On an Approximately Solution of Saint-Venant's Problems for a Beams with a Perturbed Lateral Surfaces

Gaioz Khatiashvili
2005 Georgian Electronic Scientific Journal: Computer Science and Telecommunications   unpublished
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
more » ... 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 [7]. 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.