On Some Recent Discrete-Continuum Approaches to the Solution of Shell Problems.

The fundamentals of three new discrete-continuum approaches to the solution of the stationary problems of shell theory are discussed: the discrete Fourier series approach, the spline-collocation method, and the complete systems method. The general idea of the discussed approaches consists in using some sort of transformation to convert the original two-dimensional (or three-dimensional)problems to the corresponding linear one-dimensional boundary-value problems, which are then solved numerically using the method of discrete orthogonalization. The considered problems of elastic deformations of shells employ models of various degree of accuracy: the model of Mushtari-Donnel-Vlasov, the first-order model of Timoshenko-Mindlin, and the model based on three-dimensional theory of elasticity. Combining those models with the proposed solution methods for multi-dimesional problems investigations of the deformation and stress fields in a number of shells, as well as of their free vibration properties, are conducted. The considered shells are described by surface-varying geometrical and physical parameters and it is shown that variation of those parameters on the distribution of their displacement fields, stress fields, and on their dynamic characteristics is significant. Special attention is dedicated to the issue of the accuracy of the obtained numerical solutions.