Analysis of Two-Dimensional Thin Structures (From Micro- to Nano-Scales) Using the Singular Boundary Method

E-ISSN： 2075-1354|7|5|597-609

ISSN： 2070-0733

Source： Advances in Applied Mathematics and Mechanics, Vol.7, Iss.5, 2015-07, pp. : 597-609

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Abstract

This study investigates the applicability of the singular boundary method (SBM), a recent developed meshless boundary collocation method, for the analysis of two-dimensional (2D) thin structural problems. The troublesome nearly-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 boundary nodes are obtained for thin structures with the thickness-to-length ratio is as small as 1E-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 (FEM) and boundary element methods (BEM), are also discussed.