The application of a coupled ®nite element± element-free Galerkin (EFG) method to problems in threedimensional fracture is presented. The EFG method is based on moving least square (MLS) approximations and uses only a set of nodal points and a CAD-like description of the body to formulate the discrete model. The EFG method is coupled with the ®nite element method which allows for the use of the...

The element-free Galerkin method is employed for two-dimensional analysis of steady-state heat transfer. The unknown response of the system, i.e. temperature is approximated using the moving least squares technique. Numerical integration of governing simultaneous system of equations is performed by Gauss quadrature and new modified nodal integration techniques. Numerical examples and tests have...

We consider numerical solutions of second-order elliptic partial di erential equations, such as Laplace's equation, or linear elasticity, in two-dimensional, non-convex domains by the element-free Galerkin method (EFG). This is a meshless method, in which the shape functions are constructed by using weight functions of compact support. For non-convex domains, two approaches to the determination...

In the present study, free vibration behaviors of of carbon nanotube (CNT) and boron nitride nanotube (BNNT) have been investigated via Eringen’s nonlocal continuum theory. Size effect has been considered via nonlocal continuum theory. Nanotubes have become popular in the world of science thanks to their characteristic properties. In this study, free vibrations of Boron Nitride Nanotube (BNNT) ...

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...

In this paper, we present a new numerical method, the Immersed Element-Free Galerkin Method (IEFGM), for the solution of fluid-structure interaction problems. The technique is a variation of the Immersed Finite Element Method developed by (L. Zhang et al., Journal of Fluids and Structures, 23(6):836-857 (2007)) in which the fluid-solid interaction force is represented as a volumetric force in t...

A meshless approach to the analysis of arbitrary Kirchhoff shells by the Element-Free Galerkin (EFG) method is presented. The shell theory used is geometrically exact and can be applied to deep shells. The method is based on moving least squares approximant. The method is meshless, which means that the discretization is independent of the geometric subdivision into “finite elements”. The satisf...