A mixed formulation of B-spline and a new class of spherical Hankel shape functions for modeling elastostatic problems

Abstract

• Utilizing the combination of B-spline and new class of spherical Hankel shape functions for solving elastostatic problems . • Modeling geometric and physical variables through separate techniques, unlike the classical isoparametric mapping. • Proposing novel shape functions with the advantages of both RBFs and spherical Bessel functions in element-based framework. • Satisfying polynomial, and the first and second kind of Bessel function fields for proposed basis, unlike classical ones. In this paper, a mixed formulation based on non-uniform rational B-splines (NURBS) and a new class of spherical Hankel basis functions is offered. Spherical Hankel basis functions are a kind of radial basis functions that satisfy both spherical Bessel function field and polynomial functions. In this article, the geometry of the problems is modeled through NURBS as they are precise in the modeling of the geometry. On the other hand, based on reported literature, using Hankel basis functions provides us with extremely precise results. Hence, a mixed formulation based on NURBS and spherical Hankel basis functions should result in more accurate outcomes. To evaluate the accuracy and efficiency of the proposed formulation, three numerical examples are solved. In the numerical examples, it is tried to use few degrees of freedom with the aim of reducing computational cost. By comparing the proposed formulation outcomes with classical FEM and isogeometric analysis, it can be interestingly concluded that using the mixed formulation leads to much more accurate outcomes.