First kind Bessel function (J-Bessel) as radial basis function for plane dynamic analysis using dual reciprocity boundary element method

Abstract

This paper presents a new radial basis function (RBF) for the boundary element method in the analysis of plane transient elastodynamic problems. The dual reciprocity method (DRM) is reconsidered by using the first kind Bessel (J-Bessel) function as a new generation of RBFs to approximate the inertia term. Employing the initial value theorem of Laplace transform, the particular solution kernels of the proposed RBFs corresponding to displacement and traction, with no singular terms, has been explicitly derived. Furthermore, the limiting values of the particular solution kernels have been evaluated. To illustrate the validity and accuracy of the present RBFs, three numerical examples are examined and compared to the results of analytical and other RBFs reported in the literature. In comparison with other RBFs, J-Bessel RBFs represent more accurate results, using a smaller degree of freedom, and hence they are more efficient.