A detailed literature review on the development and applications of several numerical methods in solid mechanics and electromagnetic field analysis is presented in the thesis. Despite the great achievements in this research area, there are always the needs to develop new numerical methods or to explore alternative techniques for the purpose of solving the complicate problems and improve the efficiency and accuracy of the existing or new numerical methods. This thesis presents the development of a novel numerical method, the moving least square Ritz (MLS-Ritz) method, and its applications for solving science and engineering problems. The MLS-Ritz method is based on the moving least square (MLS) data interpolation technique and the Ritz minimization principle. The MLS technique is utilized to establish the Ritz trial functions for two-dimensional (2-D) and three-dimensional (3-D) cases. A point substitution approach is developed to enforce boundary conditions. The proposed MLS-Ritz method has the ability to expand the applicability of the conventional Ritz method and meshless method for analysing problems with complex geometries and multiple mediums. The applications of the MLS-Ritz method are also extended to the analysis of the electromagnetic field problems. Three cases including electrical potential problems in a uniform trough and with dielectric medium and a waveguide eigenvalue problem are analysed and compared with solutions obtained by other methods. Comparison studies show that excellent agreement is achieved for the three cases when comparing with existing results in the open literature. The future directions in the development of the MLS-Ritz method for science and engineering computations are discussed. / Doctor of Philosophy (PhD)
| Identifer | oai:union.ndltd.org:ADTP/181766 |
| Date | January 2007 |
| Creators | Zhou, Li, University of Western Sydney, College of Health and Science, School of Computing and Mathematics |
| Source Sets | Australiasian Digital Theses Program |
| Language | English |
| Detected Language | English |
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