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| A new radial basis function differential quadrature method with fictitious points and its application in thin plate bending |
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Abstract In this paper, the radial basis function differential quadrature method with fictitious points (FRBF-DQ) is proposed and applied to simulate thin plate bending problems. The FRBF-DQ method is a new meshless method based on the traditional radial basis function differential quadrature method. While the traditional radial basis function differential quadrature method (RBF-DQ) method places the centers exclusively inside the solution domain, the proposed method expands the region for the centers allowing them to place both inside and outside the computational domain. The FRBF-DQ method applies radial basis functions and weight coefficients to solve differential equations approximately. Meanwhile, the solution accuracy has been significantly improved without the increasing of calculation cost and storage. The thin plate bending problems are controlled by the fourth order partial differential equation based on the Kirchhoff and the Winkler hypothesis. The examples reveal that the FRBF-DQ method works even for arbitrary distributed nodes with better computational convergence and higher computational accuracy than the traditional RBF-DQ method. The proposed method can be considered as a good alternative method for engineering problems.
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Received: 27 October 2020
Published: 14 December 2021
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2021, Vol. 42 
