A local radial basis functions—Finite differences technique for the analysis of composite plates

Abstract

Radial basis functions are a very accurate means of solving interpolation and partial differential equations problems. The global radial basis functions collocation technique produces ill-conditioning matrices when using multiquadrics, making the choice of the shape parameter a crucial issue. The use of local numerical schemes, such as finite differences produces much better conditioned matrices. However, finite difference schemes are limited to special grids. For scattered points, a combination of finite differences and radial basis functions would be a possible solution. In this paper, we use a higher-order shear deformation plate theory and a radial basis function—finite difference technique for predicting the static behavior of thin and thick composite 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.