The fundamental solution for shallow circular cylindrical shells - Part I: Derivations

The equations which model the elastostatic shallow circular cylindrical shell (see, e.g., [6,15,23,29]) constitute an important elliptic partial differential equation (PDE) system in the study of shell structures. When the system is subjected to a concentrated point load, the response is described by a fundamental solution of the PDE system. We have found some mathematical inconsistencies in the existing literature. Therefore, in this paper, we discuss these errors, then we use partial fractions and Fourier transform techniques to determine the fundamental solution. Explicit expressions in terms of special functions and convolution integrals are derived and simplified so that the formulas are suitable for algorithmic evaluation and for application elsewhere.