Subtraction, expansion and regularising transformation methods for singular kernel integrations in elastostatics

✍ Scribed by W.S. Hall; T.T. Hibbs

• Publisher: Elsevier Science
• Year: 1991
• Tongue: English
• Weight: 758 KB
• Volume: 15
• Category: Article
• ISSN: 0895-7177
• DOI: 10.1016/0895-7177(91)90076-j

✦ Synopsis

Two methods of integrating the singular kernels arising in the Boundary Element Method for t,hree dimensional elastostatic problems are treated. The fist method involves the identification of the singular part of the kernel using series expansions and its subtraction out of the integrals. The second method involves the transformation of the domain of integration from a triangular region to a square region which introduces a regularising Jacobian. A feature of the treatment given is the combination of the subtraction and regularising polar coordinate transformation. This enables a simple accurate integration of the singular part to be performed and an analysis to be carried out of the nature of the non-sing&r, but nevertheless badly behaved, remainder integral. Results are presented for triangular elements on spheres and ellipsoids which illustrate the effect of the integration methods, and incidentally provide exact integrals which may be used for comparison purposes by other authors.