Stress analysis for thin multilayered coating systems using a sinh transformed boundary element method

In this paper, the boundary element method (BEM) based on the elasticity theory is developed for two-dimensional (2-D) thin-structural problems with thickness-to-length ratio in the micro ( 10 - 6 ) or nano ( 10 - 9 ) scales. An efficient non-linear co-ordinate transformation, based on the sinh function, is developed to deal with the troublesome nearly-singular integrals arising in the BEM formulation for thin structures. The proposed BEM formulation with thin-body capabilities is also extended to the multi-domain problems and applied to the stress analysis of multilayered coating systems. Promising BEM results with only a small number of elements are obtained for thin films and coatings with the thickness-to-length ratio is as small as 10 - 9 , which is sufficient for modeling most thin layered coating systems as used in smart materials and micro-electro-mechanical systems. The advantages, disadvantages and potential applications of the proposed method, as compared with the finite element method (FEM), are discussed in the last section.