Optimal shape parameter for the solution of elastostatic problems with the RBF method Articles uri icon

publication date

  • April 2014

start page

  • 115

end page

  • 129

issue

  • 1

volume

  • 85

international standard serial number (ISSN)

  • 0022-0833

electronic international standard serial number (EISSN)

  • 1573-2703

abstract

  • Radial basis functions (RBFs) have become a popular method for the solution of partial differential equations. In this paper we analyze the applicability of both the global and the local versions of the method for elastostatic problems. We use multiquadrics as RBFs and describe how to select an optimal value of the shape parameter to minimize approximation errors. The selection of the optimal shape parameter is based on analytical approximations to the local error using either the same shape parameter at all nodes or a node-dependent shape parameter. We show through several examples using both equispaced and nonequispaced nodes that significant gains in accuracy result from a proper selection of the shape parameter.

keywords

  • meshless; radial basis function (rbf); rbf-fd; shape parameter; radial basis functions; functionally graded plates; vibration analysis; meshless method; static deformations; composite plates; layerwise