Virtual boundary meshless least square collocation method for calculation of 2D multi-domain elastic problems

A virtual boundary meshless least square collocation method is developed for calculation of two-dimensional multi-domain elastic problems in this paper. This method is different from the conventional virtual boundary element method (VBEM) since it incorporates the point interpolation method (PIM) with the compactly supported radial basis function (CSRBF) to approximately construct the virtual source function of the VBEM. Consequently, this method has the advantages of boundary-type meshless methods. In addition, it does not have to deal with singular integral and has the symmetric coefficient matrix, and the pre-processing operation is also very simple. This method can be used to analyze multi-domain composite structures with each subdomain having different materials or geometries. Since the configuration of virtual boundary has a certain preparability, the integration along the virtual boundary can be carried out over the smooth simple curve that can be structured beforehand (for 2D problems) to reduce the complicity and difficulty of calculus without loss of accuracy, while “Vertex Question” existing in BEM can be avoided. In the end, several numerical examples are analyzed using the proposed method and some other commonly used methods for verification and comparison purposes. The results show that this method leads to faster convergence and higher accuracy in comparison with the other methods considered in this study.