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...

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 ...

(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....

We discuss a discretization approach for the p Laplacian equation and a variational inequality associated to fourth order elliptic operators, via a meshless approach based on duality theory. MSC: 35J20, 35J25, 65N99. keywords: nonlinear elliptic equations, Fenchel theorem, approximation, meshless method.

The root of this study, comes from the lack of regularity where exists in shape function selection in direct meshless methods. In this work, we are going to establish a technique which is based on both analytical and simulated results; helps select a well-behaved shape function for which the shape parameters have been predetermined. This work has been focused on wave equation as the most import...

A subdomain variational inequality and its meshless linear complementary formulation are developed in the present paper for solving two-dimensional contact problems. The subdomain variational inequality will be defined in detail. The meshless method is based on a local weighted residual method with the Heaviside step function as the weighting function over a local subdomain and radial basis fun...

Meshless Finite Element Methods, namely elementfree Galerkin and point-interpolation method were implemented and tested concerning their applicability to typical engineering problems like electrical fields and structural mechanics. A class-structure was developed which allows a consistent implementation of these methods together with classical FEM in a common framework. Strengths and weaknesses...

Many numerical and analytical schemes exist for solving heat transfer problems. The meshless method is a particularly attractive method that is receiving attention in the engineering and scientific modeling communities. The meshless method is simple, accurate, and requires no polygonalisation. In this study, we focus on the application of meshless methods using radial basis functions (RBFs) – w...

For simulation of numerical problems, meshless methods have emerged as an alternative to mesh based methods and become popular due to several reasons. Primarily, mesh generation is a difficult problem, Also these methods have generated promising results in the accuracy of the simulations. Similar to mesh generation problems, meshless methods also induce challenging geometric problems. Partition...

a meshless method namely, discrete least square method (dlsm), is presented in the paper for the solution of free surface seepage problem. in this method computational domain is discredited by some nodes and then the set of simultaneous equations are built using moving least square (mls) shape functions and least square technique. the proposed method does not need any background mesh therefore ...