In this paper, a truly meshless method, the Meshless Local Petrov-Galerkin (MLPG) Method, is developed for three-dimensional elasto-statics. The two simplest members of MLPG family of methods, the MLPG type 5 and MLPG type 2, are combined, in order to reduce the computational requirements and to obtain high efficiency. The MLPG5 method is applied at the nodes inside the 3-D domain, so that any ...

In this study, a cellular automaton (CA) is developed o combine the advantages of finite element method (FEM) and meshless method to analyze two-dimensional elastic problems. By the CA, a two-dimensional domain is discretized into a grid of nodes which are distributed randomly in the domain. For convenience, the nodes are classified into the FEM group and the meshless group. In the FEM zone tha...

Recently the Meshless and Generalized FEM became to be in the center of interest, especially in the engineering community. I have identified more than 200 engineering papers and four books ([1],[2],[3],[4]). I found very few papers of mathematical character (assumptions, theorems, proofs). Hence there is a large experience and heuristics but not too much mathematical understanding of the method...

The propagation of cracks in three dimensions is analyzed by a meshless method. The cracks are modeled by a set of triangles that are added when the propagation occurs. Since the method is meshless, no remeshing of the domain is necessary during the propagation. To avoid using a large number of degrees of freedom, the stress singularity along the front of the cracks is taken into account by an ...

Development of a new meshless technique is described that presents certain advantages over conventional meshless schemes due to unique weights that force alignment of the derivative approximation. The method is completelymeshless, yet retains the low storage and simple fluxdistribution technique that are characteristic of finite volumemethods. The newmethod is based on thewell-knownTaylor serie...

Numerical solutions of the Helmholtz equation suffer from numerical pollution especially for the case of high wavenumbers. The major component of the numerical pollution is, as has been reported in the literature, the dispersion error which is defined as the phase difference between the numerical and the exact wave. The dispersion error for the meshless methods can be a priori determined at an ...

In this paper, we explore the effect of numerical integration on the meshless method used to approximate the solution of an elliptic partial differential equation with non-constant coefficients with Neumann boundary conditions. We considered meshless methods with shape functions that reproduce polynomials of degree k ≥ 1. We have obtained an estimate for the energy norm of the error in the appr...

We study meshless collocation methods using radial basis functions to approximate regular solutions of systems of equations with linear diier-ential or integral operators. Our method can be interpreted as one of the emerging meshless methods, cf. 1]. Its range of application is not conned to elliptic problems. However, the application to the boundary value problem for an elliptic operator, conn...

Recent years saw a rise in the application of bonding techniques engineering industry. This fact is due to various advantages this technique when compared traditional joining methods, such as riveting or bolting. The growth methods demands faster and more powerful tools analyze behavior products. For that reason, adhesive joints have been subject intensive investigation over past few years. Rec...

(2001) A Meshless Local Petrov-Galerkin (MLPG) method for free and forced vibration analyses for solids. Abstract The Meshless Local Petrov-Galerkin (MLPG) method is an effective truly meshless method for solving partial differential equations using Moving Least Squares (MLS) interpolants and local weak forms. In this paper, a MLPG formulation is proposed for free and forced vibration analyses....