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

Chen, Guangsong; Qian, Linfang; Ma, Jia

doi:10.1155/2019/8610790

Cited by 6 publications

(5 citation statements)

References 55 publications

(80 reference statements)

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“…However, the standard direct nodal integration is not suitable for dynamic problems with large deformation due to its spatial and temporal instability. [28][29][30][31][32] The proposed stable nodal integration can effectively resolve these problems by implementing the gradient strain field over the smoothing domains. Additionally, the standard no-slip condition can introduce supplementary elements and pressure concentration near solid walls.…”

Section: Slip Boundary Conditionmentioning

confidence: 99%

“…Note that the proposed methods basically belong to the class of node‐based PFEM. However, the standard direct nodal integration is not suitable for dynamic problems with large deformation due to its spatial and temporal instability 28–32 . The proposed stable nodal integration can effectively resolve these problems by implementing the gradient strain field over the smoothing domains.…”

Section: Sns‐pfem‐fic Formulation For Incompressible Flowmentioning

confidence: 99%

“…Among these, a stabilization method termed stabilized NS-FEM (SNS-FEM) that considered the strain gradient over the smoothing domain was able to provide temporally stable solutions. [28][29][30][31][32] The SNS-PFEM was then proposed by introducing the stabilized nodal integration into the framework of NS-PFEM for simulating geotechnical problems with large deformation. 19,33,34 Nevertheless, this algorithm has not been applied in fluid analysis.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, some stabilization algorithms have been proposed to deal with the drawbacks. Among these, a stabilization method termed stabilized NS‐FEM (SNS‐FEM) that considered the strain gradient over the smoothing domain was able to provide temporally stable solutions 28–32 . The SNS‐PFEM was then proposed by introducing the stabilized nodal integration into the framework of NS‐PFEM for simulating geotechnical problems with large deformation 19,33,34 .…”

Section: Introductionmentioning

confidence: 99%

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A novel stabilized nodal integration formulation using particle finite element method for incompressible flow analysis

Yu,

Jin,

Yin

et al. 2024

Numerical Methods in Fluids

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In simulations using the particle finite element method (PFEM) with node‐based strain smoothing technique (NS‐PFEM) to simulate the incompressible flow, spatial and temporal instabilities have been identified as crucial problems. Accordingly, this study presents a stabilized NS‐PFEM‐FIC formulation to simulate an incompressible fluid with free‐surface flow. In the proposed approach, (1) stabilization is achieved by implementing the gradient strain field in place of the constant strain field over the smoothing domains, handling spatial and temporal instabilities in direct nodal integration; (2) the finite increment calculus (FIC) stabilization terms are added using nodal integration, and a three‐step fractional step method is adopted to update pressures and velocities; and (3) a novel slip boundary with the predictor–corrector algorithm is developed to deal with the interaction between the free‐surface flow with rigid walls, avoiding the pressure concentration induced by standard no‐slip condition. The proposed stabilized NS‐PFEM‐FIC is validated via several classical numerical cases (hydrostatic test, water jet impinging, water dam break, and water dam break on a rigid obstacle). Comparisons of all simulations to the experimental results and other numerical solutions reveal good agreement, demonstrating the strong ability of the proposed stabilized NS‐PFEM‐FIC to solve incompressible free‐surface flow with high accuracy and promising application prospects.

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Section: Slip Boundary Conditionmentioning

confidence: 99%

Section: Sns‐pfem‐fic Formulation For Incompressible Flowmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A novel stabilized nodal integration formulation using particle finite element method for incompressible flow analysis

Yu,

Jin,

Yin

et al. 2024

Numerical Methods in Fluids

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“…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

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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.

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Stabilized node‐based smoothed radial point interpolation method for micromechanical analysis of the magneto‐electro‐elastic structures in thermal environment

Ren

Meng

et al. 2020

Math Methods in App Sciences

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In this paper, the stabilized node‐based smoothed radial point interpolation method (SNS‐RPIM) is combined with asymptotic homogenization method (AHM) to investigate the static and transient responses of magneto‐electro‐elastic (MEE) structures in thermal environment. Stabilization terms are applied to construct a “close‐to‐exact” stiffness for the model; the temporal instability is also cured. To study the microscopic multi‐physics coupling problems more accurately, the effective material parameters related to the volume fraction of fiber are obtained based on AHM. Through numerical calculation, it is confirmed that SNS‐RPIM could simulate the responses of MEE structures well when combined with AHM. Therefore, the combination of SNS‐RPIM and AHM has great potential in studying nanostructures including nanobeams, nanoplates, and nanotubes.

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

Cited by 6 publications

References 55 publications

A novel stabilized nodal integration formulation using particle finite element method for incompressible flow analysis

A novel stabilized nodal integration formulation using particle finite element method for incompressible flow analysis

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

Stabilized node‐based smoothed radial point interpolation method for micromechanical analysis of the magneto‐electro‐elastic structures in thermal environment

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