RI-IGABEM for 3D viscoelastic problems with body force

Abstract

A novel radial integration IGABEM (RI-IGABEM) is proposed to solve the 3D viscoelastic problems with body force in this paper. The derivation of boundary integral equations for the viscoelastic problems is proposed. To reduce computing costs, the time-dependent shear modulus is expressed in the form of Prony series, and the memory stress is calculated by using the genetic integral. Since the fundamental solution of elastostatics is applied to derive the boundary integral equations, which leads to the existence of domain integrals. To ensure that this algorithm only needs to discretize the boundary, we use radial integration method (RIM) to transform the domain integrals related to body force and memory stress into equivalent boundary integrals through applied points. Moreover, the strongly singular integral of the boundary integral equation is solved by the rigid-body displacement technique after a simple transformation between control points and collocation points, and the power series expansion method is used to solve the weakly singular integrals in RI-IGABEM. Furthermore, the 3D surface traction recovery method (TRM) of the viscoelastic mechanics is proposed to solve the strain and stress of the boundary points, and the regularized strain and stress integral equations are given in this work to solve the strain and stress of the internal points. Some 3D examples are applied to prove the effectiveness of the present method for the viscoelastic problems with body force.