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. (C) 2013 Elsevier Ltd. All rights reserved.