Smoothed FE-Meshfree method for solid mechanics problems

In this paper, a gradient stable node-based smoothed discrete shear gap method (GS-DSG) using 3-node triangular elements is presented for Reissner–Mindlin plates in elastic-static, free vibration, and buckling analyses fields. By applying the smoothed Galerkin weak form, the discretized system equations are obtained. In order to carry out the smoothing operation and numerical integration, the smoothing domain associated with each node is defined. The modified smoothed strain with gradient information is derived from the Hu–Washizu three-field variational principle, resulting in the stabilization terms in the system equations. The stabilized discrete shear gap method is also applied to avoid transverse shear-locking problem. Several numerical examples are provided to illustrate the accuracy and effectiveness. The results demonstrate that the presented method is free of shear locking and can overcome the temporal instability issues, simultaneously obtaining excellent solutions.

show abstract

“…ere still exist a variety of gradient term constructions available for different cases [37,40,[62][63][64][65][66][67].…”

Section: Introductionmentioning

confidence: 99%

A Gradient Stable Node-Based Smoothed Discrete Shear Gap Method for Analysis of Reissner–Mindlin Plates

Chen

Tang

2020

Shock and Vibration

Self Cite

View full text Add to dashboard Cite

show abstract

“…Hybrid schemes composed of meshfree and FEM methodologies may encompass the advantages of both while mitigating their respective shortcomings [11][12][13], such as the partition of the unity finite element method (PUFEM) [14], generalized finite element method (GFEM) [15], FEmeshfree [16,17], meshfree-enriched FEM (ME-FEM) [18], and RKPM [5,19]. Zeng and Liu [20] combined the strain-smoothing technique of meshfree methods [21] and the existing FEM technology to establish smoothed finite element methods (S-FEMs) including the CS-SFEM for both 2D and 3D problems [22,23], node-based SFEM (NS-FEM) for both 2D and 3D [24,25], edge-based SFEM (ES-FEN) for 2D and 3D [26,27], face-based SFEM (FS-FEM) for 3D [28], and other hybrid schemes such as αFEM [29,30], βFEM [31], and smoothed FE-meshfree [32].…”

Section: Introductionmentioning

confidence: 99%

A Gradient Stable Node‐Based Smoothed Finite Element Method for Solid Mechanics Problems

Chen

Qian

2019

Shock and Vibration

Self Cite

View full text Add to dashboard Cite

This paper presents a gradient stable node-based smoothed finite element method (GS-FEM) which resolves the temporal instability of the node-based smoothed finite element method (NS-FEM) while significantly improving its accuracy. In the GS-FEM, the strain is expanded at the first order by Taylor expansion in a node-supported domain, and the strain gradient is then smoothed within each smoothing domain. Therefore, the stiffness matrix includes stable terms derived by the gradient of the strain. The GS-FEM model is softer than the FEM but stiffer than the NS-FEM and yields far more accurate results than the FEM-T3 or NS-FEM. It even has comparative accuracy compared with those of the FEM-Q4. The GS-FEM owns no spurious nonzero-energy modes and is thus temporally stable and well-suited for dynamic analyses. Additionally, the GS-FEM is demonstrated on static, free, and forced vibration example analyses of solids.

show abstract

A gradient continuous smoothed GFEM for heat transfer and thermoelasticity analyses

2021

View full text Add to dashboard Cite

Smoothed FE-Meshfree method for solid mechanics problems

Cited by 6 publications

References 52 publications

A Gradient Stable Node-Based Smoothed Discrete Shear Gap Method for Analysis of Reissner–Mindlin Plates

A Gradient Stable Node-Based Smoothed Discrete Shear Gap Method for Analysis of Reissner–Mindlin Plates

A Gradient Stable Node‐Based Smoothed Finite Element Method for Solid Mechanics Problems

A gradient continuous smoothed GFEM for heat transfer and thermoelasticity analyses

Contact Info

Product

Resources

About