Solid analysis of micron-sized thin structures with BEM for steady-state heat conduction

Accurate thermal or mechanical analysis of thin structures has been a challenging task for various numerical methods, due to the exceeding closeness of the two neighboring surfaces. In this paper, the micron-sized interior-like thin structures for steady-state heat conduction is investigated with BEM. Three major difficulties would be encountered during solid analysis of thin structures with BEM: 1) degeneracy of the linear systems of equations; 2) evaluation of singular integrals over distorted elements; 3) evaluation of various orders of nearly singular integrals. To investigate the effect of singular and nearly singular integrals independently, the singularity subtraction technique (SST) and nonlinear distance transformation combined with adaptive subdivision method are employed to deal with singular and nearly singular integrals, respectively. Besides, a conformal mapping procedure aligned with sigmoidal transformation in angular direction is proposed to eliminate the near singularity derived from the distortion of element shape. Several challenging numerical examples with characteristic thickness h=10−3h=10−3, including annular disk, hollow sphere and hollow torus examples, are solved with coarse meshes compared to original methods, and some meaningful conclusions have been obtained.