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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/50351

Title: Degenerate-scale problem of the boundary integral equation method/boundary element method for the bending plate analysis
Authors: Jeng-Tzong Chen
Shyh-Rong Kuo
Yu-Lung Chang
Shing-Kai Kao
Contributors: 國立臺灣海洋大學:河海工程學系
Keywords: Boundary integral equation
Arbitrary shapes
Circular plate
Degenerate kernel
Degenerate scales
Eigenproblem of the 4 by 4 matrix
Date: 2016-10
Issue Date: 2018-10-05T03:11:46Z
Publisher: Engineering Computations
Abstract: Abstract: Purpose
The purpose of this paper is to detect the degenerate scale of a 2D bending plate analytically and numerically.

To avoid the time-consuming scheme, the influence matrix of the boundary element method (BEM) is reformulated to an eigenproblem of the 4 by 4 matrix by using the scaling transform instead of the direct-searching scheme to find degenerate scales. Analytical degenerate scales are derived from the boundary integral equation (BIE) by using the degenerate kernel only for the circular case. Numerical results of the direct-searching scheme and the eigen system for the arbitrary shape are also considered.

Results using three methods, namely, analytical derivation, the direct-searching scheme and the 4 by 4 eigen system, are also given for the circular case and arbitrary shapes. Finally, addition of a constant for the kernel function makes original eigenvalues (2 real roots and 2 complex roots) of the 4 by 4 matrix to be all real. This indicates that a degenerate scale depends on the kernel function.

The analytical derivation for the degenerate scale of a 2D bending plate in the BIE is first studied by using the degenerate kernel. Through the reformed eigenproblem of a 4 by 4 matrix, the numerical solution for the plate of an arbitrary shape can be used in the plate analysis using the BEM.
Relation: 34(5)
URI: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/50351
Appears in Collections:[河海工程學系] 期刊論文

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