NURBS-enhanced line integration BEM for thermo-elastic problems considering the gravity load

Abstract

This paper is aimed at solving the thermo-elastic problems with the gravity load by the line integration boundary element method (LIBEM). The boundary-only discretization, as one of the significant advantages of BEM, will disappear due to considering the thermal and gravity loads, specifically, domain integrals turn up in the original boundary integral equations (BIEs). Hence, the LIBEM, owning the dimension reduction ability, is introduced to reduce domain integrals dimensionally to ensure that no domain discretization appears during the numerical simulation. Furthermore, as a well-known isogeometry characterization method, the non-uniform rational B-spline (NURBS), is exerted during geometrical construction. Thus, the boundary shape of the numerical models will not change during the refinement and the error of model discretization will be prevented. It is worth mentioning that, to ensure boundary conditions are imposed without difficulty, the field approximation is conducted by the Lagrangian basis functions (LBFs) owning the characteristic of the Kronecker delta function.