Spherical Hankel-Based Creep Analysis of Time-Dependent Materials Using Boundary-Element Theories

Abstract

In this article, the boundary-element method (BEM) is applied to solve viscoelastic problems with any alteration in load, time, or boundary condition. The innovation of using spherical Hankel element framework instead of the classical Lagrangian approach is an effort to estimate the state variables of essential differential equations of BEM. This approach leads to the simultaneous satisfaction of the first- and second-order Bessel functions and the customary polynomial functions. A computer code has been generated to validate this progressive method. The results of various numerical examples, in which the analytical solution is measured and compared with Lagrangian- and Hankel-based BEM, are illustrated by means of comparative graphs. This evaluation reveals that the new method portrays much better agreement with the analytical solution in contrast to the classic BEM and maintains the accuracy while using the least degrees of freedom, indicating that it has significantly less error percentage owing to the fact that by utilizing the least number of elements, the desired precision is acquired. Thus, the current method is introduced and recommended as it is more economical and time-saving.