Interpolating Meshless Methods for 3D Elastic Problems

Interpolating meshless methods can directly impose boundary conditions because of the interpolation property which shows advantages in dealing with problems with boundary conditions. The interpolating element-free Galerkin method (IEFGM), the improved interpolating element-free Galerkin method (IIEFGM), and the radial point interpolation method (RPIM) are applied in this paper to solve the two-dimensional and three-dimensional elastic problems. IEFGM and IIEFGM are two different ways to change the status that the traditional element-free Galerkin method (EFG) does not have the interpolation property. IEFGM uses an improved interpolating moving least-squares (IMLS) method that employed singular weight functions while IIEFGM takes the improved interpolating moving least-squares method based on non-singular weight function. RPIM, one of the most widely used interpolating meshless methods, is compared with IEFGM and IIEFGM in this paper. The numerical results of two-dimensional and three-dimensional elastic problems show that the three types of interpolating meshless methods obtain high precision displacement solutions and stress solutions.