Analyticity of the solution of a plane elastoplastic problem

Elastoplastic problems of the theory of ideal plasticity were studied numerically by the method of small parameter in the monographs [1-3], and strengthening elastoplastic problems were studied in the monograph [4], where a rather complete bibliography of studies in this direction is given. The conditions for the continuous dependence of the the stress-strain state characteristics on the boundary conditions and the material inhomogeneity are defined using the implicit function theorem in [5, 6]. In the present paper, in the framework of the perturbation method, we determine the stress state in a cylindrical tube with nearly circular boundaries under the action of pressure. Using the implicit function theorem, we examine the existence and uniqueness of the solution of the problem. We show that its solution can be obtained in the case of any analytic shape of the boundary and any number of material physical-mechanical characteristics depending on finitely many small parameters. The results can be generalized to more complicated models of media. The results obtained in this paper are compared with already known results. © Allerton Press, Inc., 2008.