An AOIMLS enhanced LIBEM and for solving 3D thermo-elastic problems and non-homogeneous heat conduction problems with heat generation

Abstract In this paper, a novel boundary element method (BEM) is proposed to solve thermo-elastic problems and non-homogeneous heat conduction problems with heat generation. Because of considering thermal stress in thermo-elastic problems and the non-homogeneous thermal conductivity along with heat generation in heat conduction problems, domain integrals appear in boundary integral equations (BIEs). Hence, to avoid losing the well-known advantage of BEM, boundary-only discretization, the line integration boundary element method (LIBEM), which can reduce the domain integrals dimensionally, is introduced in the current research for the first time. However, like some other domain integration processing methods, the LIBEM only can deal with domain integrals with known integral function, i.e., for thermo-elastic problems, temperature distribution should be known, while when it comes to the case, only temperature boundary conditions are known, the LIBEM cannot be applied directly. Further, for heat conduction problems, the heat generation function can be obtained directly and the relevant domain integral can be computed by LIBEM directly, while the domain integral caused by non-homogeneous thermal conductivity, contains an unknown integral function related to the regularized temperature is beyond the capability of the traditional LIBEM. Thereby a new adaptive orthogonal interpolating moving least-square method (AOIMLS) based LIBEM is proposed for dealing with the case when the BIEs contain domain integrals with unknown function, as all the necessary temperature values for the integral points in the line integration method (LIM) can be interpolated from discretize nodes by AOIMLS, and the accuracy of this new kind of BEM is testified by numerical examples.