Recent advances in singular boundary method for ultra-thin structural problems

This study makes the first attempt to apply the singular boundary method (SBM), a meshless boundary collocation method, for the analysis of two-dimensional (2D) thin structural problems. The troublesome near-singular kernels, which are crucial in the applications of SBM to thin shapes, are dealt with efficiently by using a non-linear transformation technique. Promising SBM 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 1E-9, which is sufficient for modeling most thin structures 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 (FEM) and boundary element (BEM) methods, are also discussed