Multi-region boundary element analysis and multi-layered Green's functions

Xu, Jiandong (2007) Multi-region boundary element analysis and multi-layered Green's functions. PhD thesis, University of Glasgow.

Abstract

This thesis aims to improve some aspects of the boundary element techniques in elastostatics and in particular its treatment of layered media. These include two areas of work: 1. The development of the partially discontinuous element method, that is, elements which are continuous on smooth boundaries but discontinuous at edges and comers, in order to address the well-known comer problem. This approach is relatively simple to implement whilst avoiding the computational disadvantages of discontinuous elements. We examine the effect of the offset distance between the free nodes and the element edges on accuracy and stability. This approach is implemented with automatic edge detection software, which incorporates partially discontinuous elements into BEM program without intervention by the user. This greatly reduces data preparation effort and makes the BEM an attractive option in practice. 2. In order to preserve the boundary-only discretization advantages of BEM, three-dimensional Green's functions in multi-layered systems are explored. These are computed using the cylindrical system of vector functions and the propagator matrix method. Numerical integration of these functions is problematic but a singularity extraction method is used to them accurately in the vicinity of the singularity. In this process, the Green's functions for the bi-material full space, are adopted instead of those for the homogeneous full space. The analytic work, which was necessary' to derive the necessary transformed functions in cylindrical vector space, is described in some detail. Numerical trials show that the current method is accurate and efficient, and superior to the previous approaches.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Additional Information: Adviser: Trevor G Davies
• Keywords: Applied mathematics
• Date of Award: 2007
• Depositing User: Enlighten Team
• Unique ID: glathesis:2007-73996
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 23 Sep 2019 15:33
• Last Modified: 23 Sep 2019 15:33
• URI: https://theses.gla.ac.uk/id/eprint/73996