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...

Title of dissertation: MESHLESS COLLOCATION METHODS FOR THE NUMERICAL SOLUTION OF ELLIPTIC BOUNDARY VALUED PROBLEMS AND THE ROTATIONAL SHALLOW WATER EQUATIONS ON THE SPHERE Christopher D. Blakely, Doctor of Philosophy, 2009 Dissertation directed by: Professor John Osborn Department of Mathematics Professor Ferdinand Baer Department of Atmospheric and Oceanic Science This dissertation thesis has...

In this paper, a simple approach is presented for the calculation of deflection of a semi trailer chassis since the less deflection become a unique selling point of a semi trailer. First of all, by using the 3D data of the chassis a function for the moment of inertia of the cross section is created and then the chassis is modelled as a Euler Bernoulli Beam. Different loading conditions coming f...

Though the technique introduced by E. Kansa [7, 8] is very successful in engineering applications, there were no proven results so far on the unsymmetric meshless collocation method for solving PDE boundary value problems in strong form. While the original method cannot be proven to be fail–safe in general, we prove asymptotic feasibility for a generalized variant using separated trial and test...

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...

In this work we address the problem of numerically simulating the Friction Stir Welding process. Due to the special characteristics of this welding method (i.e., high speed of the rotating pin, very large deformations, etc.) finite element methods encounter several difficulties. Meshless methods somewhat alleviate this problems, allowing for an updated Lagrangian framework in the simulation. Ac...

Paper focuses on application of the Meshless Finite Difference Method (MFDM) solution approach and its selected extensions to the numerical homogenization of the heterogeneous material. The most commonly used method of computer modeling for the multiscale problem (at both the macro and micro (RVE) levels) is the Finite Element Method (FEM). However, this fact does not mean that one should not s...

A stochastic element-free Galerkin method was developed for reliability analysis of linear-elastic structures with spatially varying random material properties. A random ®eld representing material properties was discretized into a set of random variables with statistical properties obtained from the statistical properties of random ®eld. In conjunction with meshless formulations, the ®rst-order...

A particular meshless method, named meshless local Petrov–Galerkin is investigated. To treat the essential boundary condition problem, an alternative approach is proposed. The basic idea is to merge the best features of two different methods of shape function generation: the moving least squares (MLS) and the radial basis functions with polynomial terms (RBFp). Whereas the MLS has lower computa...

boundary integral equations (bie) are reformulations of boundary value problems for partial differential equations. there is a plethora of research on numerical methods for all types of these equations such as solving by discretization which includes numerical integration. in this paper, the neumann problem is reformulated to a bie, and then moving least squares as a meshless method is describe...