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

Published online by Cambridge University Press:  21 July 2015

Dejian Shen  and
Yan Gu
Dejian Shen
Affiliation:
Department of Civil Engineering, College of Civil and Transportation Engineering, Hohai University, Nanjing 210098, China College of Mathematics, Qingdao University, Qingdao 266071, China
Yan Gu*
Affiliation:
College of Mathematics, Qingdao University, Qingdao 266071, China
*
*Corresponding author. Email: [email protected] (Y. Gu)
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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.

Keywords

65N1565N38Singular boundary methodmeshless boundary collocation methodmethod of fundamental solutionssinh transformationthin structural problems
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 7 , Issue 5 , October 2015 , pp. 597 - 609
Copyright
Copyright © Global-Science Press 2015 

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