Comparisons of two meshfree local point interpolation methods for structural analyses

As truly meshless methods, the local point interpolation method (LPIM) and the local radial point interpolation method (LR-PIM), are based on the point interpolations and local weak forms integrated in a local domain of very simple shape. LPIM and LR-PIM are examined and compared with each other. They are also compared with the established FEM and the meshless local Petrov-Galerkin (MLPG) method. The numerical implementations of these two methods are discussed in detail. Parameters that influence the performance of them are detailedly studied. The convergence and efficiency of them are thoroughly investigated. LPIM and LR-PIM formulations are developed for structural analyses of 2-D elastodynamic problems and 1-D Timoshenko beam problems in the first time. It is found that LPIM and LR-PIM are very easy to implement, and very efficient obtaining numerical solutions to problems of computational mechanics.