Showing papers on "Smoothed finite element method published in 2021"
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TL;DR: In this paper, an edge-based smoothed finite element method (ES-FEM) associate with the mixed interpolation of tensorial components technique for the three-node triangular element (MITC3) is performed to eliminate the shear locking problem and to enhance the accuracy of the existing MITC3 element.
47 citations
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TL;DR: Wang et al. as mentioned in this paper proposed a coupling edge-based smoothed finite element method (ES-FEM) and smoothed particle hydrodynamics (SPH) method for solving fluid structure interaction (FSI) problems.
36 citations
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TL;DR: In this article, the coupling strategy of an improved particle hydrodynamics (SPH) method and smoothed finite element method (SFEM) is integrated with advanced fluid modeling techniques, and is extended and validated for modeling liquid sloshing with rigid or deformable structures.
24 citations
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TL;DR: In this article, the cell-based S-FEM was extended to three-dimensional (3D) incompressible laminar flows, and the results indicated that the present S-fem performed better than the standard FEM in dealing with pressure stability.
Abstract: Smoothed finite element method (S-FEM) has attracted lots of attentions in the fields of computational mechanics, especially in solid mechanics and heat transfer problems. In computational fluid dynamics, works on S-FEM were limited to two-dimensional problems. This work aims to extend the S-FEM to three-dimensional (3D) incompressible laminar flows. Wedge element grids and grids with mixed wedge and hexahedral elements are formulated for 3D incompressible laminar flows based on the cell-based S-FEM (CS-FEM). To reduce numerical oscillations, we implemented the streamline-upwind/Petrov-Galerkin method (SUPG) together with the stabilized pressure gradient projection (SPGP). Several examples are presented, including the Beltrami flow, lid-driven cavity flow, backward facing step flow and microchannel flow, to validate and examine the presented method. The results indicate that wedge elements and mixed wedge-hexahedral elements based on the CS-FEM have higher computational efficiency than that of hexahedral elements based on the CS-FEM for the same level of computational accuracy. It is also found that the present CS-FEM performed better than the standard FEM in dealing with pressure stability. The flow characteristics are well captured by the CS-FEM using the mixed wedge-hexahedral elements, and the numerical results are acceptable compared to those of STAR-CCM+.
22 citations
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TL;DR: In this article, the stability of two circular tunnels at different depths in cohesive-frictional soils subjected to surcharge loading using a stable node-based smoothed finite element method (SNS-FEM) was investigated.
19 citations
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TL;DR: In this article, the performance of cell-based smoothed finite element method (CS-FEM) and FEM based on SUPG/SPGP for incompressible Navier-Stokes equations are investigated.
Abstract: In this paper, the exhaustive usage and implementation of Streamline-Upwind/Petrov-Galerkin method combining with Stabilized Pressure Gradient Projection (SUPG/SPGP) for incompressible Navier-Stokes equations are investigated. We validate and explore the behavior of cell-based smoothed finite element method (CS-FEM) and finite element method (FEM) based on SUPG/SPGP on five numerical examples. First, the Taylor-Green vortex example shows that CS-FEM based on SUPG/SPGP (CSFEM-SUPG/SPGP) are more accurate and has better robustness against distorted mesh than that of FEM based on SUPG/SPGP (FEM-SUPG/SPGP). Moreover, the wider range of SPGP stability parameter for CS-FEM-SUPG/SPGP is found in the condition of maintaining accurate result. Meanwhile, the lid-driven cavity flow example shows that the SUPG/SPGP method is favorable for incompressible flow at relatively high Reynolds number. The other numerical examples show good performances of the proposed method on the unsteady flows and micro-channel flow. In summary, proposed CS-FEM-SUPG/SPGP shows good performances on obtaining accurate results.
18 citations
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TL;DR: In this paper, the authors further extended the ES-MITC3 element based on first-order shear deformation theory (FSDT) for the free vibration analysis of functionally graded porous (FGP) plates resting on the partially supported elastic foundation (PSEF).
14 citations
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TL;DR: In this paper, the viscoelastic analysis for composite laminated plates using a smoothed finite element method called cell/element based smoothed discrete shear gap method was investigated.
Abstract: In the present study, the viscoelastic analysis is investigated for composite laminated plates using a smoothed finite element method called cell/element based smoothed discrete shear gap method. M...
13 citations
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TL;DR: A historical perspective on the developments of finite element methods mainly focusing on its applications and related developments in solid and structural mechanics, with limited discussions to other fields in which it has made significant impact, such as fluid mechanics, heat transfer and fluid-structure interaction as discussed by the authors.
Abstract: This year marks the eightieth anniversary of the invention of the finite element method (FEM). FEM has become the computational workhorse for engineering design analysis and scientific modeling of a wide range of physical processes, including material and structural mechanics, fluid flow and heat conduction, various biological processes for medical diagnosis and surgery planning, electromagnetics and semi-conductor circuit and chip design and analysis, additive manufacturing, i.e. virtually every conceivable problem that can be described by partial differential equations (PDEs). FEM has fundamentally revolutionized the way we do scientific modeling and engineering design, ranging from automobiles, aircraft, marine structures, bridges, highways, and high-rise buildings. Associated with the development of finite element methods has been the concurrent development of an engineering science discipline called computational mechanics, or computational science and engineering.
In this paper, we present a historical perspective on the developments of finite element methods mainly focusing on its applications and related developments in solid and structural mechanics, with limited discussions to other fields in which it has made significant impact, such as fluid mechanics, heat transfer, and fluid-structure interaction. To have a complete storyline, we divide the development of the finite element method into four time periods: I. (1941-1965) Early years of FEM; II. (1966-1991) Golden age of FEM; III. (1992-2017) Large scale, industrial applications of FEM and development of material modeling, and IV (2018-) the state-of-the-art FEM technology for the current and future eras of FEM research. Note that this paper may not strictly follow the chronological order of FEM developments, because often time these developments were interwoven across different time periods.
13 citations
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TL;DR: In this article, a high-order cell-based smoothed finite element method (CS-FEM) using 6 nodes triangular (T6) and 8 nodes quadrilateral (Q8) elements is presented.
Abstract: This paper presents a novel high-order cell-based smoothed finite element method (CS-FEM) using 6 nodes triangular (T6) and 8 nodes quadrilateral (Q8) elements. In addition, high-order quadrilateral transition elements (Q5 and Q6) are also developed based on this method. In this method, the high order strain field in each smoothing domain is constructed using pick-out theory. And the strain field is represented by a complete polynomial. Both triangular and quadrilateral high order CS-FEM are formulated without the need to dividing the elements into smaller smoothing cells. Since there is no mapping and derivation in computation, so high-order CS-FEM has better adaptability to mesh distortion. The performance of high-order CS-FEM is examined in great detail, using a number of numerical examples. And it is found that CS-FEM results agrees with finite element method (FEM) counterpart. In addition, we found also that the edge-nodes of the high-order elements in a CS-FEM model can be quite freely placed, which is not possible in a standard high-order FEM model. All the high-order CS-FEM models are implemented through User-defined Element Library (UEL) in ABAQUS, which greatly improves work efficiency.
12 citations
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TL;DR: This work proposes a stabilization approach for semi-implicit coupling of viscoelastic fluid–structure interaction (VFSI) using the cell-based smoothed finite element method (CS-FEM), which shows visible improvements in stabilization and efficiency.
Abstract: We propose in this work a stabilization approach for semi-implicit coupling of viscoelastic fluid–structure interaction (VFSI) using the cell-based smoothed finite element method (CS-FEM). The viscoelastic fluid and nonlinear solid equations are spatially discretized by the CS-FEM and then are semi-implicitly coupled via a partitioned solution strategy. The current semi-implicit coupling framework depends on a second-order characteristic-based split (CBS(B)) scheme that solves the Navier–Stokes equations together with the Oldroyd-B constitutive model in the fractional-step manner. To enhance the stability of the semi-implicit coupling algorithm, the discrete elastic-viscous split stress-gradient (DEVSS-G) procedure is introduced into the explicit stage while the stabilized pressure gradient projection (SPGP) is earmarked for the implicit stage. Moreover, the iterated end-of-step velocity begins with the intermediate velocity during the subiterations. The DEVSS-G/CBS(B)-SPGP technique is readily applied to the CBS-based partitioned semi-implicit coupling algorithm for VFSI. Visible improvements in stabilization and efficiency are revealed in a benchmark test.
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TL;DR: In this paper, a cell-based smoothed finite element method using the arbitrary n-sided polygonal element (CS-FEM-Poly) is developed to solve fluid mechanics problems.
Abstract: In this paper, a cell-based smoothed finite element method using the arbitrary n-sided polygonal element (CS-FEM-Poly) is developed to solve fluid mechanics problems. A stabilization method, charac...
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TL;DR: In this article, a unified implementation of smoothed finite element methods (UI-SFEM) is proposed, which enables the use of different types of smoothing domains for different materials.
Abstract: The Periodontal Ligament (PDL) plays a very important role in load transmission between the teeth and alveolar bone. To capture biomechanical responses of Orthodontics, numerical analysis need to consider multiple types of materials: incompressible visco-hyperelastic for the PDL and compressible elastic for teeth. This article proposes a unified-implementation of smoothed finite element methods (UI-SFEM), which enables the use of different types of smoothing domains for different materials. It has several important properties: (1) A UI-SFEM model can use any types of smoothing domains in a combination as desired for complex systems. (2) The choice of the smoothing domain types can be done in a single model based on the user needs (material properties, incompressible numerical problems). (3) It provides a framework for designing models with different solution properties. Numerical experiments show that the UI-SFEM is efficient and robust against mesh distortion, which is works particularity well for complex biological systems.
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TL;DR: An open-source package of the parallel S-FEM for elastic problems by utilizing the Julia language on multi-core CPU and the structure and function of juSFEM are easily modularized, and the code is clear and readable, which is convenient for further development.
Abstract: The Smoothed Finite Element Method (S-FEM) proposed by Liu G.R. can achieve more accurate results than the conventional FEM. Currently, much commercial software and many open-source packages have been developed to analyze various science and engineering problems using the FEM. However, there is little work focusing on designing and developing software or packages for the S-FEM. In this paper, we design and implement an open-source package of the parallel S-FEM for elastic problems by utilizing the Julia language on multi-core CPU. The Julia language is a fast, easy-to-use, and open-source programming language that was originally designed for high-performance computing. We term our package as juSFEM. To the best of the authors’ knowledge, juSFEM is the first package of parallel S-FEM developed with the Julia language. To verify the correctness and evaluate the efficiency of juSFEM, two groups of benchmark tests are conducted. The benchmark results show that (1) juSFEM can achieve accurate results when compared to commercial FEM software ABAQUS, and (2) juSFEM only requires 543 s to calculate the displacements of a 3D elastic cantilever beam model which is composed of approximately 2 million tetrahedral elements, while in contrast the commercial FEM software needs 930 s for the same calculation model; (3) the parallel juSFEM executed on the 24-core CPU is approximately 20 × faster than the corresponding serial version. Moreover, the structure and function of juSFEM are easily modularized, and the code in juSFEM is clear and readable, which is convenient for further development.
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TL;DR: A novel approach is effective in modeling various incompressible flow problems involving FSIs and can significantly reduce the computational cost relative to the original version with a constant resolution by introducing a multi-resolution technique to the SPEM and developing an effective approach to treat multi- resolution element-particle interfaces.
Abstract: Free-surface flows, especially those associated with fluid-structure interactions (FSIs), pose challenging problems in numerical simulations. The authors of this work recently developed a smoothed particle element method (SPEM) to simulate FSIs. In this method, both the fluid and solid regions are initially modeled using a smoothed finite element method (S-FEM) in a Lagrangian frame, whereas the fluid regions undergoing large deformations are adaptively converted into particles and modeled with an improved smoothed particle hydrodynamics (SPH) method. This approach greatly improves computational accuracy and efficiency because of the advantages of the S-FEM in efficiently treating solid/fluid regions showing small deformations and the SPH method in effectively modeling moving interfaces. In this work, we further enhance the efficiency of the SPEM while effectively capturing local fluid information by introducing a multi-resolution technique to the SPEM and developing an effective approach to treat multi-resolution element-particle interfaces. Various numerical examples demonstrate that the multiresolution SPEM can significantly reduce the computational cost relative to the original version with a constant resolution. Moreover, the novel approach is effective in modeling various incompressible flow problems involving FSIs.
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TL;DR: In this article, the cell-based smoothed finite element method (CS-FEM) in conjunction with the modified Newmark scheme was used to verify the effectiveness, convergence, efficiency and the specialty in dealing with distorted elements of the proposed method, mechanical responses of an example of 2D MEE cantilever beam subjected to hygrothermal environment and timed-dependent sawtooth wave load were comprehensively studied.
Abstract: In the present paper, for the first time, the time-dependent responses of magneto-electro-elastic (MEE) structures in a hygrothermal environment are investigated via the cell-based smoothed finite element method (CS-FEM) in conjunction with the modified Newmark scheme. To verify the effectiveness, convergence, efficiency and the specialty in dealing with distorted elements of the proposed method, mechanical responses of an example of 2D MEE cantilever beam subjected to hygrothermal environment and timed-dependent sawtooth wave load were comprehensively studied. The numerical results obtained by CS-FEM were compared with the finite element method (FEM). Next, we constructed two geometric configurations of MEE sensors and investigated the effect of geometric configuration, MEE patches position, as well as applied mechanical sawtooth load on their time-dependent generalized displacements. A parametric study was conducted to show also the effect of mechanical load in conjunction with thermal and moisture loads on the time-dependent response of MEE-based structures. Comprehensive numerical results illustrate that the thermal and moisture loads have significant influences on the response of MEE structures. Additionally, the MEE patch position directly affects the energy conversion factor. The mechanical response of MEE-based structures in the hygrothermal environment was modified and potentially improved. This study characterizing the MEE material in a hygrothermal environment creates the groundwork for designing MEE-based intelligent structures in an extreme environment.
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TL;DR: In this article, the authors used the cell-based smoothed finite element method (CS-FEM) and the asymptotic homogenization method (AHM) to accurately simulate the responses of 1-3 type magneto-electro-elastic (MEE) structure under dynamic load.
Abstract: In this paper, the Cell-based smoothed finite element method (CS-FEM) and the asymptotic homogenization method (AHM) are used to accurately simulate the responses of 1–3 type magneto-electro-elastic (MEE) structure under dynamic load. The dynamic characteristics of micromechanics are discussed. Firstly, the properties of MEE materials at different composition ratios are calculated by AHM. In the next step, the CS-FEM equations for the multi-physics problems are deduced based on the MEE constitutive equations and the effective parameters. The transient reactions of the problem are solved by introducing the modified Wilson- θ approach. To illustrate the precision, reliability and convergence of CS-FEM, four numerical examples of various thin-walled structures are designed, results of CS-FEM are compared with those of the traditional finite element method (FEM) with denser elements. It shows that CS-FEM has higher accuracy, faster convergence speed and higher computational efficiency. This paper has some application value for the design and development of thin-walled intelligent sensors and energy harvesters, etc.
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TL;DR: The benefits of polygonal elements constructed based on the cell-based smoothed finite element method (SFEM) are explored and an alternate approach for modelling fracture along cohesive interfaces is introduced, enabling the interface to be represented independent of the meshes at the interface giving complete freedom on meshing.
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TL;DR: The effectiveness of the proposed methodology in the simulations of the quasi-brittle fractures is demonstrated using the edge-based smoothed finite element method (ES-FEM) and isotropic damage model.
Abstract: In this study, an effective numerical framework for fracture simulations is proposed using the edge-based smoothed finite element method (ES-FEM) and isotropic damage model. The duality between the...
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TL;DR: In this article, a phase field fracture model based on the Inner-based Edge-based Smoothed Finite Element Method (IES-FEM) is implemented to simulate the brittle fracture in ABAQUS through subroutine UEL.
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TL;DR: Three-dimensional phase-field models based on the cell-based smooth finite element method (CS-FEM) offer an effective alternative means to model 3D fracturing in elasto-plastic solids and offers important softer model behavior in solving the governing equations.
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TL;DR: In this paper, a hybrid plane wave expansion/edge-based smoothed finite element method (PWE/ES-FEM) was proposed for band structures simulation of semi-infinite beam-like phononic crystals (PCs).
Abstract: This paper presents a hybrid plane wave expansion/edge-based smoothed finite element method (PWE/ES-FEM) for band structures simulation of semi-infinite beam-like phononic crystals (PCs). The field variables are first approximated using linear shape functions in conjunction with the spatial Fourier series. Within the further formed edge-based smoothing domains, the gradient smoothing technique (GST) is employed to perform the strain smoothing operation. Based on the smoothed Galerkin weakform, the discretized system equations associated with the eigenvalue problem are finally obtained. Numerical examples demonstrate that the present method possesses higher computational accuracy in band structures simulation of semi-infinite beam-like PCs.
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TL;DR: Being furthermore free of volumetric locking problems makes S-FEM a promising alternative in modelling of active cardiac mechanics, respectively electromechanics.
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TL;DR: Numerical analysis shows that the M-SFEM can be used to predict the band structures in PCs with FSI, and can obtained more precise results as compared to FEM and SFEM.
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TL;DR: In this paper, the unusual stress fluctuation in the smoothed finite element method (SFEM) for 2D elastoplastic problems is investigated, and the governing equation of the 2D ELASP problem base is derived.
Abstract: In this study, the unusual stress fluctuation in the smoothed finite element method (SFEM) for 2D elastoplastic problems is investigated. The governing equation of the 2D elastoplastic problem base...
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TL;DR: In this paper, a stable node-based smoothed finite element method with PML (SNS-FEM-PML) is proposed to solve the scattering problem of a time-harmonic elastic plane wave by a rigid obstacle in two dimensions.
Abstract: In this paper, a stable node-based smoothed finite element method with PML (SNS-FEM-PML) is proposed to solve the scattering problem of a time-harmonic elastic plane wave by a rigid obstacle in two dimensions. In the algorithm, the stability term is constructed by the Taylor expansion of the gradient to cure the instability of the original NS-FEM. The linear variations of the gradient with respect to x and y are included in the stability term, which are calculated using four integral points in an equivalent circle of node-based smoothing domain. Meanwhile, the perfectly matched layer (PML) technique is used to truncate the unbounded domain. Furtherly, the smoothed Galerkin weak formulations of SNS-FEM-PML model are derived and the linear algebra system with the linear smoothed gradient is constructed for the Navier equation and Helmholtz equations with coupled boundaries. Besides, we also prove theoretically the softening effect and convergence of the SNS-FEM model. Several numerical examples verify the effectiveness and accuracy of SNS-FEM model. The results suggest that the convergence order of L2 and H1 semi-norm errors of the SNS-FEM model is consistent with the theory of FEM, and convergence rate of the relative error is higher than that of the FEM.
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25 May 2021
TL;DR: Structural and solid mechanics fluid mechanics general applications of the finite element method mathematical aspects of the infinite element method are studied.
Abstract: Structural and solid mechanics fluid mechanics general applications of the finite element method mathematical aspects of the finite element method.
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01 Aug 2021TL;DR: The comparison results show that the three-dimensional ES-FEM based on polyhedral mesh has better precision and convergence than the conventional FEM and better adaptability to complex geometric structures.
Abstract: This paper established the three-dimensional edge-based smoothed finite element method(ES-FEM) based on polyhedral mesh, divided the smoothed domain, constructed the shape function and derived the geometric matrix and the stiffness matrix. The MATLAB software was used to prepare the corresponding computing programs, with which the paper studied the stress distribution of a hollow sphere model and a beam model under different numbers of polyhedral elements. The paper compared the calculation results from the conventional finite element methods(FEM) that use tetrahedral elements and hexahedral elements respectively in terms of stress relative error and energy relative error. The comparison results show that the three-dimensional ES-FEM based on polyhedral mesh has better precision and convergence than the conventional FEM and better adaptability to complex geometric structures.