Mathematical Modeling of Bending of a Circular Plate with the Use of S-Splines

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• 作者：A. N. Fedosova ; D. A. Silaev
• 刊名：Journal of Mathematical Sciences
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：214
• 期：6
• 页码：854-864
• 全文大小：520 KB
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• 作者单位：A. N. Fedosova (1)
  D. A. Silaev (1)
  
  1. Moscow State University, Moscow, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：Springer New York
• ISSN：1573-8795

文摘

The present paper is concerned with the application of newly developed high-order semi-local smoothing splines (or S-splines) in solving problems in elasticity. We will consider seventh-degree S-splines, which preserve the four continuous derivatives (C 4-smooth splines) and remain stable. The problem in question can be reduced to solving an inhomogeneous biharmonic equation by the Galerkin method, where as a system of basis functions we take the C 4-smooth fundamental S-splines. Such an approach is capable not only of delivering high accuracy of the resulting numerical solution under a fairly small number of basis functions, but may also easily deliver the sought-for loads. In finding the loads, as is known, one has to twice numerically differentiate the resulting bipotential, which is the solution of the biharmonic equation. This results in roundoff propagation.