ИЗГИБ КОМБИНИРОВАННЫХ ПЛАСТИН КУСОЧНОПЕРЕМЕННОЙ ТОЛЩИНЫ. РЕШЕНИЯ В ФУНКЦИЯХ ЛЕЖАНДРА

Abstract

Abstract. The work considers the problems of flexure of plates of circular form and consisting of separate parts with different laws of thickness variation. The each part of this plate has the form of a ring. The mentioned separate sections may be made from the same or from the different materials. The material of the piece-wise variable plate parts can be isotropic or orthotropic, homogeneous or nonhomogeneous. In the places of the separate parts conjugation the plate’s thickness can be continuous or discontinuous. The action of symmetric load on piece-wise variable plate is studied. The analytical approach is used, the solutions are obtained in the closed forms in terms of Legendre functions and Legendre polynomials. Rather wide set of plates’ profiles is determined. For the satisfaction of the conditions of the separate sections conjugation the special auxiliary functions are introduced. The computation of the plate, consisting of three sections and subjected to an action of discontinuous loads, is considered as an example.