A Modified Cell-Based Strain Smoothing for Material Nonlinearity

Linear Smoothing ◽

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.

Dynamic Analysis of Functionally Graded Porous Plates Resting on Elastic Foundation Taking into Mass subjected to Moving Loads Using an Edge-Based Smoothed Finite Element Method

Shock and Vibration ◽

10.1155/2020/8853920 ◽

2020 ◽

Vol 2020 ◽

pp. 1-19

Author(s):

Trung Thanh Tran ◽

Quoc-Hoa Pham ◽

Trung Nguyen-Thoi

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Dynamic Analysis ◽

Elastic Foundation ◽

Functionally Graded ◽

Triangular Element ◽

Moving Loads ◽

Edge Based ◽

The paper presents the extension of an edge-based smoothed finite element method using three-node triangular elements for dynamic analysis of the functionally graded porous (FGP) plates subjected to moving loads resting on the elastic foundation taking into mass (EFTIM). In this study, the edge-based smoothed technique is integrated with the mixed interpolation of the tensorial component technique for the three-node triangular element (MITC3) to give so-called ES-MITC3, which helps improve significantly the accuracy for the standard MITC3 element. The EFTIM model is formed by adding a mass parameter of foundation into the Winkler–Pasternak foundation model. Two parameters of the FGP materials, the power-law index (k) and the maximum porosity distributions (Ω), take forms of cosine functions. Some numerical results of the proposed method are compared with those of published works to verify the accuracy and reliability. Furthermore, the effects of geometric parameters and materials on forced vibration of the FGP plates resting on the EFTIM are also studied in detail.

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

10.1142/s0219876213500898 ◽

2014 ◽

Vol 11 (06) ◽

pp. 1350089 ◽

Cited By ~ 10

Author(s):

SHIZHE FENG ◽

XIANGYANG CUI ◽

GUANGYAO LI

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Degrees Of Freedom ◽

Mechanical Analysis ◽

Pressure Vessels ◽

Strain Smoothing ◽

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.

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

Vietnam Journal of Mechanics ◽

10.15625/0866-7136/31/2/5485 ◽

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 ◽

Edge Based ◽

Discrete Shear Gap ◽

Transverse Shear Locking ◽

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.

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

10.1142/s0219876213400021 ◽

2013 ◽

Vol 10 (01) ◽

pp. 1340002 ◽

Cited By ~ 14

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 ◽

Central Difference 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.

A Novel Triangular Prism Element Based on Smoothed Finite Element Method

10.1142/s0219876218500585 ◽

2018 ◽

Vol 15 (07) ◽

pp. 1850058 ◽

Cited By ~ 2

Author(s):

Yongjie Pei ◽

Xiangyang Cui

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Three Dimensional ◽

Deformation Analysis ◽

Smoothing Function ◽

Triangular Prism ◽

Surface Dimension ◽

Elastic Plastic Materials ◽

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.

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

10.1142/s0219876218450093 ◽

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 ◽

Incompressible Solids ◽

Large Deformation Problems ◽

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 Smoothed Finite Element Method (S-FEM) for Large-Deformation Elastoplastic Analysis

10.1142/s0219876215400113 ◽

2015 ◽

Vol 12 (04) ◽

pp. 1540011 ◽

Cited By ~ 9

Author(s):

Jun Liu ◽

Zhi-Qian Zhang ◽

Guiyong Zhang

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Large Deformation ◽

Computational Efficiency ◽

Triangular Element ◽

Fem Method ◽

Deformation Plasticity ◽

Edge Based ◽

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.

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

10.1142/s0219876211002812 ◽

2011 ◽

Vol 08 (04) ◽

pp. 773-786 ◽

Cited By ~ 12

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 ◽

Edge Based ◽

2D Elasticity ◽

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

10.1142/s0219876213400045 ◽

2013 ◽

Vol 10 (01) ◽

pp. 1340004 ◽

Cited By ~ 22

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 ◽

Edge Based ◽

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.