A radial basis function approach in the meshless local Petrov-Galerkin method for Euler-Bernoulli beam problems

Abstract

A meshless local Petrov-Galerkin (MLPG) method that uses radial basis functions rather than generalized moving least squares (GMLS) interpolations to develop the trial functions in the study of Euler-Bernoulli beam problems is presented. The use of radial basis functions (RBF) in meshless methods is demonstrated for C¹ problems for the first time. This interpolation choice yields a computationally simpler method as fewer matrix inversions and multiplications are required than when GMLS interpolations are used. Test functions are chosen as simple weight functions as in the conventional MLPG method. Patch tests, mixed boundary value problems, and problems with complex loading conditions are considered. The radial basis MLPG method yields accurate results for deflections, slopes, moments, and shear forces, and the accuracy of these results is better than that obtained using the conventional MLPG method.