Assessment and applications of point interpolation methods for computational mechanics

Two meshfree point interpolation methods (PIMs), which are based on the polynomial and the radial basis functions, have been proposed recently in addition to the earlier work with the moving leastsquares (MLS) approximation for the field function approximation. However, it is found that PIMs cannot automatically ensure the compatibility of the solution when they are used together with the energy principles. In this paper, issues related to the compatibility of PIMs are studied. A technique of background cell-based nodal selections and a penalty method are proposed to enforce the compatibility of the solution of PIMs. The patch test is studied in great detail. The convergences and performances are investigated for both conforming and non-conforming PIMs. It is found that those methods of the PIM family are very easy to implement, and are very efficient in obtaining numerical solutions for problems of computational mechanics