Numerical integration of singular Kelvin functions applied to plates on an elastic foundation

摘要

The four Cauchy data of a Kirchhoff plate on an elastic foundation are coupled by a system of two integral equations which involve integrals of Kelvin or Bessel functions. It is therefore necessary to find fast high precision algorithms for the calculation of these Kelvin functions and to devise a practical method to handle the singular integrals. These tasks can be facilitated by splitting the integrals into a singular and a regular part. We show how we can integrate the singular part analytically and how appropriate numerical procedures for the integrals involving the Kelvin functions yield very accurate results and in short time.