# Degenerate-scale problem of the boundary integral equation method/boundary element method for the bending plate analysis

Degenerate-scale problem of the boundary integral equation method/boundary element method for the... PurposeThe purpose of this paper is to detect the degenerate scale of a 2D bending plate analytically and numerically.Design/methodology/approachTo 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.FindingsResults 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.Originality/valueThe 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Engineering Computations Emerald Publishing

# Degenerate-scale problem of the boundary integral equation method/boundary element method for the bending plate analysis

, Volume 34 (5): 24 – Jul 3, 2017
24 pages      /lp/emerald-publishing/degenerate-scale-problem-of-the-boundary-integral-equation-method-ExvmG37Sfv
Publisher
Emerald Publishing
ISSN
0264-4401
DOI
10.1108/EC-06-2016-0187
Publisher site
See Article on Publisher Site

### Abstract

PurposeThe purpose of this paper is to detect the degenerate scale of a 2D bending plate analytically and numerically.Design/methodology/approachTo 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.FindingsResults 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.Originality/valueThe 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.

### Journal

Engineering ComputationsEmerald Publishing

Published: Jul 3, 2017