An Edge-Based Smoothed Finite Element Method for Analyzing Stiffened Plates

2019 ◽  
Vol 16 (06) ◽  
pp. 1840031 ◽  
Author(s):  
Wei Li ◽  
Yingbin Chai ◽  
Xiangyu You ◽  
Qifan Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Sound Radiation ◽  
Stiffened Plates ◽  
Smoothing Technique ◽  
Gradient Smoothing Technique ◽  
Smoothed Finite Element Method ◽  
Edge Based ◽  
Gradient Smoothing ◽  
Element Method

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.

A GENERALIZED GRADIENT SMOOTHING TECHNIQUE AND THE SMOOTHED BILINEAR FORM FOR GALERKIN FORMULATION OF A WIDE CLASS OF COMPUTATIONAL METHODS

2008 ◽  
Vol 05 (02) ◽  
pp. 199-236 ◽  
Author(s):  
G. R. LIU
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Bilinear Form ◽  
Interpolation Method ◽  
Smoothing Technique ◽  
Generalized Gradient ◽  
Gradient Smoothing Technique ◽  
Smoothed Finite Element Method ◽  
Gradient Smoothing ◽  
Element Method

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.

AN APPLICATION OF THE ES-FEM IN SOLID DOMAIN FOR DYNAMIC ANALYSIS OF 2D FLUID–SOLID INTERACTION PROBLEMS

2013 ◽  
Vol 10 (01) ◽  
pp. 1340003 ◽  
Author(s):  
T. NGUYEN-THOI ◽  
P. PHUNG-VAN ◽  
T. RABCZUK ◽  
H. NGUYEN-XUAN ◽  
C. LE-VAN
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Analysis ◽  
Smoothing Technique ◽  
Coupled Method ◽  
Gradient Smoothing Technique ◽  
Triangular Elements ◽  
Gradient Smoothing ◽  
Fluid Solid Interaction ◽  
Element Method

An edge-based smoothed finite element method (ES-FEM-T3) using triangular elements was recently proposed to improve the accuracy and convergence rate of the existing standard finite element method (FEM) for the solid mechanics analyses. In this paper, the ES-FEM-T3 is further extended to the dynamic analysis of 2D fluid–solid interaction problems based on the pressure-displacement formulation. In the present coupled method, both solid and fluid domain is discretized by triangular elements. In the fluid domain, the standard FEM is used, while in the solid domain, we use the ES-FEM-T3 in which the gradient smoothing technique based on the smoothing domains associated with the edges of triangles is used to smooth the gradient of displacement. This gradient smoothing technique can provide proper softening effect, and thus improve significantly the solution of coupled system. Some numerical examples have been presented to illustrate the effectiveness of the proposed coupled method compared with some existing methods for 2D fluid–solid interaction problems.

Edge-Based Smoothed Finite Element Method Using Two-Step Taylor Galerkin Algorithm for Lagrangian Dynamic Problems

2015 ◽  
Vol 12 (05) ◽  
pp. 1550028 ◽  
Author(s):  
Xiangyang Cui ◽  
Shu Chang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Long Time ◽  
Smoothed Finite Element Method ◽  
Linear Elements ◽  
Edge Based ◽  
Gradient Smoothing ◽  
Solid Dynamics ◽  
Dynamics Problems ◽  
Element Method

An edge-based smoothed finite element method (ESFEM) using two-step Taylor Galerkin (TS-TG) algorithm is formulated for two-dimensional solid dynamics problems using linear elements. Although explicit method with classical displacement formulations is the traditional way to simulate fast impact, errors accumulate rapidly resulted from mass, momentum or energy nonconservation. The proposed method is momentum conservative so that energy fluctuations can be minimal and stay bounded for long time. In the present method, the problem areas are firstly discretized into a series of triangular cells, and edge-based smoothing domains are further formed associated with the cell edges. The strain field using the gradient smoothing technique over each smoothing domain is smoothed, which is used for performing the numerical integration. The triangular elements using ESFEM can work for extremely distorted meshes. The newly proposed method can present a good property of accuracy and conservation for a long time.

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.

scholarly journals 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

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 ◽  
Smoothed Finite Element Method ◽  
Edge Based ◽  
Element Method

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.

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