Infinite element in meshless approaches

The meshless methods combined with infinite element to deal with unbounded problems are developed in this paper. The meshless methods with moving least square algorithm, radial basis function interpolation and finite block method (Lagrange polynomial) are observed. With mapping of physical domain into a normalised square domain, the first order partial differential matrices both for regular and infinite elements (blocks) are determined. The governing equations and boundary conditions are formulated with the partial differential matrices. Numerical examples in the elasticity solid mechanics with non-homogenous and unbounded media are given to demonstrate the efficiency and accuracy of the meshless method combined with infinite elements. It is observed that the accurate numerical solutions of unbounded media can be obtained using the infinite elements at a much lesser computational effort than the conventional meshless methods in which unbounded media are represented by large number of collocation points.