National Taiwan Ocean University Research Hubhttps://scholars.ntou.edu.twThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Mon, 17 Jun 2024 03:17:02 GMT2024-06-17T03:17:02Z5021Degenerate-scale problem of the boundary integral equation method/boundary element method for the bending plate analysishttp://scholars.ntou.edu.tw/handle/123456789/1506Title: 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
Abstract: Purpose
The purpose of this paper is to detect the degenerate scale of a 2D bending plate analytically and numerically.
Design/methodology/approach
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.
Findings
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.
Originality/value
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.
Mon, 03 Jul 2017 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/15062017-07-03T00:00:00ZDual boundary element analysis for cracked bars under torsionhttp://scholars.ntou.edu.tw/handle/123456789/1685Title: Dual boundary element analysis for cracked bars under torsion
Authors: Jeng-Tzong Chen; Chen, K. H.; Wei-Chung Yeih; Shieh, N. C.
Abstract: A dual integral formulation for a cracked bar under torsion is derived, and a dual boundary element method is implemented. It is shown that as the thickness of the crack becomes thinner, the ill‐posedness for the linear algebraic matrix becomes more serious if the conventional BEM is used. Numerical experiments for solution instability due to ill‐posedness are shown. To deal with this difficulty, the hypersingular equation of the dual boundary integral formulation is employed to obtain an independent constraint equation for the boundary unknowns. For the sake of computational efficiency, the area integral for the torsion rigidity is transformed into two boundary integrals by using Green’s second identity and divergence theorem. Finally, the torsion rigidities for cracks with different lengths and orientations are solved by using the dual BEM, and the results compare well with the analytical solutions and FEM results.
Tue, 01 Sep 1998 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/16851998-09-01T00:00:00Z