Meshless Method for Searching Geodesic Line by using Moving Least Squares Interpolation

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Publication year 1999
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Title Meshless Method for Searching Geodesic Line by using Moving Least Squares Interpolation
Author Tetsuya Kawashima,Shintaro Yabashi,Hirohisa Noguchi,Kazuo Yokohori
Summary In the analysis for design of membrane structureEŒcutting analysis is indispensable. In the cutting analysisEŒcutting lines on the surface are determined so that curved surface can be expanded into several plane surfaces. In practice situationEŒgeodesic line is often regarded as cutting line. ConventionallyEŒthe geodesic line on arbitrary membrane surface is searched by using available finite element mesh. It is difficultEŒhoweverEŒto obtain the smooth geodesic line due to discontinuity of slope at the element boundary. In this paperEŒa new method for searching geodesic line by meshless approach using the moving least squares interpolation (MLSI). This method requires only nodal data and Cl continuity of approximation function of field is assured. ThereforeEŒthe variation of functional to be minimized is smoothly and efficiently. Some numerical examples are demonstrated to show the validity of the proposed method.