Infinitesimal deformations of a homogeneous and isotropic thick elastic plate have been analyzed by using a meshless local Petrov– Galerkin (MLPG) method and a higher-order shear and normal deformable plate theory (HONSDPT). Radial basis functions (RBF) are employed for constructing trial solutions, while a spline function is used as the weight function over a local subdomain. The present metho...

Electric potential measurement technique (tomography) was introduced as a nondestructive method to evaluate concrete properties and durability. In this study, numerical meshless method was developed to solve a differential equation which simulates electric potential distribution for concrete with inclusion in two dimensions. Therefore, concrete samples with iron block inclusion in different loc...

Symmetric collocation, which can be used to numerically solve linear partial differential equations, is a natural generalization of the well-established scattered data interpolation method known as radial basis function (rbf) interpolation. As with rbf interpolation, a major shortcoming of symmetric collocation is the high cost, in terms of floating point operations, of evaluating the obtained ...

Discussed is here the multipoint meshless finite difference method (MMFDM) following the original Collatz [2] multipoint concept, and the essential ideas of the meshless FDM [3]. The Collatz approach was based on interpolation, regular meshes and the local formulation of b.v. problems. On the other hand in the MFDM we deal with the moving weighted least squares (MWLS) approximation, arbitrarily...

We describe a numerical method to solve the quasistatic Maxwell equations to obtain the electric potential distribution generated by a point source of current density inside a body of arbitrary shape and constant conductivity. The method needs only a set of nodes on the surface and inside the body, but it does not need a mesh connecting the nodes. The proposed meshless method is compared agains...

In the present work, a meshless method called Finite Point Method (FPM) is developed to simulate the solidification process of a continuously cast steel bloom in both primary and secondary cooling regions. The method is based on the use of a weighted least-square interpolation procedure. A transverse slice of the bloom moving at casting speed is considered as the computational domain and two di...

A comparison study of the efficiency and accuracy of a variety of meshless trial and test functions is presented in this paper, based on the general concept of the meshless local Petrov-Galerkin (MLPG) method. 5 types of trial functions, and 6 types of test functions are explored. Different test functions result in different MLPG methods, and six such MLPG methods are presented in this paper. I...

A Point Interpolation Method (PIM) is presented for stress analysis for two-dimensional solids. In the PIM, the problem domain is represented by properly scattered points. A technique is proposed to construct polynomial interpolants with delta function property based only on a group of arbitrarily distributed points. The PIM equations are then derived using variational principles. In the PIM, t...