Analytical integration of singular kernels in symmetric boundary element analysis of Kirchhoff plates

✍ Scribed by M. Mazza; L. Leonetti; M. Aristodemo

• Publisher: John Wiley and Sons
• Year: 2008
• Tongue: English
• Weight: 390 KB
• Volume: 76
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.2292

✦ Synopsis

Abstract

An analytical integration method for evaluating the singular integrals arising in the construction of symmetric boundary element models is proposed, referring to the analysis of Kirchhoff plates. Kernels involved in the symmetric boundary formulation of Kirchhoff plates exhibit singularities up to O(1/r^4^). The proposed technique temporarily deactivates the singularities by using a limit approach and carries out the integration on contiguous boundary elements in order to smooth the singularities of the kernels through sufficiently continuous shape functions. The paper contains a brief presentation of the boundary integral formulation of the Kirchhoff plate, with the explicit expressions of the fundamental solutions involved and the derivation of the symmetric boundary element model. A detailed description of the proposed integration technique is presented, which discusses the main steps of the analytical procedure and provides the final results. The technique is illustrated through the discussion of a series of relevant cases, including high singularities and referring to both collinear and corner supports. Copyright © 2008 John Wiley & Sons, Ltd.