Non-conforming coupling RI-IGABEM for solving multidimensional and multiscale thermoelastic–viscoelastic problems

Abstract

In this paper, a novel non-conforming coupling radial integration IGABEM (RI-IGABEM) is proposed to solve the multidimensional and multiscale thermoelastic–viscoelastic​ problems. Firstly, the displacement and regularized strain boundary integral equations for the thermoviscoelastic problems are derived. Secondly, the time-dependent shear modulus is expressed in the form of Prony series, and the memory stress is calculated by using the genetic integral, which reduces computing costs. In addition, the radial integration method (RIM) is applied to transform the domain integrals related to body force, temperature and memory stress into equivalent boundary integrals through applied points, which not only allows IGABEM to retain the advantage of discretization only on the boundary, but also reduces the singularity of the integral. Moreover, the adaptive integral method based on hierarchical quadtree decomposition algorithm is proposed to deal with the nearly singular integrals more flexible and efficient at optimal computational cost. The modified surface traction recovery method (TRM) of the thermoviscoelastic mechanics is proposed to solve the strains of the boundary points, which allows us to avoid solving hypersingular integrals. Furthermore, we construct the displacement (or tractions) coupling constraints among the non-conforming interface meshes by a virtual knot insertion technique. The main advantages of this method are simplicity and robustness, as it is problem-independent and only depends on the NURBS meshes on both sides of the interface. Some 2D and 3D examples are applied to prove the accuracy and efficiency of the present method for the multiscale thermoelastic–viscoelastic problems.