Comparison of a least-square weighted residual method and the Taylor Galerkin method based on level set formulation for interface capturing

2011 ◽  
Vol 11 (3/4) ◽  
pp. 169
Author(s):  
Hyoung Gwon Choi
Keyword(s):  
Galerkin Method ◽  
Level Set ◽  
Least Square ◽  
Weighted Residual Method ◽  
Residual Method ◽  
Interface Capturing ◽  
Taylor Galerkin Method ◽  
Level Set Formulation

An Elastic Dynamic Analysis of a Nonhomogeneous Moderately Thick Plate Using the Meshless Local Petrov-Galerkin Method

2010 ◽  
Vol 34-35 ◽  
pp. 393-398
Author(s):  
Ping Xia ◽  
Wen Gui Mao ◽  
Wei Jun Hu
Keyword(s):  
Dynamic Analysis ◽  
Galerkin Method ◽  
Basis Function ◽  
Thick Plate ◽  
Delta Function ◽  
Additional Treatment ◽  
Weighted Residual Method ◽  
Residual Method ◽  
System Equation ◽  
Moderately Thick Plate

A meshless local Petrov-Galerkin method for the elastic dynamic analysis of a nonhomogeneous moderately thick plate is presented in this paper. The discretized system equation of the moderately thick plate is obtained using a locally weighted residual method. It uses a radial basis function coupled with a quadratic polynomial basis function as a trial function and a quartic spline function as a test function of the weighted residual method. The shape function has the Kronecker delta function properties, and no additional treatment to impose essential boundary conditions. In computational procedures, variations of material properties in the considered domain are modelled by adopting proper material parameters at Gauss points in integrations. Examples show that the presented method can give quite accurate results to elastic dynamic problems of the nonhomogeneous moderately thick plate.

Application of the Meshless Local Petrov-Galerkin Method in the Elasto-Plastic Fracture Problem of Moderately Thick Plate

2012 ◽  
Vol 155-156 ◽  
pp. 485-490 ◽  
Author(s):  
Ping Xia ◽  
Ke Xiang Wei
Keyword(s):  
Galerkin Method ◽  
Basis Function ◽  
Thick Plate ◽  
Weighted Residual Method ◽  
Rapid Convergence ◽  
Test Function ◽  
Residual Method ◽  
Moderately Thick Plate ◽  
System Equations ◽  
Newton Raphson

A meshless local Petrov-Galerkin method for the analysis of the elasto-plastic fracture problem of the moderately thick plate is presented. The discretized system equations of the moderately thick plate are obtained using a locally weighted residual method. It uses a radial basis function coupled with a polynomial basis function as a trial function, and uses the quartic spline function as a test function of the weighted residual method. An incremental Newton-Raphson iterative algorithm is employed to solve incremental nonlinear local Petrov-Galerkin equations. Numerical results show that the present method possesses not only feasibility, but also rapid convergence for the elasto-plastic fracture problem of the moderately thick plate.

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