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 ...

The one-dimensional shallow water equations (SWEs), coupled with bed load (Exner equation) were solved in this paper for the numerical simulation of sediment transport problem. By using an efficient meshless method based on radial basis function (RBF) that approximates unknown variables a set collocation nodes and Runge–Kutta fourth-order scheme to approximate temporal derivative. Besides, arti...

The radial basis function (RBF) collocation techniques for the numerical solution of partial differential equation problems are increasingly popular in recent years thanks to their striking merits being inherently meshless, integration-free, and highly accurate. However, the RBF-based methods have markedly been limited to handle isotropic problems due to the use of the isotropic Euclidean dista...

In modeling using diffusion equations, the relationship between fractal geometry and fractional calculus arises by modeling the conditions of the medium as a fractal whose fractional dimension determines the order of this equation. For this reason, it is very useful to have numerical methods that solve them and discretization of the domain is not determinant for the efficiency of the algorithm....

In this work, numerical solution of multi term space fractional PDE is calculated by using radial basis functions. The derivatives functions are evaluated Caputo and Riemann-Liouville definitions. Local applied to get stable accurate the problem. Accuracy method assessed double mesh procedure. Numerical solutions presented for different orders show effect introducing fractionality.

The general Meshless Local PetrovGalerkin (MLPG) type weak-forms of the displacement & traction boundary integral equations are presented, for solids undergoing small deformations. These MLPG weak forms provide the most general basis for the numerical solution of the non-hyper-singular displacement and traction BIEs [given in Han, and Atluri (2003)], which are simply derived by using the gradie...

It is widely acknowledged that 3-D mesh generation remains one of the most man-hours consuming techniques within computational mechanics. The problem of mesh generation is that the time remains unbounded, even using the most sophisticated mesh-generator. For a given distribution of points, it is possible to obtain a mesh very quickly, but it may require several iterations, including manual inte...

This study presents a meshless-based local reanalysis (MLR) method. The purpose of this study is to extend reanalysis methods to the Kriging interpolation meshless method due to its high efficiency. In this study, two reanalysis methods: combined approximations CA) and indirect factorization updating (IFU) methods are utilized. Considering the computational cost of meshless methods, the reanaly...