Local Heaviside weighted MLPG meshless method for two-dimensional solids using compactly supported radial basis functions Original Research Article

Compactly supported radial basis functions (CSRBF) are employed for constructing trial functions in the local Heaviside weighted meshless local Petrov–Galerkin method for stress analysis of two-dimensional solids, where the Heaviside step function is used as the weighting function over a local sub-domain. The present method is a truly meshless method based only on a number of randomly located nodes. No domain integration is needed, no element matrix assembly is required and no special treatment is needed to impose the essential boundary conditions. Effects of the sizes of local sub-domain and interpolation domain on the performance of the present method are investigated. In this paper, the size of the support of the basis function has been treated as a shape parameter, and then, the behaviour of this shape parameter has been systematically studied for six different CSRBFs. Example problems in elastostatics are presented and compared with closed-form solutions. Results show that the proposed method is highly accurate and possesses no numerical difficulties.