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Analysis of thick plates by local radial basis functions-finite differences method

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Abstract

Although global collocation with radial basis functions proved to be a very accurate means of solving interpolation and partial differential equations problems, ill-conditioned matrices are produced, making the choice of the shape parameter a crucial issue. The use of local numerical schemes, such as finite differences produces better conditioned matrices. For scattered points, a combination of finite differences and radial basis functions avoids the limitation of finite differences to be used on special grids. In this paper, we use a higher-order shear and normal deformation plate theory and a radial basis function—finite difference technique for predicting the static behavior of thick plates. Through numerical experiments on square and L-shaped plates, the accuracy and efficiency of this collocation technique is demonstrated, and the numerical accuracy and convergence are thoughtfully examined. This technique shows great potential to solve large engineering problems without the issue of ill-conditioning.

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Authors and Affiliations

  1. INEGI, Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    C. M. C. Roque & J. D. Rodrigues

  2. Departamento de Engenharia Mecânica, Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    A. J. M. Ferreira

Authors
  1. C. M. C. Roque
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  2. J. D. Rodrigues
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  3. A. J. M. Ferreira
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Correspondence to A. J. M. Ferreira.

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Roque, C.M.C., Rodrigues, J.D. & Ferreira, A.J.M. Analysis of thick plates by local radial basis functions-finite differences method. Meccanica 47, 1157–1171 (2012). https://doi.org/10.1007/s11012-011-9501-6

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  • DOI: https://doi.org/10.1007/s11012-011-9501-6

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