On an Approximately Solution of Saint-Venant's Problems for a Beams with a Perturbed Lateral Surfaces
Georgian Electronic Scientific Journal: Computer Science and Telecommunications
First works on an indicated problems for an isotropic beams were given by Panov D.I.,Riz P.M., Rukhadze A.K and various authors. These results were generalized on a composed bodies and anisotrpic medium by various authors. In these works indicated problems were studied with help of a transformation of a system of coordinates and differential operators and boundary conditions were approximated with accuracy up to first power of a small parameter v. As this takes place it is impossible to
... a power of an approximation and give proof of this method for anisotropic medium is difficult, because a coefficients of elasticity in this method are varying. In this paper a solution of Saint-Ven ant's problems in a domain, occupying by a body similar to prismatic (cylindrical), with perturbed cylindrical surface, is represented as a series with respect of a small parameter v , characterized a perturbation of a cylindrical surface. For each terms of a series are obtained the recurrent boundary problems of elasticity of Almansi-Michel's type for a cylindrical body. A class of surface is indicated, for which later on may be studied a question of a convergence of a double series with respect of a small parameters. Also this way gives a possibility of a solution of a problem with a required exactness. A first results on this direction were given by author of this article in papers (1981 and 1983) used methods considered in articles of A.N.Guz (1962) and I.N.Nemish (1976), where a method of a perturbation of a cross section of a surfaces of a canonical form was considered. This way as a base was used in another direction for a construction of algorithms for a solution of some problems of an elasticity, for a bodies similar to cylindrical by an arbitrary cross section. These results are given in the book . A.N. Guz, I.N. Nemish and N.M. Bloshko created the methods of a perturbation of bodies boundary's form by its further generalization (see A.N.