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A Comparative Study of Galerkin Mesh-Free and Finite Element Methods: (English)

A Comparative Study of Galerkin Mesh-Free and Finite Element Methods: (English)

          
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About the Book

This dissertation, "A Comparative Study of Galerkin Mesh-free and Finite Element Methods" by Xiaodong, Liang, 梁?東, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of the thesis entitled A comparative study of Galerkin mesh-free and finite element methods submitted by Liang Xiaodong for the degree of Master of Philosophy at the University of Hong Kong in August 2004 In the last decade, the mesh-free method has been a popular research topic in the research community of computational mechanics. While mesh generation and nodal connectivity are not required in the mesh-free method, the mesh-free method requires, for instances, node-searching, definition of integration cells and special treatment of essential boundary conditions that makes the method computationally expensive. It is interesting to note that there has not been much comparison between the mesh-free and finite element methods on their accuracy and convergence. More importantly, only the standard finite element models are employed in most, if not all, of the previous comparison. In this study, the general mesh-free method, the direct nodal integration, the stabilized conforming nodal integration and the finite element method for plane elasticity analyses are programmed. The stabilized conforming nodal integration is chosen among other mesh-free methods because it is known to be possessing good accuracy and consistency. In the finite element computer program, fully integrated, reduced-integrated and a hybrid-stress four-node quadrilateral finite element model are composed. A number of one-dimensional and two-dimensional elasticity problems with exact analytical solutions are examined by the afore- mentioned mesh-free methods and finite element models. Their displacement error norm and stress error norm at various nodal densities are computed and compared. While the general mesh-free method and the fully integrated finite element model are comparable in accuracy in many of the problems, the hybrid-stress finite element model are markedly more accurate than all the other methods and models. The mesh- free method is also noted to be considerably more computation-consuming than the finite element method and the difference in the cpu time can be as large as ten times for the same number of nodes. DOI: 10.5353/th_b3014769 Subjects: Finite element method Engineering mathematics Numerical analysis


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Product Details
  • ISBN-13: 9781374724273
  • Publisher: Open Dissertation Press
  • Publisher Imprint: Open Dissertation Press
  • Height: 279 mm
  • No of Pages: 96
  • Spine Width: 5 mm
  • Width: 216 mm
  • ISBN-10: 1374724270
  • Publisher Date: 27 Jan 2017
  • Binding: Paperback
  • Language: English
  • Series Title: English
  • Weight: 245 gr


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