Numerical investigation of the edge-based gradient smoothing technique for exterior Helmholtz equation in two dimensions

2017 ◽  
Vol 182 ◽  
pp. 149-164 ◽  
Author(s):  
Wei Li ◽  
Yingbin Chai ◽  
Ming Lei ◽  
Tianyun Li
Keyword(s):  
Helmholtz Equation ◽  
Numerical Investigation ◽  
Two Dimensions ◽  
Smoothing Technique ◽  
Gradient Smoothing Technique ◽  
Edge Based ◽  
Gradient Smoothing

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.

scholarly journals Hybrid gradient smoothing technique with discrete shear gap method for shell structures

2017 ◽  
Vol 74 (8) ◽  
pp. 1826-1855 ◽  
Author(s):  
W. Li ◽  
Z.X. Gong ◽  
Y.B. Chai ◽  
C. Cheng ◽  
T.Y. Li ◽  
...  
Keyword(s):  
Shell Structures ◽  
Smoothing Technique ◽  
Gradient Smoothing Technique ◽  
Discrete Shear Gap ◽  
Gradient Smoothing

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.

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