A novel centroid-enriched edge-based smoothed radial point interpolation method for upper bound limit analysis

2021 ◽  
Vol 140 ◽  
pp. 104473
Author(s):  
Xiwen Zhou ◽  
Fengtao Liu ◽  
Beibing Dai ◽  
Chengbo Zhang
Keyword(s):  
Upper Bound ◽  
Limit Analysis ◽  
Interpolation Method ◽  
Radial Point Interpolation Method ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Edge Based ◽  
Upper Bound Limit Analysis

MID-FREQUENCY ACOUSTIC ANALYSIS USING EDGE-BASED SMOOTHED TETRAHEDRON RADIALPOINT INTERPOLATION METHODS

2014 ◽  
Vol 11 (05) ◽  
pp. 1350103 ◽  
Author(s):  
Z. C. HE ◽  
G. Y. LI ◽  
ERIC LI ◽  
Z. H. ZHONG ◽  
G. R. LIU
Keyword(s):  
Acoustic Analysis ◽  
Interpolation Method ◽  
Building Blocks ◽  
Numerical Dispersion ◽  
Softening Effect ◽  
Radial Point Interpolation Method ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Edge Based

An edge-based smoothed tetrahedron radial point interpolation method (ES-T-RPIM) is formulated for the 3D acoustic problems, using the simplest tetrahedron mesh which is adaptive for any complicated geometry. In present ES-T-RPIM, the gradient smoothing operation is performed with respect to each edge-based smoothing domain, which is also serving as building blocks in the assembly of the stiffness matrix. The smoothed Galerkin weak form is then used to create the discretized system equations. The acoustic pressure is constructed using radial point interpolation method, and two typical schemes of selecting nodes for interpolation using RPIM have been introduced in detail. It turns out that the ES-T-RPIM provides an ideal amount of softening effect, and significantly reduces the numerical dispersion error in low- to mid-frequency range. Numerical examples demonstrate the superiority of the ES-T-RPIM for 3D acoustic analysis, especially at mid-frequency.

scholarly journals An interaction integral method for evaluating T-stress for two-dimensional crack problems using the extended radial point interpolation method

2015 ◽  
Vol 18 (2) ◽  
pp. 106-113
Author(s):  
Nha Thanh Nguyen ◽  
Hien Thai Nguyen ◽  
Minh Ngoc Nguyen ◽  
Thien Tich Truong
Keyword(s):  
Integral Method ◽  
Interpolation Method ◽  
Two Dimensional ◽  
Radial Point Interpolation Method ◽  
Interaction Integral ◽  
Crack Problems ◽  
Radial Point Interpolation ◽  
T Stress ◽  
Point Interpolation Method ◽  
Point Interpolation

The so-called T-stress, or second term of the William (1957) series expansion for linear elastic crack-tip fields, has found many uses in fracture mechanics applications. In this paper, an interaction integral method for calculating the T-stress for two-dimensional crack problems using the extended radial point interpolation method (XRPIM) is presented. Typical advantages of RPIM shape function are the satisfactions of the Kronecker’s delta property and the high-order continuity. The T-stress can be calculated directly from a path independent interaction integral entirely based on the J-integral by simply the auxiliary field. Several benchmark examples in 2D crack problem are performed and compared with other existing solutions to illustrate the correction of the presented approach.

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