Volume 7, Issue 5
Analysis of Two-Dimensional Thin Structures (From Micro- to Nano-Scales) Using the Singular Boundary Method

Dejian Shen & Yan Gu

Adv. Appl. Math. Mech., 7 (2015), pp. 597-609.

Published online: 2018-05

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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.

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@Article{AAMM-7-597, author = {Dejian Shen and Yan Gu}, title = {Analysis of Two-Dimensional Thin Structures (From Micro- to Nano-Scales) Using the Singular Boundary Method}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {7}, number = {5}, pages = {597--609}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2013.m454}, url = {http://global-sci.org/intro/article_detail/aamm/12065.html} }
TY - JOUR T1 - Analysis of Two-Dimensional Thin Structures (From Micro- to Nano-Scales) Using the Singular Boundary Method AU - Dejian Shen & Yan Gu JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 597 EP - 609 PY - 2018 DA - 2018/05 SN - 7 DO - http://dor.org/10.4208/aamm.2013.m454 UR - https://global-sci.org/intro/article_detail/aamm/12065.html KW - AB -

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.

Dejian Shen & Yan Gu. (1970). Analysis of Two-Dimensional Thin Structures (From Micro- to Nano-Scales) Using the Singular Boundary Method. Advances in Applied Mathematics and Mechanics. 7 (5). 597-609. doi:10.4208/aamm.2013.m454
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