

confidence: 99%

“…The S-FEM is a relatively recently proposed method among the several techniques mentioned above and has been successfully applied to various engineering problem [12][13][14][15][16][17][18][19][20][21][22][23][24]. In S-FEM, the strain smoothing technique originally developed for the Galerkin mesh-free method is applied to the FEM, and constant strain fields are constructed in newly defined smoothing domains [12,13].…”

Section: Introductionmentioning

confidence: 99%

“…Depending on how the smoothing domain is defined, nodebased, cell-based, edge-based, and face-based smoothed FEM have been proposed. Each S-FEM has different characteristics and performance depending on the smoothing domain, and it is generally known that edge-based S-FEM (ES-FEM) is the most effective [19][20][21][22]. The solution accuracy of the ES-FEM is more accurate compared to the ST-FEM, especially when the same lower order element mesh is used, and unlike other methods such as EX-FEM and EN-FEM, no additional degrees of freedoms (DOFs) are required [6,8,11,25].…”

Section: Introductionmentioning

confidence: 99%

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Strategy to Improve Edge-Based Smoothed Finite Element Solutions Using Enriched 2D Solid Finite Elements

Kim

2021

Applied Sciences

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In this paper, we present an automatic procedure that enhances the solution accuracy of edge-based smoothed 2D solid finite elements (three-node triangular and four-node quadrilateral elements). To obtain an enhanced solution, an adaptive enrichment scheme that uses enriched 2D solid finite elements and can effectively improve solution accuracy by applying cover functions adaptively without mesh-refinement is adopted in this procedure. First, the error of the edge-based finite element solution is estimated using a devised error estimation method, and appropriate cover functions are assigned for each node. While the edge-based smoothed finite elements provide piecewise constant strain fields, the proposed enrichment scheme uses the enriched finite elements to obtain a higher order strain field within the finite elements. Through various numerical examples, we demonstrate the accuracy improvement and efficiency achieved.

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“…Apart from that, the shape functions consist of polynomials, which are easier to evaluate compared to the conforming PFEM based on barycentric coordinates. Extension of the method to 3D can be seen in literatures [78][79][80].…”

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confidence: 99%

A Brief Review on Polygonal/Polyhedral Finite Element Methods

Perumal

2018

Mathematical Problems in Engineering

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This paper provides brief review on polygonal/polyhedral finite elements. Various techniques, together with their advantages and disadvantages, are listed. A comparison of various techniques with the recently proposed Virtual Node Polyhedral Element (VPHE) is also provided. This review would help the readers to understand the various techniques used in formation of polygonal/polyhedral finite elements.

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Polyhedral elements using an edge-based smoothed finite element method for nonlinear elastic deformations of compressible and nearly incompressible materials

Cited by 14 publications

References 50 publications

Unified three-dimensional finite elements for large strain analysis of compressible and nearly incompressible solids

Unified three-dimensional finite elements for large strain analysis of compressible and nearly incompressible solids

Strategy to Improve Edge-Based Smoothed Finite Element Solutions Using Enriched 2D Solid Finite Elements

A Brief Review on Polygonal/Polyhedral Finite Element Methods

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