A modified RI-IGABEM with only weakly singular integral for viscoelastic analysis

Abstract

In this paper, an improved isogeometric boundary element method based on radial integration method (RI-IGABEM) is proposed to solve the viscoelastic problems. Prony series are utilized to discretize the stress with the two most recent time-step strains. The boundary integral equation (BIE) for the viscoelastic problems is derived. The domain integral related to stress is decomposed into the linear combination of two sub-integrals by volumetric–deviatoric split. The radial integration method (RIM) is applied to transform all the domain integrals into equivalent boundary integrals. The present method has several advantages. Firstly, the present method eliminates the need for stress calculation at each time step, thus avoiding the error accumulation associated with the traction recovery method (TRM). Secondly, the BIE for the viscoelastic problems contains only weakly singular integrals. In addition, we provide an analytical solution for the radial component of the equivalent boundary integrals, which is transformed using RIM. To sum up, the present method improves the accuracy and efficiency of RI-IGABEM by reducing the required computational steps, eliminating error accumulation, and providing analytical solutions for certain integrals. Numerical examples demonstrate that the proposed RI-IGABEM is an efficient and accurate method suitable for viscoelastic problems.