A Proposed Approach to find shape parameters in Spherical Hankel Elements for Finite Element Analysis of Viscoelasticity Problems

In this article, the finite element analysis of two-dimensional linear viscoelastic problems was performed using nine-noded quadrilateral spherical Hankel elements, and the results compared with the classical finite element method. Spherical Hankel shape functions contain two shape parameters. Based on the experience of the authors, it was proposed that proper shape parameters for each problem adopted based on the satisfactory approximation of the problem’s geometry by a nine-noded quadrilateral spherical Hankel element. In order to obtain proper shape parameters, an optimization code developed utilizing particle swarm optimization (PSO) method. Two numerical examples solved. The results showed that FE solutions using spherical Hankel elements, employing coarse meshes, with the same number of elements, were more accurate than those obtained by classical interpolation functions.