scholarly journals Two-dimensional beams in rectangular coordinates using the radial point interpolation method

2020 ◽  
Vol 73 (1) ◽  
pp. 9-16
Author(s):  
William Luiz Fernandes ◽  
Gustavo Botelho Barbosa ◽  
Karine Dornela Rosa ◽  
Emanuel Silva ◽  
Walliston dos Santos Fernandes
Keyword(s):  
Interpolation Method ◽  
Two Dimensional ◽  
Radial Point Interpolation Method ◽  
Radial Point Interpolation ◽  
Rectangular Coordinates ◽  
Point Interpolation Method ◽  
Point Interpolation

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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