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.

THE STABILITY OF SLOPE USING CELL – BASED SMOOTHED FINITE ELEMENT METHOD AND SECOND ORDER CONE PROGRAMMING

2016 ◽  
Vol 3 (2) ◽  
Author(s):  
Hai Le Nguyen ◽  
Hai Than Nguyen ◽  
Thien Vo Minh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Optimization Problem ◽  
Second Order ◽  
Cone Programming ◽  
Second Order Cone Programming ◽  
Second Order Cone ◽  
Primal Dual ◽  
Smoothed Finite Element Method ◽  
Element Method

In this paper, the numerical limit analysis procedure, associating the cell-based smoothed finite element method (CS-FEM) with the (second-order cone) primal-dual interior point algorithm, for cohesive-frictional materials problem is described. The soil is modeled as a cohesionless frictional Mohr-Coulomb material with the associated flow rule. Kinematically admissible velocity fields are established using CS-FEM. The underlying non-smooth optimization problem is formulated as a problem of minimizing a sum of Euclidean norms, ensuring that the resulting optimization problem can be solved by an efficient second order cone programming algorithm. The core purpose of this study is to evaluate collapse loads as well as failure mechanisms of footings on slope which will be obtained directly from solving the optimization problems. In this study, the properties of soil and the width of footing and distance from footing to the edge of the slope are considered. Several numerical examples of slope stability are given to show the performance of the proposed method.

A smoothed finite element method using second-order cone programming

2020 ◽  
Vol 123 ◽  
pp. 103547 ◽  
Author(s):  
Jingjing Meng ◽  
Xue Zhang ◽  
Jinsong Huang ◽  
Hongxiang Tang ◽  
Hans Mattsson ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Second Order ◽  
Cone Programming ◽  
Second Order Cone Programming ◽  
Second Order Cone ◽  
Smoothed Finite Element Method ◽  
Element Method

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 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.

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.

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.

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