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Journal articles on the topic 'Smoothed Finite Element'

Author: Grafiati

Published: 30 June 2021

Last updated: 1 February 2022

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1

Nguyen, T. T., G. R. Liu, K. Y. Dai, and K. Y. Lam. "Selective smoothed finite element method." Tsinghua Science and Technology 12, no. 5 (October 2007): 497–508. http://dx.doi.org/10.1016/s1007-0214(07)70125-6.

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2

Zhou, Liming, Ming Li, Guangwei Meng, and Hongwei Zhao. "An effective cell-based smoothed finite element model for the transient responses of magneto-electro-elastic structures." Journal of Intelligent Material Systems and Structures 29, no. 14 (June 12, 2018): 3006–22. http://dx.doi.org/10.1177/1045389x18781258.

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To overcome the over-stiffness and the imprecise magneto-electro-elastic coupling effects of finite element model, we presented a cell-based smoothed finite element model to more accurately simulate the transient responses of magneto-electro-elastic structures. In the cell-based smoothed finite element model, the gradient smoothing technique was introduced into a magneto-electro-elastic multi-physical-field finite element model. The cell-based smoothed finite element model can achieve a close-to-exact stiffness of the continuum structures which could automatically discrete elements for complicated regions more readily and thus remarkably reduced the numerical errors. In addition, the modified Wilson- θ method was presented for solving the motion equation of magneto-electro-elastic structures. Several numerical examples were investigated and exhibited that the cell-based smoothed finite element model could receive more accurate and reliable simulation results than the standard finite element model. Besides, the cell-based smoothed finite element model was employed to calculate transient responses of magneto-electro-elastic sensor and typical micro-electro-mechanical systems–based magneto-electro-elastic energy harvester. Therefore, the cell-based smoothed finite element model can be adopted to tackle the practical magneto-electro-elastic problems such as smart vibration transducers, magnetic field sensors, and energy harvester devices in intelligent magneto-electro-elastic structures systems.

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3

Zhang, H. H., S. J. Liu, and L. X. Li. "On the smoothed finite element method." International Journal for Numerical Methods in Engineering 76, no. 8 (November 19, 2008): 1285–95. http://dx.doi.org/10.1002/nme.2460.

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4

Surendran, M., Sundararajan Natarajan, Stéphane P. A. Bordas, and G. S. Palani. "Linear smoothed extended finite element method." International Journal for Numerical Methods in Engineering 112, no. 12 (October 11, 2017): 1733–49. http://dx.doi.org/10.1002/nme.5579.

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5

Thanh, Chau Dinh, Vo Ngoc Tuyen, and Nguyen Hoang Phuc. "A cell-based smoothed three-node plate finite element with a bubble node for static analyses of both thin and thick plates." Vietnam Journal of Mechanics 39, no. 3 (September 23, 2017): 229–43. http://dx.doi.org/10.15625/0866-7136/8809.

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This paper develops the cell-based (CS) smoothed finite element method for a three-node plate finite element with a bubble node at the centroid of the element. Based on the first-order shear deformation theory, the in-plane strains are smoothed on three non-overlapped subdomains of the element to transform the numerical integration of the element stiffness matrix from the surfaces into the lines of the subdomains. The shear-locking phenomenon, which occurs when the plate's thickness becomes small, is removed by employing the mixed interpolation of tensorial components (MITC). The present element, namely CS-MITC3+, passes the patch test and behaves independently from the sequence of node numbers of the element. Numerical results given by the CS-MITC3+ elements are better than the MITC3+ elements. As compared to other smoothed three-node plate finite elements, the CS-MITC3+ is a good competitor.

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6

KUMAR, V., and R. METHA. "IMPACT SIMULATIONS USING SMOOTHED FINITE ELEMENT METHOD." International Journal of Computational Methods 10, no. 04 (April 23, 2013): 1350012. http://dx.doi.org/10.1142/s0219876213500126.

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We present impact simulations with the Smoothed Finite Element Method (SFEM). Therefore, we develop the SFEM in the context of explicit dynamic applications based on diagonalized mass matrix. Since SFEM is not based on the isoparametric concept and is based on line integration rather than domain integration, it is very promising for events involving large deformations and severe element distortion as they occur in high dynamic events such as impacts. For some benchmark problems, we show that SFEM is superior to standard FEM for impact events. To our best knowledge, this is the first time SFEM is applied in the context of impact analysis based on explicit time integration.

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7

Christiansen, Snorre H., and Ragnar Winther. "Smoothed projections in finite element exterior calculus." Mathematics of Computation 77, no. 262 (December 20, 2007): 813–30. http://dx.doi.org/10.1090/s0025-5718-07-02081-9.

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8

Lee, Chaemin, and Phill-Seung Lee. "The strain-smoothed MITC3+ shell finite element." Computers & Structures 223 (October 2019): 106096. http://dx.doi.org/10.1016/j.compstruc.2019.07.005.

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9

Oh, Min-Han, and San Kim. "Strategy to Improve Edge-Based Smoothed Finite Element Solutions Using Enriched 2D Solid Finite Elements." Applied Sciences 11, no. 8 (April 13, 2021): 3476. http://dx.doi.org/10.3390/app11083476.

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In this paper, we present an automatic procedure that enhances the solution accuracy of edge-based smoothed 2D solid finite elements (three-node triangular and four-node quadrilateral elements). To obtain an enhanced solution, an adaptive enrichment scheme that uses enriched 2D solid finite elements and can effectively improve solution accuracy by applying cover functions adaptively without mesh-refinement is adopted in this procedure. First, the error of the edge-based finite element solution is estimated using a devised error estimation method, and appropriate cover functions are assigned for each node. While the edge-based smoothed finite elements provide piecewise constant strain fields, the proposed enrichment scheme uses the enriched finite elements to obtain a higher order strain field within the finite elements. Through various numerical examples, we demonstrate the accuracy improvement and efficiency achieved.

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10

LIU, S. J., H. WANG, and H. ZHANG. "SMOOTHED FINITE ELEMENTS LARGE DEFORMATION ANALYSIS." International Journal of Computational Methods 07, no. 03 (September 2010): 513–24. http://dx.doi.org/10.1142/s0219876210002246.

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The smoothed finite element method (SFEM) was developed in order to eliminate certain shortcomings of the finite element method (FEM). SFEM enjoys some of the flexibilities of meshfree methods. One advantage of SFEM is its applicability to modeling large deformations. Due to the absence of volume integration and parametric mapping, issues such as negative volumes and singular Jacobi matrix do not occur. However, despite these advantages, SFEM has never been applied to problems with extreme large deformation. For the first time, we apply SFEM to extreme large deformations. For two numerical problems, we demonstrate the advantages of SFEM over FEM. We also show that SFEM can compete with the flexibility of meshfree methods.

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11

Pei, Yongjie, and Xiangyang Cui. "A Novel Triangular Prism Element Based on Smoothed Finite Element Method." International Journal of Computational Methods 15, no. 07 (October 12, 2018): 1850058. http://dx.doi.org/10.1142/s0219876218500585.

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In this paper, a novel triangular prism element based on smoothed finite element method (SFEM) is proposed for three-dimensional static and dynamic mechanics problems. The accuracy of the proposed element is comparable to that of the hexahedral element while keeping good adaptability as the tetrahedral element on a surface dimension. In the process of constructing the proposed element, one triangular prism element is further divided into two smoothing cells. Very simple shape functions and a constant smoothing function are used in the construction of the smoothed strains and the smoothed nominal stresses. The divergence theorem is applied to convert the volume integral to the integrals of all the surrounding surfaces of a smoothing cell. Thus, no gradient of shape function and no mapping or coordinate transformation are involved in the process of creating the discretized system equations. Afterwards, several numerical examples include elastic-static and free vibration problems are provided to demonstrate the accuracy and efficiency of the proposed element. Meanwhile, an explicit scheme of the proposed element is given for dynamic large-deformation analysis of elastic-plastic materials, and the numerical results show good agreement with the experimental data.

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12

Liu, G. R., K. Y. Dai, and T. T. Nguyen. "A Smoothed Finite Element Method for Mechanics Problems." Computational Mechanics 39, no. 6 (May 17, 2006): 859–77. http://dx.doi.org/10.1007/s00466-006-0075-4.

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13

Lee, Chaemin, San Kim, and Phill-Seung Lee. "The strain-smoothed 4-node quadrilateral finite element." Computer Methods in Applied Mechanics and Engineering 373 (January 2021): 113481. http://dx.doi.org/10.1016/j.cma.2020.113481.

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14

Kim, Hobeom, and Seyoung Im. "Polyhedral smoothed finite element method for thermoelastic analysis." Journal of Mechanical Science and Technology 31, no. 12 (December 2017): 5937–49. http://dx.doi.org/10.1007/s12206-017-1138-5.

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15

Nguyen-Xuan, H., T. Rabczuk, Stéphane Bordas, and J. F. Debongnie. "A smoothed finite element method for plate analysis." Computer Methods in Applied Mechanics and Engineering 197, no. 13-16 (February 2008): 1184–203. http://dx.doi.org/10.1016/j.cma.2007.10.008.

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16

Nguyen-Thanh, N., Timon Rabczuk, H. Nguyen-Xuan, and Stéphane P. A. Bordas. "A smoothed finite element method for shell analysis." Computer Methods in Applied Mechanics and Engineering 198, no. 2 (December 2008): 165–77. http://dx.doi.org/10.1016/j.cma.2008.05.029.

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17

Li, Eric, Z. C. He, X. Xu, and G. R. Liu. "Hybrid smoothed finite element method for acoustic problems." Computer Methods in Applied Mechanics and Engineering 283 (January 2015): 664–88. http://dx.doi.org/10.1016/j.cma.2014.09.021.

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18

CUI, X. Y., G. Y. LI, and G. R. LIU. "AN EXPLICIT SMOOTHED FINITE ELEMENT METHOD (SFEM) FOR ELASTIC DYNAMIC PROBLEMS." International Journal of Computational Methods 10, no. 01 (February 2013): 1340002. http://dx.doi.org/10.1142/s0219876213400021.

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This paper presents an explicit smoothed finite element method (SFEM) for elastic dynamic problems. The central difference method for time integration will be used in presented formulations. A simple but general contact searching algorithm is used to treat the contact interface and an algorithm for the contact force is presented. In present method, the problem domain is first divided into elements as in the finite element method (FEM), and the elements are further subdivided into several smoothing cells. Cell-wise strain smoothing operations are used to obtain the stresses, which are constants in each smoothing cells. Area integration over the smoothing cell becomes line integration along its edges, and no gradient of shape functions is involved in computing the field gradients nor in forming the internal force. No mapping or coordinate transformation is necessary so that the element can be used effectively for large deformation problems. Through several examples, the simplicity, efficiency and reliability of the smoothed finite element method are demonstrated.

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19

Pham, Quoc-Hoa, The-Van Tran, Tien-Dat Pham, and Duc-Huynh Phan. "An Edge-Based Smoothed MITC3 (ES-MITC3) Shell Finite Element in Laminated Composite Shell Structures Analysis." International Journal of Computational Methods 15, no. 07 (October 12, 2018): 1850060. http://dx.doi.org/10.1142/s0219876218500603.

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This paper proposes an improvement of the MITC3 shell finite element to analyze of laminated composite shell structures. In order to enhance the accuracy and convergence of MITC3 element, an edge-based smoothed finite element method (ES-FEM) is applied to the derivation of the membrane, bending and shear stiffness terms of the MITC3 element, named ES-MICT3. In the ES-FEM, the smoothed strain is calculated in the domain that constructed by two adjacent MITC3 triangular elements sharing an edge. On a curved geometry of shell models, two adjacent MITC3 triangular elements may not be placed on the same plane. In this case, the edge-based smoothed strain can be performed on the virtual plane based on strain transformation matrices between the global coordinate and this virtual coordinate. Furthermore, a simple modification coefficient is chosen to be [Formula: see text] times the maximum diagonal value of the element stiffness matrix at the zero drilling degree of freedom to avoid the drill rotation locking when all elements meeting at a node are coplanar. The numerical examples demonstrated that the proposed method achieves the high accuracy in comparison to others existing elements in the literature.

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20

Cui, Xiang Yang, Shu Chang, and Guang Yao Li. "A Two-Step Taylor Galerkin Smoothed Finite Element Method for Lagrangian Dynamic Problem." International Journal of Computational Methods 12, no. 04 (August 2015): 1540004. http://dx.doi.org/10.1142/s0219876215400046.

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In this paper, a two-step Taylor Galerkin smoothed finite element method (TG-SFEM) is presented to deal with the two-dimensional Lagrangian dynamic problems. In this method, the smoothed Galerkin weak form is employed to create discretized system equations, and the cell-based smoothing domains are used to perform the smoothing operation and the numerical integration. The stability and the adaptation of elements aberrations presented in the two-step TG-SFEM are studied through detailed analyses of numerical examples. In the analysis of wave propagation, the proposed method can provide smoother displacement and stress than the common SFEM does, and energy fluctuations are found to be minimal. In the large deformation problems, the TG-SFEM can acclimatize itself to the mesh distortion effectively and stay bounded for long durations because the isoparametric elements are replaced, and area integration over each smoothing cells is recast into line integration along edges and no mapping is needed. Therefore, the stability, flexibility of elements distortion and the property of energy conservation of the TG-SFEM applied on two-dimensional solid problems are well represented and clarified.

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21

ONISHI, Yuki. "Implementation of the Smoothed Finite Element Method using 10-node Tetrahedral Elements into a General Purpose Finite Element Software." Proceedings of The Computational Mechanics Conference 2018.31 (2018): 171. http://dx.doi.org/10.1299/jsmecmd.2018.31.171.

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22

Lee, Chan, Hobeom Kim, and Seyoung Im. "Polyhedral elements by means of node/edge-based smoothed finite element method." International Journal for Numerical Methods in Engineering 110, no. 11 (November 17, 2016): 1069–100. http://dx.doi.org/10.1002/nme.5449.

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23

Liu, Jun, Zhi-Qian Zhang, and Guiyong Zhang. "A Smoothed Finite Element Method (S-FEM) for Large-Deformation Elastoplastic Analysis." International Journal of Computational Methods 12, no. 04 (August 2015): 1540011. http://dx.doi.org/10.1142/s0219876215400113.

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An edge-based smoothed finite element method (ES-FEM) using 3-node triangular element was recently proposed to improve the accuracy and convergence rate of the standard finite element method (FEM) for 2D elastic solid mechanics problems. In this research, ES-FEM is extended to large-deformation plasticity analysis, and a selective edge-based/node-based smoothed finite element (selective ES/NS-FEM) method using 3-node triangular elements is adopted to address volumetric locking problem. Validity of ES-FEM for large-deformation plasticity problem is proved by benchmarks, and numerical examples demonstrate that, the proposed ES-FEM and selective ES/NS-FEM method possess (1) superior accuracy and convergence properties for strain energy solutions comparing to the standard FEM using 3-node triangular element (FEM-T3), (2) better computational efficiency than FEM-T3 and similar computational efficiency as FEM using 4-node quadrilateral element and 6-node quadratic triangular element, (3) a selective ES/NS-FEM method can successfully simulate problems with severe element distortion, and address volumetric locking problem in large-deformation plasticity analysis.

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24

Rokach, Ihor. "Stress Intensity Factor Calculation by Smoothed Finite Element Method." Solid State Phenomena 250 (April 2016): 163–68. http://dx.doi.org/10.4028/www.scientific.net/ssp.250.163.

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Accuracy of stress intensity factor (SIF) determination by three types of smooth finite element method (namely, ES-FEM, NS-FEM and α-FEM) has been investigated. Two types of simple benchmark problems (uniaxial tension of the specimens with central and edge cracks) have been considered. SIF values were calculated by virtual crack extension and modified crack closure integral methods on almost uniform meshes. It has been shown that utilizing of ES-FEM and α-FEM significantly improves accuracy of the results compared with the traditional FEM.

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25

KUMAR, V. "SMOOTHED FINITE ELEMENT METHODS FOR THERMO-MECHANICAL IMPACT PROBLEMS." International Journal of Computational Methods 10, no. 01 (February 2013): 1340010. http://dx.doi.org/10.1142/s0219876213400100.

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We present a Smoothed Finite Element Methods (SFEM) for thermo-mechanical impact problems. The smoothing is applied to the strains and the standard finite element approach is used for the temperature field. The SFEM allows for highly accurate results and large deformations. No isoparametric mapping is needed; the shape functions are computed in the physical domain. Moreover, no derivatives of the shape functions must be computed. We implemented a visco-plastic constitutive model and validate the method by comparing numerical results to experimental data.

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26

Liu, G. R., T. T. Nguyen, K. Y. Dai, and K. Y. Lam. "Theoretical aspects of the smoothed finite element method (SFEM)." International Journal for Numerical Methods in Engineering 71, no. 8 (2007): 902–30. http://dx.doi.org/10.1002/nme.1968.

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27

He, Z. C., G. Y. Zhang, L. Deng, Eric Li, and G. R. Liu. "Topology Optimization Using Node-Based Smoothed Finite Element Method." International Journal of Applied Mechanics 07, no. 06 (December 2015): 1550085. http://dx.doi.org/10.1142/s1758825115500854.

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The node-based smoothed finite element method (NS-FEM) proposed recently has shown very good properties in solid mechanics, such as providing much better gradient solutions. In this paper, the topology optimization design of the continuum structures under static load is formulated on the basis of NS-FEM. As the node-based smoothing domain is the sub-unit of assembling stiffness matrix in the NS-FEM, the relative density of node-based smoothing domains serves as design variables. In this formulation, the compliance minimization is considered as an objective function, and the topology optimization model is developed using the solid isotropic material with penalization (SIMP) interpolation scheme. The topology optimization problem is then solved by the optimality criteria (OC) method. Finally, the feasibility and efficiency of the proposed method are illustrated with both 2D and 3D examples that are widely used in the topology optimization design.

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28

Choi, J. H., and B. C. Lee. "Rotation-free triangular shell element using node-based smoothed finite element method." International Journal for Numerical Methods in Engineering 116, no. 6 (August 12, 2018): 359–79. http://dx.doi.org/10.1002/nme.5928.

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29

LIU, G. R. "A GENERALIZED GRADIENT SMOOTHING TECHNIQUE AND THE SMOOTHED BILINEAR FORM FOR GALERKIN FORMULATION OF A WIDE CLASS OF COMPUTATIONAL METHODS." International Journal of Computational Methods 05, no. 02 (June 2008): 199–236. http://dx.doi.org/10.1142/s0219876208001510.

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This paper presents a generalized gradient smoothing technique, the corresponding smoothed bilinear forms, and the smoothed Galerkin weakform that is applicable to create a wide class of efficient numerical methods with special properties including the upper bound properties. A generalized gradient smoothing technique is first presented for computing the smoothed strain fields of displacement functions with discontinuous line segments, by "rudely" enforcing the Green's theorem over the smoothing domain containing these discontinuous segments. A smoothed bilinear form is then introduced for Galerkin formulation using the generalized gradient smoothing technique and smoothing domains constructed in various ways. The numerical methods developed based on this smoothed bilinear form will be spatially stable and convergent and possess three major important properties: (1) it is variationally consistent, if the solution is sought in a Hilbert space; (2) the stiffness of the discretized model will be reduced compared to the model of the finite element method (FEM) and often the exact model, which allows us to obtain upper bound solutions with respect to both the FEM solution and the exact solution; (3) the solution of the numerical method developed using the smoothed bilinear form is less insensitive to the quality of the mesh, and triangular meshes can be used perfectly without any problems. These properties have been proved, examined, and confirmed by the numerical examples. The smoothed bilinear form establishes a unified theoretical foundation for a class of smoothed Galerkin methods to analyze solid mechanics problems for solutions of special and unique properties: the node-based smoothed point interpolation method (NS-PIM), smoothed finite element method (SFEM), node-based smoothed finite element method (N-SFEM), edge-based smoothed finite element method (E-SFEM), cell-based smoothed point interpolation method (CS-PIM), etc.

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30

Natarajan, Sundararajan, Stéphane PA Bordas, and Ean Tat Ooi. "Virtual and smoothed finite elements: A connection and its application to polygonal/polyhedral finite element methods." International Journal for Numerical Methods in Engineering 104, no. 13 (July 21, 2015): 1173–99. http://dx.doi.org/10.1002/nme.4965.

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31

Li, Wei, Yingbin Chai, Xiangyu You, and Qifan Zhang. "An Edge-Based Smoothed Finite Element Method for Analyzing Stiffened Plates." International Journal of Computational Methods 16, no. 06 (May 27, 2019): 1840031. http://dx.doi.org/10.1142/s0219876218400315.

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In this paper, an edge-based smoothed finite element method with the discrete shear gap using triangular elements (ES-DSG3) is presented for static, free vibration and sound radiation analyses of plates stiffened by eccentric and concentric stiffeners. In the present model, the ES-DSG3 for the plate element with the isoparametric thick-beam element is employed to formulate stiffened plate structures. The deflections and rotations of the plates and the stiffeners are connected at tying positions. By using Rayleigh integral, sound radiation of stiffened plates subjected to a point load can be obtained. The edge-based gradient smoothing technique is employed to perform the related numerical integrations over the edge-based smoothing domains. Compared with the original DSG3 model, the present ES-DSG3 model is relatively softer as a result of the edge-based gradient smoothing technique. From several numerical examples, it is observed that the ES-DSG3 can produce more accurate numerical solutions than the original DSG3 for stiffened plates.

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32

Cui, Xiang Yang, Xiao Bin Hu, Guang Yao Li, and Gui Rong Liu. "A Modified Smoothed Finite Element Method for Static and Free Vibration Analysis of Solid Mechanics." International Journal of Computational Methods 13, no. 06 (November 2, 2016): 1650043. http://dx.doi.org/10.1142/s0219876216500432.

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The smoothed finite element method (S-FEM) proposed recently is more accurate and has higher convergence rate compared with standard four-node isoparametric finite element method (FEM). In this work, a modified S-FEM using four-node quadrilateral elements is proposed, which greatly reduces further the computation cost while maintaining the high accuracy and convergence rate. The key idea of the proposed modification is that the strain of the element is a weighted average value of the smoothed strains in the smoothing cells (SCs), which means that only one integration point is required to construct the stiffness matrix, similar to the single cell S-FEM. A stabilization item is proposed using the differences of the smoothed strains obtained in four SCs, which installs the stability of algorithm and increases the accuracy. To verify the efficiency, accuracy and stability of the present formulation, a number of numerical examples of static and free vibration problems, are studied in comparison with different existing numerical methods.

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33

ONISHI, Yuki, and Kenji AMAYA. "Large Deformation Analysis of Rubber using Smoothed Finite Element Method with Tetrahedral Elements." Proceedings of The Computational Mechanics Conference 2014.27 (2014): 446–48. http://dx.doi.org/10.1299/jsmecmd.2014.27.446.

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34

Li, Y. H., R. P. Niu, and G. R. Liu. "Highly accurate smoothed finite element methods based on simplified eight-noded hexahedron elements." Engineering Analysis with Boundary Elements 105 (August 2019): 165–77. http://dx.doi.org/10.1016/j.enganabound.2019.03.020.

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35

Yang, Jian, Wei Xie, and Zhiwei Zhang. "Exploring three-dimensional edge-based smoothed finite element method based on polyhedral mesh to study elastic mechanics problems." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 39, no. 4 (August 2021): 747–52. http://dx.doi.org/10.1051/jnwpu/20213940747.

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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.

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36

Oshiro, Kai, Hiroka Miyakubo, Masaki Fujikawa, and Chobin Makabe. "Hexahedral-Based Smoothed Finite Element Method Using Volumetric-Deviatoric Split for Contact Problem." Materials Science Forum 940 (December 2018): 84–88. http://dx.doi.org/10.4028/www.scientific.net/msf.940.84.

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A first-order hexahedral (H8)-element-based smoothed finite element method (S-FEM) with a volumetric-deviatoric split for nearly incompressible materials was developed for highly accurate deformation analysis of large-strain problems. In the proposed method, the isovolumetric part of the deformation gradient at the integration point is derived from F based on the beta finite element method (i.e., an S-FEM), whereas the volumetric part of the deformation gradient is derived from F on the basis of the standard FEM with reduced integration elements. This method targets H8 elements that are automatically generated from tetrahedral elements, which makes it quite practical. This is because the FE mesh can be created automatically even if the targeted object has a complex shape. This method eliminates the phenomena of volumetric and shear locking, and reduces pressure oscillations. The proposed method was implemented in the commercial FE software Abaqus and applied to the large-deformation contact problem to verify its effectiveness.

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37

LI, Y., M. LI, and G. R. LIU. "A MODIFIED TRIANGULATION ALGORITHM TAILORED FOR THE SMOOTHED FINITE ELEMENT METHOD (S-FEM)." International Journal of Computational Methods 11, no. 01 (September 2, 2013): 1350069. http://dx.doi.org/10.1142/s0219876213500692.

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Meshing is one of the key tasks in using the finite element method (FEM), the smoothed finite element method (S-FEM), finite volume method (FVM), and many other discrete numerical methods. Linear triangular (T3) mesh is one of the most widely used mesh, because it can be generated and refined automatically for discrete domains of complicated geometry, and hence save significantly the time for model creation. This paper presents a modified triangulation algorithm based on the advancing front technique to provide a comprehensive linear triangular mesh generator with six connectivity lists, including element–node (Ele–N) connectivity, element–edge (Ele–Eg) connectivity, edge–node (Eg–N) connectivity, edge–element (Eg–Ele) connectivity, node–edge (N–Eg) connectivity and node–element (N–Ele) connectivity. These six connectivity lists are generated along the way when the T3 elements are created, and hence it is done in a most efficient fashion. The connectivity is recorded in the usual counter-clockwise convention for convenient utilization in various S-FEM models for effective analyses. In addition, an algorithm is developed for renumbering the nodes in the T3 mesh to obtain a minimized bandwidth of stiffness matrices for both FEM and S-FEM models.

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38

Jansari, Chintan, Sundararajan Natarajan, Lars Beex, and K. Kannan. "Adaptive smoothed stable extended finite element method for weak discontinuities for finite elasticity." European Journal of Mechanics - A/Solids 78 (November 2019): 103824. http://dx.doi.org/10.1016/j.euromechsol.2019.103824.

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39

YAO, Lingyun. "Smoothed Finite Element Method for Two-dimensional Acoustic Numerical Computation." Journal of Mechanical Engineering 46, no. 18 (2010): 115. http://dx.doi.org/10.3901/jme.2010.18.115.

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Jankowiak, T., and T. Łodygowski. "Smoothed particle hydrodynamics versus finite element method for blast impact." Bulletin of the Polish Academy of Sciences: Technical Sciences 61, no. 1 (March 1, 2013): 111–21. http://dx.doi.org/10.2478/bpasts-2013-0009.

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Abstract The paper considers the failure study of concrete structures loaded by the pressure wave due to detonation of an explosive material. In the paper two numerical methods are used and their efficiency and accuracy are compared. There are the Smoothed Particle Hydrodynamics (SPH) and the Finite Element Method (FEM). The numerical examples take into account the dynamic behaviour of concrete slab or a structure composed of two concrete slabs subjected to the blast impact coming from one side. The influence of reinforcement in the slab (1, 2 or 3 layers) is also presented and compared with a pure concrete one. The influence of mesh density for FEM and the influence of important parameters in SPH like a smoothing length or a particle distance on the quality of the results are discussed in the paper

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Shobeiri, Vahid. "Structural Topology Optimization Based on the Smoothed Finite Element Method." Latin American Journal of Solids and Structures 13, no. 2 (February 2016): 378–90. http://dx.doi.org/10.1590/1679-78252243.

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Atia, Khaled S. R., A. M. Heikal, and S. S. A. Obayya. "Efficient smoothed finite element time domain analysis for photonic devices." Optics Express 23, no. 17 (August 14, 2015): 22199. http://dx.doi.org/10.1364/oe.23.022199.

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Bordas, Stéphane P. A., and Sundararajan Natarajan. "On the approximation in the smoothed finite element method (SFEM)." International Journal for Numerical Methods in Engineering 81, no. 5 (August 12, 2009): 660–70. http://dx.doi.org/10.1002/nme.2713.

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Chen, L., J. Zhang, K. Y. Zeng, and P. G. Jiao. "An edge-based smoothed finite element method for adaptive analysis." Structural Engineering and Mechanics 39, no. 6 (September 25, 2011): 767–93. http://dx.doi.org/10.12989/sem.2011.39.6.767.

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Zhang, Juan, Mingquan Zhou, Youliang Huang, Pu Ren, Zhongke Wu, Xuesong Wang, and Shi Feng Zhao. "A Smoothed Finite Element-Based Elasticity Model for Soft Bodies." Mathematical Problems in Engineering 2017 (2017): 1–14. http://dx.doi.org/10.1155/2017/1467356.

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One of the major challenges in mesh-based deformation simulation in computer graphics is to deal with mesh distortion. In this paper, we present a novel mesh-insensitive and softer method for simulating deformable solid bodies under the assumptions of linear elastic mechanics. A face-based strain smoothing method is adopted to alleviate mesh distortion instead of the traditional spatial adaptive smoothing method. Then, we propose a way to combine the strain smoothing method and the corotational method. With this approach, the amplitude and frequency of transient displacements are slightly affected by the distorted mesh. Realistic simulation results are generated under large rotation using a linear elasticity model without adding significant complexity or computational cost to the standard corotational FEM. Meanwhile, softening effect is a by-product of our method.

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Li, Eric, C. C. Chang, Z. C. He, Zhongpu Zhang, and Q. Li. "Smoothed finite element method for topology optimization involving incompressible materials." Engineering Optimization 48, no. 12 (April 6, 2016): 2064–89. http://dx.doi.org/10.1080/0305215x.2016.1153926.

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Zhang, Wei, Beibing Dai, Zhen Liu, and Cuiying Zhou. "Modeling discontinuous rock mass based on smoothed finite element method." Computers and Geotechnics 79 (October 2016): 22–30. http://dx.doi.org/10.1016/j.compgeo.2016.05.020.

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Meng, Jingjing, Xue Zhang, Jinsong Huang, Hongxiang Tang, Hans Mattsson, and Jan Laue. "A smoothed finite element method using second-order cone programming." Computers and Geotechnics 123 (July 2020): 103547. http://dx.doi.org/10.1016/j.compgeo.2020.103547.

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Lee, Changkye, Sundararajan Natarajan, Jack S. Hale, Zeike A. Taylor, Jurng-Jae Yee, and St閜hane P. A. Bordas. "Bubble-Enriched Smoothed Finite Element Methods for Nearly-Incompressible Solids." Computer Modeling in Engineering & Sciences 127, no. 2 (2021): 411–36. http://dx.doi.org/10.32604/cmes.2021.014947.

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XU, XU, YUANTONG GU, and GUIRONG LIU. "A HYBRID SMOOTHED FINITE ELEMENT METHOD (H-SFEM) TO SOLID MECHANICS PROBLEMS." International Journal of Computational Methods 10, no. 01 (February 2013): 1340011. http://dx.doi.org/10.1142/s0219876213400112.

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In this paper, a hybrid smoothed finite element method (H-SFEM) is developed for solid mechanics problems by combining techniques of finite element method (FEM) and node-based smoothed finite element method (NS-FEM) using a triangular mesh. A parameter α is equipped into H-SFEM, and the strain field is further assumed to be the weighted average between compatible stains from FEM and smoothed strains from NS-FEM. We prove theoretically that the strain energy obtained from the H-SFEM solution lies in between those from the compatible FEM solution and the NS-FEM solution, which guarantees the convergence of H-SFEM. Intensive numerical studies are conducted to verify these theoretical results and show that (1) the upper- and lower-bound solutions can always be obtained by adjusting α; (2) there exists a preferable α at which the H-SFEM can produce the ultrasonic accurate solution.

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