The strain-smoothed 4-node quadrilateral finite element

Lee, Chaemin; Kim, San; Lee, Phill-Seung

doi:10.1016/j.cma.2020.113481

Cited by 27 publications

(13 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where Ω ⊂ R 2 is a bounded polygonal domain. For simplicity, we consider the case of three-node triangular elements throughout this paper; see [27] and [12] for formulations of polygonal finite elements adopting the S-FEM and SSE method, respectively. Let T h be a quasi-uniform triangulation of Ω with a maximum element diameter h > 0.…”

Section: Finite Element Methods With Strain Smoothingmentioning

confidence: 99%

“…The strain-smoothed elements adopting the SSE method have been verified to pass the three basic tests (zero energy mode, isotropic element, and patch tests) and show more improved convergence behaviors compared with other competitive elements in various numerical problems [10,11,12].…”

Section: Strain-smoothed Element Methodsmentioning

confidence: 99%

“…Several studies were conducted to establish the theoretical properties of the S-FEMs [5,8,9]. Recently, the strain-smoothed element (SSE) method has been developed [10,11,12]. Whereas the S-FEMs construct strain fields for specifically defined smoothing domains, the SSE method constructs strain fields for elements.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Preconditioning for finite element methods with strain smoothing

Lee¹,

Park²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

Strain smoothing methods such as the smoothed finite element methods (S-FEMs) and the strain-smoothed element (SSE) method have successfully improved the performance of finite elements, and there have been numerous applications of them in finite element analysis. For the sake of efficient applications to large-scale problems, it is important to develop a mathematically and numerically well-elaborated iterative solver for the strain smoothing methods. In this paper, inspired by the spectral properties of the strain smoothing methods, we propose efficient ways of preconditioning for the methods. First, we analyze the spectrums of the stiffness matrices of the edge-based S-FEM and the SSE method. Then, we propose an improved two-level additive Schwarz preconditioner for the strain smoothing methods by modifying local solvers appropriately. For the sake of convenience of implementation, an alternative form of the preconditioner is also proposed by defining the coarse-scale operation in terms of the standard FEM. We verify our theoretical results through numerical experiments.

show abstract

Section: Finite Element Methods With Strain Smoothingmentioning

confidence: 99%

Section: Strain-smoothed Element Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Preconditioning for finite element methods with strain smoothing

Lee¹,

Park²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Using the SSE method, smoothed strain fields are constructed for elements, not for the smoothing domains, and strains of all adjacent elements are fully utilized for the strain smoothing. The method has been successfully applied to 3-node triangular and 4-node tetrahedral solid elements [20], 4-node quadrilateral solid element [22] and the MITC3+ shell element [21]. It has been verified by various numerical experiments that the strain-smoothed elements yield highly accurate solutions compared with other competitive elements.…”

Section: Introductionmentioning

confidence: 94%

“…Recently, a new strain smoothing method called the strain-smoothed element (SSE) method has been developed [20,21,22]. Using the SSE method, smoothed strain fields are constructed for elements, not for the smoothing domains, and strains of all adjacent elements are fully utilized for the strain smoothing.…”

Section: Introductionmentioning

confidence: 99%

A variational framework for the strain-smoothed element method

Lee,

Park

2020

Preprint

Self Cite

View full text Add to dashboard Cite

Recently, the strain-smoothed element (SSE) method has been developed for the finite element analysis of solids and shells. Although the SSE method has been verified to show improved convergence behaviors compared to other strain smoothing methods in various numerical examples, there has been no theoretical evidence for the convergence behavior. In this paper, we establish a mathematical foundation for the SSE method. We propose a mixed variational principle in which the SSE method can be interpreted as a Galerkin approximation of that. The proposed variational principle is a generalization of the well-known Hu-Washizu variational principle, and various existing methods such as smoothed finite element methods can be expressed in terms of the proposed variational principle. With a unified view to the SSE method and other existing ones through the proposed variational principle, we analyze the convergence behavior of the SSE method and explain the reason for improved performance compared to others. Numerical experiments that support our theoretical results are presented.

show abstract

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

2022

Numerical Methods in Fluids

View full text Add to dashboard Cite

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.

show abstract

The strain-smoothed 4-node quadrilateral finite element

Cited by 27 publications

References 53 publications

Preconditioning for finite element methods with strain smoothing

Preconditioning for finite element methods with strain smoothing

A variational framework for the strain-smoothed element method

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

Contact Info

Product

Resources

About