Comparative Study of Methods to Generate C^2 Continuous Mesh-free Basis using the Moving Least Squares Method

Abstract

This study investigates the ability of three different approaches for constructing smooth and continuous mesh-free basis functions, namely: (i) assuming one degree of freedom per node with the moving least squares method, (ii) assuming six degrees of freedom per node with moving least squares method, and (iii) assuming six degrees of freedom per node with Hermite-type moving least squares method. Further, it provides evidence that all three approaches can generate continuous mesh-free basis functions;however, the first and third approach results in a C2 continuous mesh-free basis, where the function and its first and second-order derivatives are related. Finally, a comparative study is performed among the three approaches using fourth-order polynomial basis and fifth-order spline weight function.