scholarly journals PERFORMANCE OF RADIAL POINT INTERPOLATION METHOD IN SOLVING KINEMATIC WAVE EQUATION FOR HYDROLOGIC MODELLING

2020 ◽  
Vol 82 (3) ◽  
Author(s):  
H. Hirol ◽  
M. A. Mohd Noor ◽  
M. Z. Abd Jamil ◽  
M. H. Mokhtaram ◽  
E. H. Kasiman ◽  
...  
Keyword(s):  
Wave Equation ◽  
Interpolation Method ◽  
Kinematic Wave ◽  
Weighted Residual Method ◽  
Time Step ◽  
Radial Point Interpolation Method ◽  
Kinematic Wave Equation ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
Point Interpolation

This paper presents the solution of the kinematic wave equation using a meshless radial point interpolation method (RPIM). The partial differential equation is discretized using a Galerkin weighted residual method employing RPIM shape functions. A forward difference scheme is used for temporal discretization, while the direct substitution method is employed to solve the nonlinear system at each time step. The formulation is validated against solutions from conventional numerical techniques and physical observation. In all cases, excellent agreements are achieved and hence the validation of the proposed formulation. Optimum values of the multi-quadrics shape parameters were then determined before the assessment of the performance of the method. Based on the convergence rate, it has been shown that the proposed method performs better than the finite difference method and equivalent to the finite element method. This highlights the potential of RPIM as an alternative method for hydrologic modeling.

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.

scholarly journals Meshless Radial Point Interpolation Method for Hyperelastic Materials

10.29007/r7sp ◽  
2020 ◽  
Author(s):  
Trong Khiem Bui ◽  
Vu Tuong Nguyen ◽  
Thanh Nha Nguyen ◽  
Tich Thien Truong
Keyword(s):  
Large Deformation ◽  
Interpolation Method ◽  
Biological Tissues ◽  
Material Behavior ◽  
Nonlinear Material ◽  
Radial Point Interpolation Method ◽  
Hyperelastic Materials ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
Point Interpolation

Hyperelastic materials are special types of material that tends to behavior elastically when they are subjected to very large strains. These materials show not only the nonlinear material behavior but also the large deformation and stress-strain relationship is derived from a strain energy density function. Hyperelastic materials are widely used in many applications such as biological tissues, polymeric foams, and moreover. Neo - Hookean is a material model for hyperelastic solid which contains only two material parameters: bulk modulus and shear modulus. In the field of numerical analysis, the radial point interpolation method (RPIM) is a well-known meshfree method based on Garlekin's weak form. With the property of “free of mesh”, the RPIM approach shows its advantage for large deformation problems. In this study, a meshless radial point interpolation method is applied to demonstrate the elastic response of rubber-like materials based on the Mooney- Rivlin model. The obtained results are compared with the reference solutions given by other methods to verify the accuracy of the proposed method.

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