Generalized Taylor polynomials for axisymmetric plates and shells

Abstract

This work proposes the use of a mesh-free technique, derived from the generalized Taylor polynomials, for the analysis of axisymmetric plates and shells. The primary solution variable(s) is/are assumed to take the form of a truncated Taylor series around a point c, and the unknown coefficients of the expansion are determined using the governing differential equation(s) and boundary conditions. The method is free of shape-parameter calibration needed in some other famous mesh-free techniques such as the RBF, and is quite easy to formulate and program. Successful application of the method to several benchmark problems of axisymmetric plate and shell structures proves its robustness. The results have been verified using the existing rigorous analytical solutions that are in most cases not suited to practical engineering calculations.