A meshfree radial point interpolation method (RPIM) is developed for stress analysis of threedimensional (3D) solids, based on the Galerkin weak form formulation using 3D meshfree shape functions constructed using radial basis functions (RBFs). As the RPIM shape functions have the Kronecker delta functions property, essential boundary conditions can be enforced as easily as in the finite elemen...

The classical radial point interpolation method (RPIM) is a powerful meshfree numerical technique for engineering computation. In the original RPIM, moving support domain quadrature usually employed field function approximation, but local supports of nodal shape functions are always not in alignment with integration cells constructed integration. This misalignment can result additional error an...

It has been proven by the authors that both the upper and lower bounds in energy norm of the exact solution to elasticity problems can now be obtained by using the fully compatible finite element method (FEM) and linearly conforming point interpolation method (LC-PIM). This paper examines the upper bound property of the linearly conforming radial point interpolation method (LC-RPIM), where the ...

The protocol independent multicast-sparse mode (PIM-SM) protocol establishes core-base tree to forward multicast datagrams in a network. In PIM-SM, the core or rendezvous point (RP) of a group is determined at each multicast router by hashing a group address, i.e. a class-D IP address, to one of the candidate RPs. The hash function is characterized by its ability to evenly and uniquely choose t...

In this paper, a meshfree method called adaptive CTM–RPIM is developed to model geotechnical problems with large deformation. The combination of the Cartesian transformation (CTM), radial point interpolation (RPIM) and alpha shape method. To reduce requirement for meshes, CTM adopted transform domain integrals into line integrals, RPIM applied construct functions. method, which capable capturin...

In this paper three numerical techniques are proposed for solving the system of N-coupled nonlinear Schrödinger (CNLS) equations. Firstly, we obtain a time discrete scheme by approximating the first-order time derivative via the forward finite difference formula, then for obtaining a full discretization scheme, we use the Kansa’s approach to approximate the spatial derivatives via radial basis ...

Hyperelastic materials are considered as special category of elastic solid because their nonlinear complicated constitutive laws. Due to large strain state, the behaviour such is often in finite deformation analysis. The behavior important. In this study, a novel meshless radial point interpolation method (RPIM) enhanced by Cartesian transformation (CTM), an effective numerical integration, pre...

This work presents a novel simulation approach to couple the meshfree radial point interpolation method (RPIM) with implicit direct time integration for transient analysis of wave propagation dynamics in non-homogeneous media. In this approach, RPIM is adopted discretization overall space domain, while domain completed by employing efficient Bathe stepping scheme. The dispersion demonstrates th...