Revisit of degenerate scales in the BIEM/BEM for 2D elasticity problems

ABSTRACT

The boundary integral equation method in conjunction with the degenerate kernel, the direct searching technique (singular value decomposition), and the only two-trials technique (2 × 2 matrix eigenvalue problem) are analytically and numerically used to find the degenerate scales, respectively. In the continuous system of boundary integral equation, the degenerate kernel for the 2D Kelvin solution in the polar coordinates is reviewed and the degenerate kernel in the elliptical coordinates is derived. Using the degenerate kernel, an analytical solution of the degenerate scales for the elasticity problem of circular and elliptical cases is obtained and compared with the numerical result. Further, the triangular case and square case were also numerically demonstrated.

KEYWORDS:

• Boundary element method
• boundary integral equation method
• two-dimensional elasticity
• degenerate scale
• degenerate kernel
• eigenvalue problem

Funding

Financial support from the Ministry of Science and Technology under Grant No. NSC 101-2221-E019-050 -MY3 for National Taiwan Ocean University is gratefully acknowledged.