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

The equations which model the elastostatic shallow circular cylindrical she ll (see, e.g., [6,15,23,29]) constitute an important elliptic partial diffe rential equation (PDE) system in the study of shell structures. When the sy stem is subjected to a concentrated point load, the response is described b y a fundamental solution of the PDE system. We have found some mathematical inconsistencies in the existing literature, Therefore, in this paper, we d iscuss these errors, then we use partial fractions and Fourier transform te chniques to determine the fundamental solution. Explicit expressions in ter ms of special functions and convolution integrals are derived and simplifie d so that the formulas are suitable for algorithmic evaluation and for appl ication elsewhere. (C) 2000 Elsevier Science Ltd. All rights reserved.