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Chan Lee Hobeom Kim Seyoung Im 《International journal for numerical methods in engineering》2017,110(11):1069-1100
The node‐based or edge‐based smoothed finite element method is extended to develop polyhedral elements that are allowed to have an arbitrary number of nodes or faces, and so retain a good geometric adaptability. The strain smoothing technique and implicit shape functions based on the linear point interpolation make the element formulation simple and straightforward. The resulting polyhedral elements are free from the excessive zero‐energy modes and yield a robust solution very much insensitive to mesh distortion. Several numerical examples within the framework of linear elasticity demonstrate the accuracy and convergence behavior. The smoothed finite element method‐based polyhedral elements in general yield solutions of better accuracy and faster convergence rate than those of the conventional finite element methods. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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G. R. Liu T. T. Nguyen K. Y. Dai K. Y. Lam 《International journal for numerical methods in engineering》2007,71(8):902-930
This paper examines the theoretical bases for the smoothed finite element method (SFEM), which was formulated by incorporating cell‐wise strain smoothing operation into standard compatible finite element method (FEM). The weak form of SFEM can be derived from the Hu–Washizu three‐field variational principle. For elastic problems, it is proved that 1D linear element and 2D linear triangle element in SFEM are identical to their counterparts in FEM, while 2D bilinear quadrilateral elements in SFEM are different from that of FEM: when the number of smoothing cells (SCs) of the elements equals 1, the SFEM solution is proved to be ‘variationally consistent’ and has the same properties with those of FEM using reduced integration; when SC approaches infinity, the SFEM solution will approach the solution of the standard displacement compatible FEM model; when SC is a finite number larger than 1, the SFEM solutions are not ‘variationally consistent’ but ‘energy consistent’, and will change monotonously from the solution of SFEM (SC = 1) to that of SFEM (SC → ∞). It is suggested that there exists an optimal number of SC such that the SFEM solution is closest to the exact solution. The properties of SFEM are confirmed by numerical examples. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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T. Nguyen‐Thoi G. R. Liu K. Y. Lam G. Y. Zhang 《International journal for numerical methods in engineering》2009,78(3):324-353
This paper presents a novel face‐based smoothed finite element method (FS‐FEM) to improve the accuracy of the finite element method (FEM) for three‐dimensional (3D) problems. The FS‐FEM uses 4‐node tetrahedral elements that can be generated automatically for complicated domains. In the FS‐FEM, the system stiffness matrix is computed using strains smoothed over the smoothing domains associated with the faces of the tetrahedral elements. The results demonstrated that the FS‐FEM is significantly more accurate than the FEM using tetrahedral elements for both linear and geometrically non‐linear solid mechanics problems. In addition, a novel domain‐based selective scheme is proposed leading to a combined FS/NS‐FEM model that is immune from volumetric locking and hence works well for nearly incompressible materials. The implementation of the FS‐FEM is straightforward and no penalty parameters or additional degrees of freedom are used. The computational efficiency of the FS‐FEM is found better than that of the FEM. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
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T. Nguyen‐Thoi P. Phung‐Van H. Nguyen‐Xuan C. Thai‐Hoang 《International journal for numerical methods in engineering》2012,91(7):705-741
The cell‐based strain smoothing technique is combined with discrete shear gap method using three‐node triangular elements to give a so‐called cell‐based smoothed discrete shear gap method (CS‐DSG3) for static and free vibration analyses of Reissner–Mindlin plates. In the process of formulating the system stiffness matrix of the CS‐DSG3, each triangular element will be divided into three subtriangles, and in each subtriangle, the stabilized discrete shear gap method is used to compute the strains and to avoid the transverse shear locking. Then the strain smoothing technique on whole the triangular element is used to smooth the strains on these three subtriangles. The numerical examples demonstrated that the CS‐DSG3 is free of shear locking, passes the patch test, and shows four superior properties such as: (1) being a strong competitor to many existing three‐node triangular plate elements in the static analysis; (2) can give high accurate solutions for problems with skew geometries in the static analysis; (3) can give high accurate solutions in free vibration analysis; and (4) can provide accurately the values of high frequencies of plates by using only coarse meshes. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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G. R. Liu T. Nguyen‐Thoi H. Nguyen‐Xuan K. Y. Dai K. Y. Lam 《International journal for numerical methods in engineering》2009,77(13):1863-1869
This paper is written in response to the recently published paper (Int. J. Numer. Meth. Engng 2008; 76 :1285–1295) at IJNME entitled ‘On the smoothed finite element method’ (SFEM) by Zhang HH, Liu SJ, Li LX. In this paper we
- (1) repeat briefly the important essence of the original SFEM presented in (Comp. Mech. 2007; 39 : 859–877; Int. J. Numer. Meth. Engng 2007; 71 :902–930; Int. J. Numer. Meth. Engng 2008; 74 :175–208; Finite Elem. Anal. Des. 2007; 43 :847–860; J. Sound Vib. 2007; 301 :803–820), and
- (2) examine further issues in the evaluation of the shape functions used in the SFEM.
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Y. Onishi R. Iida K. Amaya 《International journal for numerical methods in engineering》2017,109(11):1582-1606
A new smoothed finite element method (S‐FEM) with tetrahedral elements for finite strain analysis of nearly incompressible solids is proposed. The proposed method is basically a combination of the F‐bar method and edge‐based S‐FEM with tetrahedral elements (ES‐FEM‐T4) and is named ‘F‐barES‐FEM‐T4’. F‐barES‐FEM‐T4 inherits the accuracy and shear locking‐free property of ES‐FEM‐T4. At the same time, it also inherits the volumetric locking‐free property of the F‐bar method. The isovolumetric part of the deformation gradient ( F iso) is derived from the F of ES‐FEM‐T4, whereas the volumetric part ( F vol) is derived from the cyclic smoothing of J(=det( F )) between elements and nodes. Some demonstration analyses confirm that F‐barES‐FEM‐T4 with a sufficient number of cyclic smoothings suppresses the pressure oscillation in nearly incompressible materials successfully with no increase in DOF. Moreover, they reveal that our method is capable of relaxing the corner locking issue arising at the corner in the cylinder barreling analysis. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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H.‐H. Zhang S.‐J. Liu L.‐X. Li 《International journal for numerical methods in engineering》2008,76(8):1285-1295
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Z. C. He A. G. Cheng G. Y. Zhang Z. H. Zhong G. R. Liu 《International journal for numerical methods in engineering》2011,86(11):1322-1338
The paper reports a detailed analysis on the numerical dispersion error in solving 2D acoustic problems governed by the Helmholtz equation using the edge‐based smoothed finite element method (ES‐FEM), in comparison with the standard FEM. It is found that the dispersion error of the standard FEM for solving acoustic problems is essentially caused by the ‘overly stiff’ feature of the discrete model. In such an ‘overly stiff’ FEM model, the wave propagates with an artificially higher ‘numerical’ speed, and hence the numerical wave‐number becomes significantly smaller than the actual exact one. Owing to the proper softening effects provided naturally by the edge‐based gradient smoothing operations, the ES‐FEM model, however, behaves much softer than the standard FEM model, leading to the so‐called very ‘close‐to‐exact’ stiffness. Therefore the ES‐FEM can naturally and effectively reduce the dispersion error in the numerical solution in solving acoustic problems. Results of both theoretical and numerical studies will support these important findings. It is shown clearly that the ES‐FEM suits ideally well for solving acoustic problems governed by the Helmholtz equations, because of the crucial effectiveness in reducing the dispersion error in the discrete numerical model. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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A novel finite element (FE) formulation with adaptive mesh rezoning for large deformation problems is proposed. The proposed method takes the advantage of the selective smoothed FE method (S‐FEM), which has been recently developed as a locking‐free FE formulation with strain smoothing technique. We adopt the selective face‐based smoothed/node‐based smoothed FEM (FS/NS‐FEM‐T4) and edge‐based smoothed/node‐based smoothed FEM (ES/NS‐FEM‐T3) basically but modify them partly so that our method can handle any kind of material constitutive models other than elastic models. We also present an adaptive mesh rezoning method specialized for our S‐FEM formulation with material constitutive models in total form. Because of the modification of the selective S‐FEMs and specialization of adaptive mesh rezoning, our method is locking‐free for severely large deformation problems even with the use of tetrahedral and triangular meshes. The formulation details for static implicit analysis and several examples of analysis of the proposed method are presented in this paper to demonstrate its efficiency. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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C. T. Wu Wei Hu G. R. Liu 《International journal for numerical methods in engineering》2014,100(5):374-398
This paper presents a bubble‐enhanced smoothed finite element formulation for the analysis of volume‐constrained problems in two‐dimensional linear elasticity. The new formulation is derived based on the variational multi‐scale approach in which unequal order displacement‐pressure pairs are used for the mixed finite element approximation and hierarchical bubble function is selected for the fine‐scale displacement approximation. An area‐weighted averaging scheme is employed for the two‐scale smoothed strain calculation under the framework of edge‐based smoothed FEM. The smoothed fine‐scale solution is shown to naturally contain the stress field jump of the smoothed coarse‐scale solution across the boundary of edge‐based smoothing domain and thus provides the possibility to stabilize the global solution for volume‐constrained problems. A global monolithic solution strategy is employed, and the fine‐scale solution is solved without the consideration of approximating the strong form of the fine‐scale equation. Several numerical examples are analyzed to demonstrate the accuracy of the present formulation. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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Zhi‐Qian Zhang G. R. Liu Boo Cheong Khoo 《International journal for numerical methods in engineering》2012,90(10):1292-1320
A novel method called immersed smoothed FEM using three‐node triangular element is proposed for two‐dimensional fluid–structure interaction (FSI) problems with largely deformable nonlinear solids placed within incompressible viscous fluid. The fluid flows are solved using the semi‐implicit characteristic‐based split method. Smoothed FEMs are employed to calculate the transient responses of solids based on explicit time integration. The fictitious fluid with two assumptions is introduced to achieve the continuous form of the FSI conditions. The discrete formulations to calculate the FSI forces are obtained in terms of the characteristic‐based split scheme, and the algorithm based on a set of fictitious fluid mesh is proposed for evaluating the FSI force exerted on the solid. The accuracy, stability, and convergence properties of immersed smoothed FEM are verified by numerical examples. Investigations on the mesh size ratio indicate that the stability is fairly independent of the wide range of the mesh size ratio. No additional volume correction is required to satisfy the incompressible constraints. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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In this work, an enhanced cell‐based smoothed finite element method (FEM) is presented for the Reissner–Mindlin plate bending analysis. The smoothed curvature computed by a boundary integral along the boundaries of smoothing cells in original smoothed FEM is reformulated, and the relationship between the original approach and the present method in curvature smoothing is established. To improve the accuracy of shear strain in a distorted mesh, we span the shear strain space over the adjacent element. This is performed by employing an edge‐based smoothing technique through a simple area‐weighted smoothing procedure on MITC4 assumed shear strain field. A three‐field variational principle is utilized to develop the mixed formulation. The resultant element formulation is further reduced to a displacement‐based formulation via an assumed strain method defined by the edge‐smoothing technique. As the result, a new formulation consisting of smoothed curvature and smoothed shear strain interpolated by the standard transverse displacement/rotation fields and smoothing operators can be shown to improve the solution accuracy in cell‐based smoothed FEM for Reissner–Mindlin plate bending analysis. Several numerical examples are presented to demonstrate the accuracy of the proposed formulation.Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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Nicola Zani Magnus Ekh Anders Ekberg Angelo Mazz 《Fatigue & Fracture of Engineering Materials & Structures》2022,45(1):222-238
A semianalytical model is introduced to assess rolling contact fatigue problems in railway applications. The constitutive law is based on the nonlinear kinematic and isotropic hardening model of Chaboche–Lemaitre, which allows the cyclic elastoplastic strain under the contact surface to be evaluated. The much higher computational effectiveness in comparison with finite element (FE) analyses is quantified. The Dang Van multiaxial fatigue criterion is implemented to evaluate the rolling contact fatigue in the subsurface elastic region where cracking is relatively rare but more dangerous than surface cracks. The influence of the presence of sulfides in the wheel matrix in decreasing fatigue strength is also assessed by means of Murakami's approach. The model is used to compare conditions under small-scale twin-disk experiments to full-scale wheel/rail contact conditions. It is found that, for the same Hertzian pressure, the small-scale contact is more conservative in that it causes a deeper plasticized layer as compared with the elliptical full-scale contact. In the investigated cases, crack initiation is also not expected according to Dang Van criterion in neither of the studied contact conditions. 相似文献
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Markus Gitterle Alexander Popp Michael W. Gee Wolfgang A. Wall 《International journal for numerical methods in engineering》2010,84(5):543-571
A two‐dimensional, finite deformation frictional contact formulation with Coulomb's law is presented. The approach considers multibody contact and is based on a mortar formulation. The enforcement of contact constraints is realized with dual Lagrange multipliers. These alternative multiplier spaces are constructed in a way that the multipliers can easily be eliminated from the global system of equations by static condensation such that the system size does not increase. Friction kinematic variables are formulated in an objective way and enter non‐smooth complementarity functions for expressing the contact constraints. An active set strategy is derived by applying a semi‐smooth Newton method, which treats contact nonlinearities, material and geometrical nonlinearities in one single iterative scheme. By further carrying out a consistent linearization for both normal and frictional contact forces and constraints, a robust and highly efficient algorithm for linear and higher‐order (quadratic) interpolation is achieved. Efficiency of the proposed method and quality of results are demonstrated in several examples. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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Chen Jiang Zhi‐Qian Zhang Xu Han Guirong Liu Guang‐Jun Gao Tao Lin 《International journal for numerical methods in engineering》2018,114(2):147-171
In this paper, a novel characteristic–based penalty (CBP) scheme for the finite‐element method (FEM) is proposed to solve 2‐dimensional incompressible laminar flow. This new CBP scheme employs the characteristic‐Galerkin method to stabilize the convective oscillation. To mitigate the incompressible constraint, the selective reduced integration (SRI) and the recently proposed selective node–based smoothed FEM (SNS‐FEM) are used for the 4‐node quadrilateral element (CBP‐Q4SRI) and the 3‐node triangular element (CBP‐T3SNS), respectively. Meanwhile, the reduced integration (RI) for Q4 element (CBP‐Q4RI) and NS‐FEM for T3 element (CBP‐T3NS) with CBP scheme are also investigated. The quasi‐implicit CBP scheme is applied to allow a large time step for sufficient large penalty parameters. Due to the absences of pressure degree of freedoms, the quasi‐implicit CBP‐FEM has higher efficiency than quasi‐implicit CBS‐FEM. In this paper, the CBP‐Q4SRI has been verified and validated with high accuracy, stability, and fast convergence. Unexpectedly, CBP‐Q4RI is of no instability, high accuracy, and even slightly faster convergence than CBP‐Q4SRI. For unstructured T3 elements, CBP‐T3SNS also shows high accuracy and good convergence but with pressure oscillation using a large penalty parameter; CBP‐T3NS produces oscillated wrong velocity and pressure results. In addition, the applicable ranges of penalty parameter for different proposed methods have been investigated. 相似文献
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Alexander Popp Michael W. Gee Wolfgang A. Wall 《International journal for numerical methods in engineering》2009,79(11):1354-1391
In recent years, nonconforming domain decomposition techniques and, in particular, the mortar method have become popular in developing new contact algorithms. Here, we present an approach for 2D frictionless multibody contact based on a mortar formulation and using a primal–dual active set strategy for contact constraint enforcement. We consider linear and higher‐order (quadratic) interpolations throughout this work. So‐called dual Lagrange multipliers are introduced for the contact pressure but can be eliminated from the global system of equations by static condensation, thus avoiding an increase in system size. For this type of contact formulation, we provide a full linearization of both contact forces and normal (non‐penetration) and tangential (frictionless sliding) contact constraints in the finite deformation frame. The necessity of such a linearization in order to obtain a consistent Newton scheme is demonstrated. By further interpreting the active set search as a semi‐smooth Newton method, contact nonlinearity and geometrical and material nonlinearity can be resolved within one single iterative scheme. This yields a robust and highly efficient algorithm for frictionless finite deformation contact problems. Numerical examples illustrate the efficiency of our method and the high quality of results. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
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A novel singular ES-FEM method for simulating singular stress fields near the crack tips for linear fracture problems 总被引：1，自引：0，他引：1
This paper presents a novel numerical method for effectively simulating the singular stress field for mode-I fracture problems based on the edge-based smoothed finite element method (ES-FEM). Using the unique feature of the ES-FEM formulation, we need only the assumed displacement values (not the derivatives) on the boundary of the smoothing domains, and hence a new technique to construct singular shape functions is devised for the crack tip elements. Some examples have demonstrated that results of the present singular ES-FEM in terms of strain energy, displacement and J-integral are much more accurate than the finite element method using the same mesh. 相似文献
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A Smoothed Finite Element Method for Mechanics Problems 总被引：6，自引：4，他引：6
In the finite element method (FEM), a necessary condition for a four-node isoparametric element is that no interior angle
is greater than 180° and the positivity of Jacobian determinant should be ensured in numerical implementation. In this paper,
we incorporate cell-wise strain smoothing operations into conventional finite elements and propose the smoothed finite element
method (SFEM) for 2D elastic problems. It is found that a quadrilateral element divided into four smoothing cells can avoid
spurious modes and gives stable results for integration over the element. Compared with original FEM, the SFEM achieves more
accurate results and generally higher convergence rate in energy without increasing computational cost. More importantly,
as no mapping or coordinate transformation is involved in the SFEM, its element is allowed to be of arbitrary shape. Hence
the restriction on the shape bilinear isoparametric elements can be removed and problem domain can be discretized in more
flexible ways, as demonstrated in the example problems. 相似文献