Showing papers on "Smoothed finite element method published in 2019"
Book•
04 Jun 2019
180 citations
TL;DR: Wang et al. as discussed by the authors proposed a hybrid approach of an improved Smoothed Particle hydrodynamics and smoothed finite element method (SPEM) for modeling FSI problems.
51 citations
TL;DR: In this article, elasto-plastic creep crack growth simulations are performed using continuum damage mechanics and extended finite element method using Liu-Murakami creep damage model and explicit ti...
Abstract: In the present work, elasto-plastic creep crack growth simulations are performed using continuum damage mechanics and extended finite element method. Liu–Murakami creep damage model and explicit ti...
46 citations
TL;DR: Through this operation without the introducing of any uncertain parameter, the SNS-FEM not only significantly cures the temporal instability of NS-F EM but also performs better in effectiveness and efficiency than FEM, which is well validated by several numerical examples containing benchmark cases.
Abstract: In this paper, a stable node-based smoothed finite element method (SNS-FEM) is presented for analyzing metal forming problems using linear triangular or tetrahedral elements. In present method, the numerical integration domains are approximately circular or spherical regions of the node-based smoothing domains generated by the node-based smoothed finite element method (NS-FEM). Four or six supplementary integration points, which are symmetrically located at the crossover points of the region and the coordinate axis, are employed for each node to form the stabilization items associated with the variance of smoothed shape function gradient. Through this operation without the introducing of any uncertain parameter, the SNS-FEM not only significantly cures the temporal instability of NS-FEM but also performs better in effectiveness and efficiency than FEM, which is well validated by several numerical examples containing benchmark cases. Additionally, a simple but effective contact algorithm including contact searching and contact force computation is presented.
40 citations
TL;DR: In this paper, the recently proposed linear smoothed extended finite element method (LSmXFEM) is employed to simulate the fatigue crack growth, which does not require special numerical integration technique to integrate the terms in the stiffness matrix.
40 citations
TL;DR: The S-FEM is ideal for automation in computations and adaptive analyses, and hence has profound impact on AI-assisted modeling and simulation, and can now purposely design an S-fEM model to obtain solutions with special properties as wish, meaning that S- FEM offers a framework for design numerical models with desired properties.
Abstract: The smoothed finite element method (S-FEM) was originated by G R Liu by combining some meshfree techniques with the well-established standard finite element method (FEM). It has a family of models carefully designed with innovative types of smoothing domains. These models are found having a number of important and theoretically profound properties. This article first provides a concise and easy-to-follow presentation of key formulations used in the S-FEM. A number of important properties and unique features of S-FEM models are discussed in detail, including 1) theoretically proven softening effects; 2) upper-bound solutions; 3) accurate solutions and higher convergence rates; 4) insensitivity to mesh distortion; 5) Jacobian-free; 6) volumetric-locking-free; and most importantly 7) working well with triangular and tetrahedral meshes that can be automatically generated. The S-FEM is thus ideal for automation in computations and adaptive analyses, and hence has profound impact on AI-assisted modeling and simulation. Most importantly, one can now purposely design an S-FEM model to obtain solutions with special properties as wish, meaning that S-FEM offers a framework for design numerical models with desired properties. This novel concept of numerical model on-demand may drastically change the landscape of modeling and simulation. Future directions of research are also provided.
34 citations
TL;DR: The new developed high-order strain NS-FEM is applied for static, free and forced vibration analyses of solids, and the numerical results support the theorems.
31 citations
TL;DR: An innate ability of the cell-based smoothed finite element method to settle convection-dominated flows is unveiled, free of isoparametric mapping and accepts severely distorted elements.
27 citations
TL;DR: In this paper, a cell-based smoothed finite element method is proposed for thin and thick plates based on Reissner-Mindlin plate theory and assumed shear strain fields.
23 citations
TL;DR: In this article, a cell-based smoothed finite element method (CS-FEM) was proposed to characterize the steady-state magneto-electro-elastic (MEE) structures in the thermal environment.
23 citations
TL;DR: In this paper, a mass-redistributed alpha finite element method (MR-αFEM) was proposed to provide an optimal balance between discretized mass and smoothed stiffness.
Posted Content•
TL;DR: This work presents the Griffith-type phase-field formation at large deformation in the framework of adaptive edge-based smoothed finite element method (ES-FEM) for the first time and a well-designed multi-level adaptive mesh strategy was developed, which considerably improved the computational efficiency.
Abstract: This work presents the Griffith-type phase-field formation at large deformation in the framework of adaptive edge-based smoothed finite element method (ES-FEM) for the first time. Therein the phase-field modeling of fractures has attracted widespread interest by virtue of its outstanding performance in dealing with complex cracks. The ES-FEM is an excellent member of the S-FEM family developed in combination with meshless ideas and finite element method (FEM), which is characterized by higher accuracy, softer stiffness, and insensitive to mesh distortion. Given that, the advantages of the phase-field method (PFM) and ES-FEM are fully combined by the approach proposed in this paper. With the costly computational overhead of PFM and ES-FEM in mind, a well-designed multi-level adaptive mesh strategy was developed, which considerably improved the computational efficiency. Furthermore, the detailed numerical implementation for the coupling of PFM and ES-FEM is outlined. Several representative numerical examples were recalculated based on the proposed method, and its effectiveness is verified by comparison with the results in experiments and literature. In particular, an experiment in which cracks deflected in rubber due to impinging on a weak interface was firstly reproduced.
TL;DR: Both the consistent and lumped mass matrices are developed for five-node crack-tip elements for dynamic cases and their effects are compared on the numerical results, which shows the effectiveness of present method.
Abstract: This paper presents an effective numerical approach for dynamic brittle crack growth problems implemented on singular edge-based smoothed finite element method (sES-FEM). Both the consistent and lumped mass matrices are developed for five-node crack-tip elements for dynamic cases and their effects are compared on the numerical results. Further, to minimize the energy introduced or dissipated during continuous mesh rezoning, a balance recovery method is utilized in the computation. The interaction integral method is used to evaluate mixed dynamic stress intensity factors. Several numerical examples are presented to demonstrate the accuracy and applicability of the present approach in modeling dynamic crack propagation. The numerical results are examined in detail by comparisons with analytical solutions or experimental results, which shows the effectiveness of present method.
TL;DR: In this paper, the cell-based smoothed three-node Mindlin plate element (CS-MIN3) has been extended by integrating itself with homogenization models to give homogenisation methods.
Abstract: Homogenization is a promising approach to capture the behavior of complex structures like corrugated panels. It enables us to replace high-cost shell models with stiffness-equivalent orthotropic plate alternatives. Many homogenization models for corrugated panels of different shapes have been proposed. However, there is a lack of investigations for verifying their accuracy and reliability. In addition, in the recent trend of development of smoothed finite element methods, the cell-based smoothed three-node Mindlin plate element (CS-MIN3) based on the first-order shear deformation theory (FSDT) has been proposed and successfully applied to many analyses of plate and shell structures. Thus, this paper further extends the CS-MIN3 by integrating itself with homogenization models to give homogenization methods. In these methods, the equivalent extensional, bending, and transverse shear stiffness components which constitute the equivalent orthotropic plate models are represented in explicit analytical expressions. Using the results of ANSYS and ABAQUS shell simulations as references, some numerical examples are conducted to verify the accuracy and reliability of the homogenization methods for static analyses of trapezoidally and sinusoidally corrugated panels.
TL;DR: In this article, a modified smoothed finite element method (M-SFEM) was proposed to calculate the band structures of two-dimensional in-plane elastic waves in phononic crystals (PCs).
Abstract: The present work proposes a novel modified smoothed finite element method (M-SFEM) to calculate the band structures of two-dimensional in-plane elastic waves in phononic crystals (PCs). Using the gradient smoothing technique over the cell-based smoothing domains, the cell-based gradient smoothing operation can offer ‘proper softening effects’ in SFEM modeling. According to the generalized integration rules, by simply shifting integration points to an unconventional location in the mass matrix, the accuracy of the M-SFEM model can be further improved. Numerical examples are presented for PCs using the proposed method for the computation of band gap (BG) frequency regions. The accuracy and efficiency of the modified SFEM are compared with those of the corresponding FEM and SFEM. The advantages of the modified SFEM for computing the BGs in PCs are discussed as compared to the conventional FEM. The results show the performance improvement of the M-SFEM compared to the FEM and SFEM.
TL;DR: In this article, the authors generalize the cell-based smoothed finite element method (CS-FEM) to viscoelastic fluid flows under the fractional-step umbrella.
TL;DR: In this article, an inhomogeneous cell-based smoothed finite element method (ICS-FEM) was proposed to overcome the over-stiffness of finite element methods in calculating transient responses of func...
Abstract: In this article, an inhomogeneous cell-based smoothed finite element method (ICS-FEM) was proposed to overcome the over-stiffness of finite element method in calculating transient responses of func...
TL;DR: In this article, a cell-based smoothed finite element method (CS-FEM) incorporating characteristic-based split (CBS) scheme is developed to compute viscoelastic fluid flow.
Abstract: In this paper, a cell-based smoothed finite element method (CS-FEM) incorporating characteristic-based split (CBS) scheme is developed to compute viscoelastic fluid flow. The system of the Navier–Stokes and Oldroyd-B constitutive equations is decoupled in tandem with equal low-order approximation of the triple primitive variables. The spatial discretization is based upon CS-FEM which readily smooths all gradient-related entries of the governing equations over bilinear four-node quadrilateral elements. Moreover, the cell-based smoothing concept is applied to evaluation of viscoelastic fluid force. Four benchmark problems are replicated to demonstrate the applicability and robustness of the smoothed CBS finite element formulation. A good agreement is exposed between the present and previous results.
TL;DR: A novel adaptive technique is developed that combines a newly developed quadtree algorithm with the cell-based smoothed finite element method (CS-FEM) for automatic mesh adaptation using quadrilateral elements for more proficient analysis of complex geometry.
Abstract: For finite element analysis of structures with irregular geometry, unsatisfactory meshing quality could be the major concern. Adaptive meshing technique is usually applied to modulate the mesh to approach the geometry. The stress solution from triangular elements is understood less accurate than that of quadrilateral elements. Therefore, adaptive technique for quadrilateral elements is desirable for more proficient analysis of complex geometry. This paper develops a novel adaptive technique that combines a newly developed quadtree algorithm with the cell-based smoothed finite element method (CS-FEM) for automatic mesh adaptation using quadrilateral elements. Since the quadtree algorithm generates a grid with different sizes of quadrilaterals, a number of new CS-FEM elements of n-sided polygon are concomitantly constituted. In the adaptation process, the energy error norm and the geometrical feature are applied as the calibrations for the adaptive refinement. The elements on curved boundaries are either cut or merged with the surrounding elements automatically. It is found that the present new quadtree algorithm works very effectively with the CS-FEM formulation in view of stability and convergence. The results by the current S-FEM are found generally more accurate than those of the general finite element method (FEM) counterpart, especially in terms of strain energy solutions.
TL;DR: In this article, a modified immersed smoothed finite element method (mIS-FEM) is proposed for fluid-structure interactions (FSI) using linear triangular elements, which reconstructs the fluid velocity field near interface using auxiliary triangles, leading to better resolutions without much extra efforts.
Abstract: A modified immersed smoothed finite element method (mIS-FEM) is proposed for fluid–structure interactions (FSI) using linear triangular elements in this paper. A sharp interface treatment is proposed and implemented to modify the original IS-FEM. The proposed treatment reconstructs the fluid velocity field near interface using auxiliary triangles, leading to better resolutions without much extra efforts. In the proposed method, the fluid solver is the FEM with a semi-implicit characteristic-based split (CBS) scheme using linear triangles. For the solid solver, the S-FEM based on explicit total Lagrangian formulation is used to solve finite solid deformation. Several numerical examples are employed to verify proposed mIS-FEM, and to examine the improvements. The results demonstrate that mIS-FEM is a reliable and robust numeric method for interactions between fluid and solids undergo large deformation.
TL;DR: In this article, a gradient stable node-based smoothed finite element method (GS-FEM) is proposed to resolve the temporal instability of the node-Based SFA method while improving its accuracy.
Abstract: 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.
TL;DR: In this article, a cell-based smoothed finite element method with discrete shear gap technique is used to study the stochastic free vibration behavior of functionally graded plates with material uncertainty.
Abstract: A cell-based smoothed finite element method with discrete shear gap technique is used to study the stochastic free vibration behavior of functionally graded plates with material uncertainty. The pl...
TL;DR: In this article, a coupled multi-physical cell-based smoothed finite element method (CPCS-FEM) was proposed to investigate the static behavior of functionally grade magneto-electro-elastic (FG-MEEs) structures under thermal conditions.
TL;DR: The phase-field modeling is formulated in the framework of cell-based smoothed finite element method for predicting the crack propagation in solids with attractive features, and a user-friendly interface for ABAQUS is established based on Qt.
TL;DR: An edge-based smoothed finite element method (ES-FEM) combined with the mixed interpolation of tensorial components technique for triangular shell element (MITC3), called ES- MITC3, for free vibration analysis of functionally graded shells is investigated.
Abstract: An edge-based smoothed finite element method (ES-FEM) combined with the mixed interpolation of tensorial components technique for triangular shell element (MITC3), called ES-MITC3, for free vibration analysis of functionally graded shells is investigated in this work. In the formulation of the ES-MITC3, the stiffness matrices are obtained by using the strain-smoothing technique over the smoothing domains that are formed by two adjacent MITC3 triangular shell elements sharing an edge. The strain-smoothing technique can improve significantly the accuracy and convergence of the original MITC3. The material properties of functionally graded shells are assumed to vary through the thickness direction by a power–rule distribution of volume fractions of the constituents. The numerical examples demonstrated that the present ES-MITC3method is free of shear locking and achieves the high accuracy compared to the reference solutions in the literature.
TL;DR: A cell-based smoothed finite element method (CS-FEM) is adopted to solve the Navier–Stoke equations under the arbitrary Lagrangian–Eulerian description to solve partitioned fluid–structure interaction problems.
Abstract: This article presents a three-field smoothed formulation for partitioned fluid–structure interaction problems. The cell-based smoothed finite element method (CS-FEM) is adopted to solve the Navier–...
TL;DR: In this paper, an edge-based finite element method (ES-FEM-T3) combining with the perfectly matched layer (PML) technique is established for solving the elastic wave scattering in bounded domains with PML to eliminate wave reflections.
Abstract: Scattering of a time-harmonic plane elastic wave by a rigid obstacle embedded in an isotropic homogeneous elastic medium has wide applications in science and engineering. This paper presents a novel method to study elastic wave scattering problems satisfying the Navier equation and Helmholtz equations with coupled boundary obtained by Helmholtz decomposition. We derive first smoothed Galerkin weak forms of Navier equation and Helmholtz equations to create effective smoothed finite element method (S-FEM) models. On the top of a three-noded triangular mesh, an edge-based S-FEM (ES-FEM-T3) combining with the perfectly matched layer (PML) technique is then established for solving the elastic wave scattering in bounded domains with PML to eliminate wave reflections. Some numerical experiments demonstrate that ES-FEM-T3 is more stable and accurate than the standard FEM for the elastic wave scattering.
TL;DR: A smoothed stable extended finite element method (S2XFEM) is proposed by combining the strain smoothing with the stable extended infinite element method to efficiently treat inclusions and/or voids in hyperelastic matrix materials.
Abstract: In this paper, we propose a smoothed stable extended finite element method (S2XFEM) by combining the strain smoothing with the stable extended finite element method (SXFEM) to efficiently treat inclusions and/or voids in hyperelastic matrix materials. The interface geometries are implicitly represented through level sets and a geometry based error indicator is used to resolve the geometry. For the unknown fields, the mesh is refined based on a recovery based error indicator combined with a quadtree decomposition guarantee the method's accuracy with respect to the computational costs. Elements with hanging nodes (due to the quadtree meshes) are treated as polygonal elements with mean value coordinates as the basis functions. The accuracy and the convergence properties are compared to similar approaches for several numerical examples. The examples indicate that S2XFEM is computationally the most efficient without compromising the accuracy.
TL;DR: Coupling electromechanical cell-based smoothed finite element method (CSFEM) with the asymptotic homogenization method (AHM) is presented to overcome the overstiffness of FEM as discussed by the authors.
Abstract: Coupling electromechanical cell-based smoothed finite element method (CSFEM) with the asymptotic homogenization method (AHM) is presented to overcome the overstiffness of FEM. This method could accurately simulate the dynamic responses and electromechanical coupling effects of piezoelectric composite material (PCM) structures. Firstly, the efficient performances for active compounds of round cross-section fibers are calculated based on AHM. Secondly, in the CSFEM, electromechanical multi-physic-field FEM is coupled with gradient smoothing technique. CSFEM returns the nearly exact stiffness of continuum structures, which auto discretes the elements in complex areas more readily and thus remarkably reduces the numerical errors. Static and dynamic characteristics of four PCM structures are investigated using CSFEM with AHM. Results are compared with analytical solution and those of FEM, which proves that CSFEM with AHM is more accurate and reliable than the standard FEM when solving problems of complex structures. Additionally, CSFEM could provide results of higher accuracy even using distorted meshes. Therefore, such method is a robust tool for analyzing mechanical properties of PCM structures.