A new strain smoothing method for triangular and tetrahedral finite elements

Lee, Chaemin; Lee, Phill-Seung

doi:10.1016/j.cma.2018.07.022

Cited by 35 publications

(20 citation statements)

References 32 publications

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“…This study only examined the four-node finite element. However, the proposed concept can be extended to various types of finite elements, including solid, plate, and shell elements [31][32][33][34][35][36]. The conduct of research on such elements in the future will certainly be advantageous.…”

Section: Discussionmentioning

confidence: 99%

Self-updated four-node finite element using deep learning

2021

Self Cite

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This paper introduces a new concept called self-updated finite element (SUFE). The finite element (FE) is activated through an iterative procedure to improve the solution accuracy without mesh refinement. A mode-based finite element formulation is devised for a four-node finite element and the assumed modal strain is employed for bending modes. A search procedure for optimal bending directions is implemented through deep learning for a given element deformation to minimize shear locking. The proposed element is called a self-updated four-node finite element, for which an iterative solution procedure is developed. The element passes the patch and zero-energy mode tests. As the number of iterations increases, the finite element solutions become more and more accurate, resulting in significantly accurate solutions with a few iterations. The SUFE concept is very effective, especially when the meshes are coarse and severely distorted. Its excellent performance is demonstrated through various numerical examples.

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Section: Discussionmentioning

confidence: 99%

Self-updated four-node finite element using deep learning

2021

Self Cite

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“…Strain‐smoothed element method for the three‐node triangular element: A, strains of a target element and its neighbouring elements; B, strain smoothing between the target and each neighbouring element; C, three Gauss integration points in the natural coordinate system ( r , s ); D, construction of the smoothed strain field through Gauss points (after Lee and Lee ) [Colour figure can be viewed at wileyonlinelibrary.com]…”

Section: Explicit Edge‐based Smoothed Pfemmentioning

confidence: 99%

“…To overcome the volumetric locking problem caused by the strain constant in three‐node triangular elements, a simple and effective strain smoothing method (the strain‐smoothed element method) for three‐node triangular elements, developed by Lee and Lee was employed in the original PFEM. Using the adopted strain smoothing method, the strains of all neighbouring elements are fully used in the strain smoothing process.…”

Section: Explicit Edge‐based Smoothed Pfemmentioning

confidence: 99%

“…According to Lee and Lee , the three‐node triangular elements subject to the edge‐based strain smoothing method pass all the basic tests (patch, isotropy, and zero‐energy mode tests). Thus, the edge‐based strain smoothing method shows best performance among the various S‐FEM methods . We thus selected this method to improve the accuracy of the PFEM calculation.…”

Section: Explicit Edge‐based Smoothed Pfemmentioning

confidence: 99%

“…In fact, the implementation of strain smoothing in the original PFEM has already been conducted by Zhang et al implicitly and Yuan et al explicitly, adopting a node‐based strain smoothing technique for nodal integration proposed by Liu et al. However, among various smoothing methods, the edge‐based S‐FEM is generally known to be the most effective . Thus, the edge‐based strain smoothing technique is worth incorporating into original PFEM to improve accuracy while simultaneously reducing the computational cost.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An edge‐based strain smoothing particle finite element method for large deformation problems in geotechnical engineering

Jin

Yuan

Yin

et al. 2020

Num Anal Meth Geomechanics

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Summary To solve large deformation geotechnical problems, a novel strain‐smoothed particle finite element method (SPFEM) is proposed that incorporates a simple and effective edge‐based strain smoothing method within the framework of original PFEM. Compared with the original PFEM, the proposed novel SPFEM can solve the volumetric locking problem like previously developed node‐based smoothed PFEM when lower‐order triangular element is used. Compared with the node‐based smoothed PFEM known as “overly soft” or underestimation property, the proposed SPFEM offers super‐convergent and very accurate solutions due to the implementation of edge‐based strain smoothing method. To guarantee the computational stability, the proposed SPFEM uses an explicit time integration scheme and adopts an adaptive updating time step. Performance of the proposed SPFEM for geotechnical problems is first examined by four benchmark numerical examples: (a) bar vibrations, (b) large settlement of strip footing, (c) collapse of aluminium bars column, and (d) failure of a homogeneous soil slope. Finally, the progressive failure of slope of sensitive clay is simulated using the proposed SPFEM to show its outstanding performance in solving large deformation geotechnical problems. All results demonstrate that the novel SPFEM is a powerful and easily extensible numerical method for analysing large deformation problems in geotechnical engineering.

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On the edge‐based smoothed finite element approximation of viscoelastic fluid flows

2022

Numerical Methods in Fluids

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This article discusses the numerical simulation of viscoelastic fluid flows using the edge-based smoothed finite element method (ESFEM). The incompressible Navier-Stokes equations coupled with the Oldroyd-B constitutive relation are decoupled via the characteristic-based split scheme that enables the use of equal-order interpolation for the triple primitive variables. For this reason, the spatial discretization is implemented with linear three-node triangular elements which work very well with the ESFEM. Edge-based smoothing cells (SCs) are constructed on grounds of existing elements, directly underpinning the essential gradient smoothing procedure. New integration points are proposed within local SCs since the ESFEM enjoys the tremendous flexibility of the smoothed Galerkin weak-form integral. The discrete viscoelastic system is entirely formulated in the edge-based notion such that all gradient-related terms are readily smoothed cell-by-cell. Finally, several numerical examples are presented to demonstrate the desirable capability of the ESFEM.

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A new strain smoothing method for triangular and tetrahedral finite elements

Cited by 35 publications

References 32 publications

Self-updated four-node finite element using deep learning

Self-updated four-node finite element using deep learning

An edge‐based strain smoothing particle finite element method for large deformation problems in geotechnical engineering

On the edge‐based smoothed finite element approximation of viscoelastic fluid flows

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