Analysis of Two-Dimensional Thin Structures (from Micro- to Nano-Scales) Using the Singular Boundary Method (Advances in Applied Mathematics and Mechanics, 2018)
This study investigates the applicability of the singular boundary method(SBM), a recent developed meshless boundary collocation method, for the analysisof two-dimensional (2D) thin structural problems. The troublesome nearly-singularkernels, which are crucial in the applications of SBM to thin shapes, are dealt withefficiently by using a non-linear transformation technique. Promising SBM resultswith only a small number of boundary nodes are obtained for thin structures withthe thickness-to-length ratio is as small as 1E-9, which is sufficient for modeling mostthin layered coating systems as used in smart materials and micro-electro-mechanicalsystems. The advantages, disadvantages and potential applications of the proposedmethod, as compared with the finite element (FEM) and boundary element methods(BEM), are also discussed.