Combining the hybrid displacement variational formulation and the radial basis point interpolation, a truly meshless and boundary-only method is developed in this paper for the numerical solution of solid mechanics problems in two and three dimensions. In this method, boundary conditions can be applied directly and easily. Besides, it is truly meshless, that is, it only requires nodes generated...

A radial basis function implementation of the meshless local Petrov-Galerkin (MLPG) method is presented to study Euler-Bernoulli beam problems. Radial basis functions, rather than generalized moving least squares (GMLS) interpolations, are used to develop the trial functions. This choice yields a computationally simpler method as fewer matrix inversions and multiplications are required than whe...

This paper describes a new topology optimization (TO) technique based on meshless method to evolve two-dimensional truss structures. The meshless method has been considered as a very attractive computational technique since it does not need any mesh generation process during the analysis. It has been gradually and widely used in many engineering disciplines and a particular weak point such as t...

In this paper, the conventional moving least squares interpolation scheme is generalized, to incorporate the information concerning the derivative of the ®eld variable into the interpolation scheme. By using this generalized moving least squares interpolation, along with the MLPG (Meshless Local Petrov±Galerkin) paradigm, a new numerical approach is proposed to deal with 4th order problems of t...

For the first time in mathematical finance field, we propose the local weak form meshless methods for option pricing; especially in this paper we select and analysis two schemes of them named local boundary integral equation method (LBIE) based on moving least squares approximation (MLS) and local radial point interpolation (LRPI) based on Wu’s compactly supported radial basis functions (WCS-RB...

The Meshless Finite Volume Method (MFVM) is developed for solving elasto-static problems, through a new Meshless Local Petrov-Galerkin (MLPG) “Mixed” approach. In this MLPG mixed approach, both the strains as well as displacements are interpolated, at randomly distributed points in the domain, through local meshless interpolation schemes such as the moving least squares(MLS) or radial basis fun...

An improvement to the traditional Finite Volume Method (FVM) for the solution of boundary value problems is presented. The new method applies the local Hermitian interpolation with Radial Basis Functions (RBF) as an interpolation scheme to the FVM discretization. This approach, called the Control Volume-Radial Basis Function (CV-RBF) method, uses an interpolation scheme based on the meshless Sy...

The root of this study, comes from the lack of regularity where exists in shape function selection in meshless methods. Up to now, shape functions in meshless methods were being established by basis functions. In other words, there was no predictable rule by which the shape functions be predetermined, without any need to basis functions. In presented approach, the authors are going to establish...