AN EXPLICIT SMOOTHED FINITE ELEMENT METHOD (SFEM) FOR ELASTIC DYNAMIC PROBLEMS

2013 ◽  
Vol 10 (01) ◽  
pp. 1340002 ◽  
Author(s):  
X. Y. CUI ◽  
G. Y. LI ◽  
G. R. LIU
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Time Integration ◽  
Internal Force ◽  
Dynamic Problems ◽  
Central Difference ◽  
Strain Smoothing ◽  
Smoothed Finite Element Method ◽  
Central Difference Method ◽  
Element Method

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.

Fracture simulations using edge-based smoothed finite element method for isotropic damage model via Delaunay/Voronoi dual tessellations

2021 ◽  
pp. 105678952110405
Author(s):  
Young Kwang Hwang ◽  
Suyeong Jin ◽  
Jung-Wuk Hong
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Voronoi Tessellation ◽  
Damage Model ◽  
Time Integration ◽  
Voronoi Cell ◽  
Smoothed Finite Element Method ◽  
Isotropic Damage ◽  
Edge Based ◽  
Element Method

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 Delaunay triangulation and Voronoi tessellation is utilized for the mesh construction and the compatible use of the finite element solution with the Voronoi-cell lattice geometry. The mesh irregularity is introduced to avoid calculating the biased crack path by adding random variation in the nodal coordinates, and the ES-FEM elements are defined along the Delaunay edges. With the Voronoi tessellation, each nodal mass is calculated and the fractured surfaces are visualized along the Voronoi edges. The rotational degrees of freedom are implemented for each node by introducing the elemental formulation of the Voronoi-cell lattice model, and the accurate visualizations of the rotational motions in the Voronoi diagram are achieved. An isotropic damage model is newly incorporated into the ES-FEM formulation, and the equivalent elemental length is introduced with an additional geometric factor to simulate the consistent softening behaviors with reducing the mesh sensitivity. The full matrix form of the smoothed strain-displacement matrix is constructed for optimal use in the element-wise computations during explicit time integration, and parallel computing is implemented for the enhancement of the computational efficiency. The simulated results are compared with the theoretical solutions or experimental results, which demonstrates the effectiveness of the proposed methodology in the simulations of the quasi-brittle fractures.

THERMO-MECHANICAL ANALYSIS OF COMPOSITE PRESSURE VESSELS USING EDGE-BASED SMOOTHED FINITE ELEMENT METHOD

2014 ◽  
Vol 11 (06) ◽  
pp. 1350089 ◽  
Author(s):  
SHIZHE FENG ◽  
XIANGYANG CUI ◽  
GUANGYAO LI
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Mechanical Analysis ◽  
Pressure Vessels ◽  
Strain Smoothing ◽  
Smoothed Finite Element Method ◽  
Edge Based ◽  
Element Method ◽  
Composite Pressure Vessels

In this paper, an edge-based smoothed finite element method (ES-FEM) is further formulated to deal with the thermo-mechanical analysis of composite pressure vessels. In the ES-FEM, the problem domain is first discretized into a set of triangular elements, and the edge-based smoothing domains are further formed along the edges of the triangular meshes. In order to improve the accuracy, the stiffness matrices are calculated using the strain smoothing technique in these smoothing domains. The thermal and mechanical properties are assumed to vary between different layers. The present formulation is straight-forward and no penalty parameters or additional degrees of freedom are used. Several numerical examples are given to demonstrate the effectivity of ES-FEM for thermo-mechanical analysis of composite pressure vessels.

scholarly journals A Modified Cell-Based Strain Smoothing for Material Nonlinearity

2019 ◽  
Author(s):  
Chang Kye Lee ◽  
Sundararajan Natarajan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Main Idea ◽  
Nonlinear Problems ◽  
Triangular Element ◽  
Smoothing Function ◽  
Strain Smoothing ◽  
Smoothed Finite Element Method ◽  
Linear Smoothing ◽  
Element Method

This work presents a linear smoothing scheme over high-order triangular elements in the framework of a cell-based strain smoothed finite element method for two-dimensional nonlinear problems. The main idea behind the proposed linear smoothing scheme for strain-smoothed finite element method (S-FEM) is no subdivision of finite element cells to sub-cells while the classical S-FEM needs sub-cells. Since the linear smoothing function is employed, S-FEM is able to use quadratic triangular or quadrilateral elements. The modified smoothed matrix obtained node-wise is evaluated. In the same manner with the computation of the strain-displacement matrix, the smoothed stiffness matrix and deformation graident are obtained over smoothing domains. A series of benchmark tests are investigated to demonstrate validity and stability of the proposed scheme. The validity and accuracy are confirmed by comparing the obtained numerical results with the standard FEM using 2nd-order triangular element and the exact solutions.

scholarly journals About the edge-based smoothed finite element method for the Reissner-Mindlin plate-bending problem

2009 ◽  
Vol 31 (2) ◽  
pp. 75-86
Author(s):  
Nguyen Xuan Hung ◽  
Nguyen Thoi Trung
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mindlin Plate ◽  
Stiffness Matrices ◽  
Strain Smoothing ◽  
Smoothed Finite Element Method ◽  
Edge Based ◽  
Discrete Shear Gap ◽  
Transverse Shear Locking ◽  
Element Method

The paper further develops the edge-based smoothed finite element method (ES-FEM) for analysis of Reissner-Mindlin plates using triangular meshes. The bending and shearing stiffness matrices are obtained using strain smoothing technique over the smoothing domains associated with edges of elements. Transverse shear locking can be avoided with help of the discrete shear gap (DSG) method. The numerical examples show that the present ES-FEM-DSG method obtains very accurate results compared to the exact solution and other existing elements.

IMPACT SIMULATIONS USING SMOOTHED FINITE ELEMENT METHOD

2013 ◽  
Vol 10 (04) ◽  
pp. 1350012 ◽  
Author(s):  
V. KUMAR ◽  
R. METHA
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Impact Analysis ◽  
Mass Matrix ◽  
Time Integration ◽  
Benchmark Problems ◽  
Smoothed Finite Element Method ◽  
Domain Integration ◽  
Impact Simulations ◽  
Element Method

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.

A Concept of Cell-Based Smoothed Finite Element Method Using 10-Node Tetrahedral Elements (CS-FEM-T10) for Large Deformation Problems of Nearly Incompressible Solids

2019 ◽  
Vol 17 (02) ◽  
pp. 1845009
Author(s):  
Yuki Onishi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Large Deformation ◽  
Hydrostatic Stress ◽  
Reaction Force ◽  
Strain Smoothing ◽  
Smoothed Finite Element Method ◽  
Incompressible Solids ◽  
Large Deformation Problems ◽  
Element Method

A new concept of smoothed finite element method (S-FEM) using 10-node tetrahedral (T10) elements, CS-FEM-T10, is proposed. CS-FEM-T10 is a kind of cell-based S-FEM (CS-FEM) and thus it smooths the strain only within each T10 element. Unlike the other types of S-FEMs [node-based S-FEM (NS-FEM), edge-based S-FEM (ES-FEM), and face-based S-FEM (FS-FEM)], CS-FEM can be implemented in general finite element (FE) codes as a piece of the element library. Therefore, CS-FEM-T10 is also compatible with general FE codes as a T10 element. A concrete example of CS-FEM-T10 named SelectiveCS-FEM-T10 is introduced for large deformation problems of nearly incompressible solids. SelectiveCS-FEM-T10 subdivides each T10 element into 12 four-node tetrahedral (T4) subelements with an additional dummy node at the element center. Two types of strain smoothing are conducted for the deviatoric and hydrostatic stress evaluations and the selective reduced integration (SRI) technique is utilized for the stress integration. As a result, SelectiveCS-FEM-T10 avoids the shear/volumetric locking, pressure checkerboarding, and reaction force oscillation in nearly incompressible solids. In addition, SelectiveCS-FEM-T10 has a relatively long-lasting property in large deformation problems. A few examples of large deformation analyses of a hyperelastic material confirm the good accuracy and robustness of SelectiveCS-FEM-T10. Moreover, an implementation of SelectiveCS-FEM-T10 in the FE code ABAQUS as a user-defined element (UEL) is conducted and its capability is discussed.

A COMBINED EXTENDED AND EDGE-BASED SMOOTHED FINITE ELEMENT METHOD (ES-XFEM) FOR FRACTURE ANALYSIS OF 2D ELASTICITY

2011 ◽  
Vol 08 (04) ◽  
pp. 773-786 ◽  
Author(s):  
L. CHEN ◽  
G. R. LIU ◽  
K. Y. ZENG
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Partition Of Unity ◽  
Fracture Analysis ◽  
Softening Effect ◽  
Strain Smoothing ◽  
Smoothed Finite Element Method ◽  
Edge Based ◽  
2D Elasticity ◽  
Element Method

This study combines the edge-based smoothed finite element method (ES-FEM) and the extended finite element method (XFEM) to develop a new simulation technique (ES-XFEM) for fracture analysis of 2D elasticity. In the XFEM, the need for the mesh alignment with the crack and remeshing, as the crack evolves, is eliminated because of the use of partition of unity. The ES-FEM uses the generalized smoothing operation over smoothing domain associated with edges of simplex meshes, and produces a softening effect leading to a close-to-exact stiffness, "super-convergence" and "ultra-accurate" solutions for the numerical model. Taking advantage of both ES-FEM and XFEM, the present method introduces the edge-based strain smoothing technique into the context of XFEM. Thanks to strain smoothing, the necessity of sub-division in elements cut by discontinuities is suppressed via transforming interior integration into boundary integration. Hence, it simplifies the numerical integration procedure in the XFEM. Numerical examples showed that the proposed method improves significantly the accuracy of stress intensity factors and achieves a quasi optimal convergence rate in the energy norm without geometrical enrichment or blending correction.

COMPUTATION OF LIMIT LOAD USING EDGE-BASED SMOOTHED FINITE ELEMENT METHOD AND SECOND-ORDER CONE PROGRAMMING

2013 ◽  
Vol 10 (01) ◽  
pp. 1340004 ◽  
Author(s):  
C. V. LE ◽  
H. NGUYEN-XUAN ◽  
H. ASKES ◽  
T. RABCZUK ◽  
T. NGUYEN-THOI
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Second Order ◽  
Cone Programming ◽  
Second Order Cone Programming ◽  
Second Order Cone ◽  
Strain Smoothing ◽  
Smoothed Finite Element Method ◽  
Edge Based ◽  
Element Method

This paper presents a novel numerical procedure for limit analysis of plane problems using edge-based smoothed finite element method (ES-FEM) in combination with second-order cone programming. In the ES-FEM, the discrete weak form is obtained based on the strain smoothing technique over smoothing domains associated with the edges of the elements. Using constant smoothing functions, the incompressibility condition only needs to be enforced at one point in each smoothing domain, and only one Gaussian point is required, ensuring that the size of the resulting optimization problem is kept to a minimum. The discretization problem is transformed into the form of a second-order cone programming problem which can be solved using highly efficient interior-point solvers. Finally, the efficacy of the procedure is demonstrated by applying it to various benchmark plane stress and strain problems.

scholarly journals A Hybrid Smoothed Finite Element Method for Predicting the Sound Field in the Enclosure with High Wave Numbers

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Haitao Wang ◽  
Xiangyang Zeng ◽  
Ye Lei
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Sound Field ◽  
Numerical Dispersion ◽  
Computational Accuracy ◽  
Dispersion Error ◽  
High Wave ◽  
Wave Numbers ◽  
Smoothed Finite Element Method ◽  
Element Method

Wave-based methods for acoustic simulations within enclosures suffer the numerical dispersion and then usually have evident dispersion error for problems with high wave numbers. To improve the upper limit of calculating frequency for 3D problems, a hybrid smoothed finite element method (hybrid SFEM) is proposed in this paper. This method employs the smoothing technique to realize the reduction of the numerical dispersion. By constructing a type of mixed smoothing domain, the traditional node-based and face-based smoothing techniques are mixed in the hybrid SFEM to give a more accurate stiffness matrix, which is widely believed to be the ultimate cause for the numerical dispersion error. The numerical examples demonstrate that the hybrid SFEM has better accuracy than the standard FEM and traditional smoothed FEMs under the condition of the same basic elements. Moreover, the hybrid SFEM also has good performance on the computational efficiency. A convergence experiment shows that it costs less time than other comparison methods to achieve the same computational accuracy.

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