scholarly journals An improved radial point interpolation method applied for elastic problem with functionally graded material

2015 ◽  
Vol 18 (2) ◽  
pp. 131-138
Author(s):  
Viet Quoc Phung ◽  
Nha Thanh Nguyen ◽  
Thien Tich Truong
Keyword(s):  
Interpolation Method ◽  
Functionally Graded ◽  
Thin Plates ◽  
Graded Materials ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
Graded Material ◽  
Point Interpolation ◽  
Support Domain ◽  
The One

A meshless method based on radial point interpolation was developed as an effective tool for solving partial differential equations, and has been widely applied to a number of different problems. Besides its advantages, in this paper we introduce a new way to improve the speed and time calculations, by construction and evaluation the support domain. From the analysis of two-dimensional thin plates with different profiles, structured conventional isotropic materials and functional graded materials (FGM), the results are compared with the results had done before that indicates: on the one hand shows the accuracy when using the new way, on the other hand shows the time count as more economical

scholarly journals Extended radial point interpolation method for dynamic crack analysis in functionally graded materials

2015 ◽  
Vol 18 (2) ◽  
pp. 59-66
Author(s):  
Nha Thanh Nguyen ◽  
Bang Kim Tran ◽  
Tinh Quoc Bui ◽  
Thien Tich Truong
Keyword(s):  
Functionally Graded Materials ◽  
Dynamic Stress ◽  
Interpolation Method ◽  
Functionally Graded ◽  
Dynamic Crack ◽  
Dynamic Stress Intensity Factors ◽  
Graded Materials ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
Point Interpolation

Functionally graded materials (FGMs) have been widely used as advanced materials characterized by variation in properties as the dimension varies. Studies on their physical responses under in-serve or external loading conditions are necessary. Especially, crack behavior analysis for these advanced material is one of the most essential in engineering. In this present, an extended meshfree radial point interpolation method (RPIM) is applied for calculating static and dynamic stress intensity factors (SIFs) in functionally graded materials. Typical advantages of RPIM shape function are the satisfactions of the Kronecker’s delta property and the high-order continuity. To assess the static and dynamic stress intensity factors, non-homogeneous form of interaction integral with the nonhomogeneous asymptotic near crack tip fields is used. Several benchmark examples in 2D crack problem are performed such as static and dynamic crack parameters calculation. The obtained results are compared with other existing solutions to illustrate the correction of the presented approach.

On the Usage of Tetrahedral Background Cells in Nodal Integration of RPIM for 3D Elasto-Static Problems

2015 ◽  
Vol 12 (06) ◽  
pp. 1550036
Author(s):  
M. M. Yavuz ◽  
B. Kanber
Keyword(s):  
Taylor Series ◽  
Interpolation Method ◽  
Shape Parameters ◽  
Radial Point Interpolation Method ◽  
Nodal Integration ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Support Domain ◽  
Fifth Order

In this paper, tetrahedral background cells are used in nodal integration of radial point interpolation method (RPIM). The nodal integration is based on Taylor series terms and it is originally applied for the solutions of 2D problems in literature. Therefore, in this study, it is attempted that the tetrahedral integration cells are used in the solution of 3D elasto-static problems. The accuracy is seriously affected by order of Taylor series terms and it is investigated up to fifth order. A methodology is developed for prevention of negative volumes and calculation problems in subdivision of integration cells for each node. Three different case studies are solved with different support domain sizes and shape parameters. The best accuracy is achieved with fourth-order Taylor terms in nodal integration radial point interpolation method (NI-RPIM). [Formula: see text]-value of 3.00 and [Formula: see text] value of 1.03 in radial basis functions give good results in all cases.

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