A novel node-based smoothed finite element method with linear strain fields for static, free and forced vibration analyses of solids

Li, Y.; Liu, G.R.

doi:10.1016/j.amc.2019.01.043

Cited by 29 publications

(25 citation statements)

References 28 publications

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“…According to Figure 2, when the penalty factor α varies within the range between 10 and 10 8 , the objective function value will be close to zero, namely, the nonpenetrating constraints expressed in equation (7) can be satisfied and the system will be stable. So, the penalty factor α can be taken as 10 8 .…”

Section: Selection Of Penalty Factor From Equations (3) and (23)mentioning

confidence: 99%

“…For the contact problems, only very few of them can be solved by analytical methods, and most of them need to be simulated by numerical methods such as the Finite Element Method (FEM) [3,4] and the Boundary Element Method (BEM) [5,6]. e FEM is relatively mature and widely used [7][8][9][10]. However, the BEM has the advantages of dimension reduction, singularity adaptation, high precision, and so on [11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

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A Kind of FM-BEM Penalty Function Method for a 3D Elastic Frictional Contact Nonlinear System

Jing

et al. 2021

Journal of Mathematics

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In this paper, a kind of node_face frictional contact FM-BEM penalty function method is presented for 3D elastic frictional contact nonlinear problems. According to the principle of minimum potential energy, nonpenetrating constraints are introduced into the elastic frictional contact system as a penalty term. By using the least square method and penalty function method, an optimization mathematical model and a mathematical programming model with a penalty factor are established for the node_face frictional contact nonlinear system. For the two models, a penalty optimization IGMRES (m) algorithm is proposed, and the influences of different penalty factors on the solution of the whole system are analyzed. Finally, a numerical simulation is carried out for two elastic frictional contact objects, and some important results including displacements, pressures, friction forces, and friction slips in the contact area are presented. Theoretical analysis and numerical experiment show that the newly presented FM-BEM penalty function method not only is efficient and practical but also has much superiority. It is easy to implement, and it is fast convergent with good stability.

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Section: Selection Of Penalty Factor From Equations (3) and (23)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Kind of FM-BEM Penalty Function Method for a 3D Elastic Frictional Contact Nonlinear System

Jing

et al. 2021

Journal of Mathematics

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“…With the ability to simultaneously describe multivariate microstructure factors and complex process parameters (such as the melting factor model), we can indirectly establish the quantitative relationship between process and microstructure, and provide scientific guidance for coating performance improvement. At the same time, first-principles as well as finite element calculations [18] are used to optimize the composition and structure of the material. Some examples are: Establishing multiple regression equations, performing a significance test, removing insignificant variables and quantifying the magnitude of each influencing factor.…”

Section: Data Collection and Processing Of Materials Datamentioning

confidence: 99%

Information Fusion for Multi-Source Material Data: Progress and Challenges

2019

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The development of material science in the manufacturing industry has resulted in a huge amount of material data, which are often from different sources and vary in data format and semantics. The integration and fusion of material data can offer a unified framework for material data representation, processing, storage and mining, which can further help to accomplish many tasks, including material data disambiguation, material feature extraction, material-manufacturing parameters setting, and material knowledge extraction. On the other side, the rapid advance of information technologies like artificial intelligence and big data, brings new opportunities for material data fusion. To the best of our knowledge, the community is currently lacking a comprehensive review of the state-of-the-art techniques on material data fusion. This review first analyzes the special properties of material data and discusses the motivations of multi-source material data fusion. Then, we particularly focus on the recent achievements of multi-source material data fusion. This review has a few unique features compared to previous studies. First, we present a systematic categorization and comparison framework for material data fusion according to the processing flow of material data. Second, we discuss the applications and impact of recent hot technologies in material data fusion, including artificial intelligence algorithms and big data technologies. Finally, we present some open problems and future research directions for multi-source material data fusion.

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“…, 2007), edge-based smoothed finite element method (ES-FEM) (Nguyen-Xuan et al. , 2012), node-based smoothed finite element method (NS-FEM) (Li and Liu, 2019) and smoothed extended finite element methods (Sm-XFEM) (Bordas et al. , 2010; Surendran et al.…”

Section: Introductionmentioning

confidence: 99%

“…To remedy this issue, Duan et al (2012aDuan et al ( , b, 2014 developed a set of quadratically consistent integration (QCI) schemes for EFGM using quadratic base functions by correcting the nodal derivatives based on the consistency integration constrain between a nodal shape function and its derivatives. By combining the strain smoothing technique with the FEM and the XFEM, a series of numerical methods have been proposed for engineering analysis, such as smoothed finite element method (S-FEM) (Liu et al, 2007), edge-based smoothed finite element method (ES-FEM) (Nguyen-Xuan et al, 2012), node-based smoothed finite element method (NS-FEM) (Li and Liu, 2019) and smoothed extended finite element methods (Sm-XFEM) (Bordas et al, 2010;Surendran et al, 2017Surendran et al, , 2019Zhao et al, 2020), to name a few. Chen et al (2013) proposed the variationally consistent integration (VCI) by correcting test functions to the desire order.…”

Section: Introductionmentioning

confidence: 99%

A linear smoothed meshfree method with intrinsic enrichment functions for 2D crack analysis

Ban

Zhang

et al. 2022

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PurposeThis article aims to develop an accurate and efficient meshfree Galerkin method based on the strain smoothing technique for linear elastic continuous and fracture problems.Design/methodology/approachThis paper proposed a generalized linear smoothed meshfree method (LSMM), in which the compatible strain is reconstructed by the linear smoothed strains. Based on the idea of the weighted residual method and employing three linearly independent weight functions, the linear smoothed strains can be created easily in a smoothing domain. Using various types of basic functions, LSMM can solve the linear elastic continuous and fracture problems in a unified way.FindingsOn the one hand, the LSMM inherits the properties of high efficiency and stability from the stabilized conforming nodal integration (SCNI). On the other hand, the LSMM is more accurate than the SCNI, because it can produce continuous strains instead of the piece-wise strains obtained by SCNI. Those excellent performances ensure that the LSMM has the capability to precisely track the crack propagation problems. Several numerical examples are investigated to verify the accurate, convergence rate and robustness of the present LSMM.Originality/valueThis study provides an accurate and efficient meshfree method for simulating crack growth.

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A novel node-based smoothed finite element method with linear strain fields for static, free and forced vibration analyses of solids

Cited by 29 publications

References 28 publications

A Kind of FM-BEM Penalty Function Method for a 3D Elastic Frictional Contact Nonlinear System

A Kind of FM-BEM Penalty Function Method for a 3D Elastic Frictional Contact Nonlinear System

Information Fusion for Multi-Source Material Data: Progress and Challenges

A linear smoothed meshfree method with intrinsic enrichment functions for 2D crack analysis

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