Enhanced meshfree RPIM with NURBS basis function for analysis of irregular boundary domain

Abstract

Radial Point Interpolation Method (RPIM) has become a powerful tool to numerical analysis due to its ability to provide a higher-order approximation function with the Kronecker delta property, by which the field nodes can be fitted exactly. However, one of the major drawbacks of RPIM is the inefficiency in handling irregular domain problems. This paper presents an enhanced RPIM formulation that employs Non-Uniform Rational B-Splines (NURBS) basis functions to represent the exact geometry of the boundary domain. The NURBS is a mathematical model which provides an efficient and numerically stable algorithm to exactly represent all conic sections in engineering modelling. Taking advantage of the flexibility and adaptivity of RPIM approximation and the accuracy of geometric representations by NURBS, this new method is able to improve geometry accuracy and flexibility in numerical analysis, thus providing a better and more rational approach to analyze irregular domain problems. Numerical problem of steady heat transfer considering curved beam is presented to verify the validity and accuracy of the developed method. The essential boundary condition can simply be imposed using direct imposition as in Finite Element Method (FEM). The result shows that the RPIM/NURBS achieved the converged solution much faster than conventional RPIM and FEM, with the number of nodes required only less than 200 for an error of less than 0.01%. This shows the potential of the developed method as a powerful numerical technique for future development.