A Numerical Method of Hankel Transform for Axisymmetric Problems of Elasticity

Abstract

In numerical calculations of the Hankel Transform to solve axisymmetric elastic problems of semi-infinite bodies or infinite thick plates, Simpson's rule is usually adopted. But it is difficult to obtain accurate results by Simpson's rule because the Bessel function in the kernel of the Hankel transform oscillates. In this paper, f(x), a function to be transformed, xf(x) is approximated piecewise by the quadratic and the result of the Hankel transform is expressed by Lommel's functions. In this way accurate Hankel transforms are obtained. Two examples are illustrated to show the availability of this method.