A modified scaled boundary finite-element method for problems with parallel side-faces. Part I. Theoretical developments |
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| Institution: | 1. School of Civil and Resource Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia;2. State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, China;1. University of Cagliari, DICAAR – Department of Civil and Environmental Engineering and Architecture, 2, via Marengo, I-09123 Cagliari, Italy;2. Technische Universität Dresden, Institut Statik und Dynamik der Tragwerke, D-01062 Dresden, Germany;1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha City 410082, PR China;2. School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW 2052, Australia;1. School of Civil Engineering and Architecture, Nanchang Hangkong University, Nanchang, Jiangxi 330063, China;2. College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100084, China;1. Department of Mathematics and Computer Science “U. Dini”- University of Florence, V.le Morgagni 67/a, Florence 50134, Italy;2. Department of Mathematics “G. Peano”- University of Turin, V. Carlo Alberto 10, Turin 10123, Italy |
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| Abstract: | A modified scaled boundary finite-element method (SBFEM) for problems with parallel side-faces is presented in this study. To overcome the inherent difficulty of the original SBFEM for domains with parallel side-faces, a new type of local co-ordinate system is proposed. The new local co-ordinate system allows the so-called scaling centre of the SBFEM to move freely along an arbitrary curve and thus eliminates the non-parallel side-face restriction in the original SBFEM. The modified SBFEM equations are derived based on a weighted residual approach. It is found that the modified SBFEM solution retains the analytical feature in the direction parallel to the side-faces and satisfies the boundary conditions at infinity exactly, as in the original SBFEM. This paper develops a complete scaled boundary finite-element solution to a two-dimensional Laplace's equation with Neumann and Robin boundary conditions in a semi-infinite domain with parallel boundaries. |
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