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We investigate the thermoelastoplastic state of an isotropic homogeneous medium under the action of temperature loads. A mathematical model of plastic flow is considered. We propose a method for constructing an unconditionally stable numerical scheme of the finite-element method for the solution of such problems. The process of propagation of the primary and secondary unloading zones in a body is shown. The time distribution of the intensity of plastic strain at a corner point of the body is presented. Results obtained without regard for the dependence of the yield strength on temperature and with regard for it are investigated.A number of works, a review of which is presented in [1, 6-8, 9, 12], are devoted to the investigation of thermoplastic deformation in bodies of revolution. A series of works [3,5,11,12] is devoted to the use of the finite-element method and Newton-Raphson-Kantorovich methods for the solution of spatial problems on studying the thermoelastoplastic stress-strain state [3,5,11,12]. Methods for computing these problems were developed using an explicit step-by-step integration scheme, which is numerically unstable and requires very small steps. In [10], a systematic approach to the numerical computation of plastic flow processes and construction of a numerical scheme of the Newton iteration process was developed. In [2,13], the implicit numerically stable scheme of intermediate points is used for the solution of problems of force elastoplastic deformation. In the proposed work, this scheme is used to improve the accuracy and efficiency of determination of thermoplastic strains.The aim of this work is also to investigate the character of unloading in an axisymmetric thick-walled body of revolution for different dependences of the limit of elasticity on temperature. For this purpose, the nonstationary problem of heat conduction [4] is solved by the Newton-Kantorovich method. On the basis of obtained temperature fields, the problem of thermoplastic deformation is reduced to a sequence of nonlinear boundaryvalue problems each of which is linearized by the Newton method. The solution of the linearized problem is performed on the basis of schemes of the finite-element method. Finite elements are constructed relative to a some basic surface. This makes it possible to solve easily the problem of identification of spatial finite elements. On the basis of the described method, the problem of investigation of the propagation of plastic and unloading zones in an axisymmetric thick-walled body of revolution is solved. The obtained results indicate the reliability and efficiency of the proposed method. Statement of the Problem and Main RelationsConsider the deformation process of a solid isotropic body located in a volume V bounded by a surface S and subjected to force and thermal loads that do not lead to loss of its stability. Let us use a mathematical

The paper presents results of applying a heterogeneous mathematical model "elastic body-Timoshenko shell" to design shells with massive ribs. Numerical results are obtained for a cylindrical shell with ribs. They are compared with results obtained using the theory of elasticity and the theory of Timoshenko shells with piecewise-constant thickness Keywords: heterogeneous mathematical model elastic body-Timoshenko shell, shells with massive ribs, cylindrical shell with ribs 1. Introduction. An approach for the mathematical modeling of junctions in elastic multistructures, i.e., H-shaped beams, shells with stiffeners, shells clamped in three-dimensional foundations, etc. on the basis of heterogeneous models was suggested in [1,2,[5][6][7][14][15][16]. Within the framework of this approach, the heterogeneous model "elastic body-Timoshenko shell" is considered in [8][9][10][11]. The theoretical background of the heterogeneous model is given in [12]. FEM analysis of structures on the basis of the "elastic body-Timoshenko shell" model is performed in [8,10,11]. The problem of coupling the BEM and the FEM for the analysis of junctions in elastic multistructures on the basis of the heterogeneous mathematical model was considered in [9]. The present paper applies the heterogeneous mathematical model "elastic body-Timoshenko shell" to design shells with massive ring ribs. Within the framework of the heterogeneous model, a ring of a stiffened shell is modeled by the 3D theory of elasticity and a thin-walled part of stiffened structures is modeled by 2D Timoshenko's shell theory.The boundary and variational formulation of the heterogeneous mathematical model are given. To illustrate the approach, the results of numerical analysis of cylindrical shells with stiffeners performed on the basis of the heterogeneous model (model 1) are presented. These results are compared with those obtained on the basis of the 3D theory of elasticity (model 2) and the 2D Timoshenko's shell theory (model 3). Heterogeneous Mathematical Model.Let an elastic body occupy a bounded, connected domain W W

An algorithm drawn from the method of superelements for weighted optimization problems involving compound shell structures and based on strength conditions is described. The conditions are stated in terms of nonlinear mathematical programming methods. The thickness of the shell constitutes the control. Techniques are proposed for reducing the length of the computations, and the effectiveness of these techniques is' illustrated by the solution of an optimization problem for a glass envelope.