A formulation is presented for the problem of elastoplastic deformation of the system of electrically conductive bodies under the action of pulsed electromagnetic field. The numerical technique for solving the problem is based on the finite element method. Deformation of bodies interacting through contact during the pulsed magnetic treatment of materials is analyzed. The influence of the manufacturing and design parameters of the inductor–workpiece system on its stress-strain state is investigated.

A method is described to calculate creep and damage in structural elements under cyclic loading. Materials exhibiting anisotropic creep-damage behavior are considered. The results of calculating the deformation and fracture of structural elements at a plane stress state are presented.

Для расчета цилиндрических оболочек, подкрепленных продольными ребрами жесткости, предложен полуаналитический метод конечных элементов. С помощью предложенного метода численно исследуются свойства напряженно-деформированного состояния оболочек.

Within framework of the numerical studies of creep resource of a thin spherical cover of a vacuum chamber, we present mathematical formulation and the calculation method for the solution of the initial boundary value problems of the creep theory of thin shells with account of the damage accumulation process of the material. The effect of edge fixing along the normal and tangential lines to the median surface, as well as angular edge fixings, on the cover life in creep are studied under atmospheric pressure creep conditions. The calculation data obtained made it possible to determine the dependence between the cover life in creep and its edge fixing conditions: this effect is strong by the latent fracture time and weak by the allowable deflection values.

On the basis of the continual model of corrosion crack growth proposed earlier and the well-known incremental-type creep theory, we make an attempt to predict the corrosion cracking of structures under the conditions of high-temperature creep. We propose the mathematical statement of the problem taking into account the influence on corrosion cracking of the properties of corrosive media and the redistribution of stresses in time caused by creep. The Bubnov–Galerkin method is applied for the solution of this problem. An example of prediction of the phenomenon of corrosion cracking in the case of creep of a pipe under the action of internal pressure is analyzed.

On the basis of the mechanics of dispersed fracture, we develop a continual model of propagation of corrosion cracks for the evaluation of the service life of structural elements. The results of numerical simulation of the process of crack growth in specimens made of austenitic stainless steel of the 18-8 type performed on the basis of the experimental data available from the literature demonstrate the reliability of the proposed model. We obtain the solutions of the problem of service life of the rectilinear segments of heat-exchange pipes of steam generators of nuclear power plants and apply these solutions to establish a noticeable dependence of the service life on the size of the pipes, pressure in the primary coolant circuit, and chemical compositions of corrosive media.

The analysis of impact deformation of a ceramic container for transporting and evaluating of radioactive material to the strength and tightness under regulatory requirements to projects such facilities. The analysis was completed for estimations of the strength and tightness of the container project. The problem was solved by finite element method in displacement with helping of modern program complex ANSYS. The distribution of maximal stress intensity is described.

The Galerkin–Bubnov method with global approximations is used to find approximate solutions to initial–boundary-value creep problems. It is shown that this approach allows obtaining solutions available in the literature. The features of how the solutions of initial–boundary-value problems for oneand three-dimensional models are found are analyzed. The approximate solutions found by the Galerkin–Bubnov method with global approximations is shown to be invariant to the form of the equations of the initial–boundary-value problem. It is established that solutions of initial–boundary-value creep problems can be classified according to the form of operators in the mathematical problem formulation

The method and results of calculation on durability and rigidity of a tubular wall from carbon-carbon of a composite material (CCCM) used in NSC «KhFTI» for vacuum objects are presented. The wall with rigidly fixed cold edges divides vacuum volume of the chamber and an atmosphere, and getting bending form is deformed in conditions of heats (250 °С) under internal pressure. The analysis of durability is based on a method of finite elements (FEM) and the numerical decision on a personal computer of system of resolving equations FEM. Settlement data for bending form of a wall and the maximal values of intensity of stress. Estimations of durability and rigidity of a tubular wall are given.

The method and results of calculation on durability and rigidity of a tubular wall from carbon-carbon of a composite material (CCCM) used in NSC «KhFTI» for vacuum objects are presented. The wall with rigidly fixed cold edges divides vacuum volume of the chamber and an atmosphere, and getting bending form is deformed in conditions of heats (2500С) under internal pressure. The analysis of durability is based on a method of finite elements (FEM) and the numerical decision on a personal computer of system of resolving equations FEM. Settlement data for bending form of a wall and the maximal values of intensity of stress. Estimations of durability and rigidity of a tubular wall are given.

The equations of nonlinear flexural-flexural-torsional vibrations of rotating beams with asymmetric cross-sections are derived. As the cross-section is asymmetric the centre of gravity and shear centre of a beam cross-section are not assumed to coincide. The nonlinear vibrations are expanded into flexural-torsional vibrational mode series. Using the Galerkin technique, the large-scale system of ordinary differential equations is derived. The non-linear modes are used to study teh free vibrations of a rotating beam, and the backbone curves of the free vibrations and the surfaces of the non-linear modes are also presented.

In article strength-stress state of the boundary wall of the chamber of outlet electronic and proton beams from the accelerator in an atmosphere is considered. The method of the solution is constructed on the basis of finite element method. Influence on strength of a geometrical configuration of a wall, and also a combined effect temperature and load is explored.

The method and outcomes of the strength analysis of a two-layer thick-walled matrix and central core, which one reshapes an internal surface of item, moulds for pressing powdered materials are submitted. The analyses of strength of structural members of a mould by a finite element method (FEM) are executed. The predicted data on the basis of which one it is possible to execute designing elements of moulds to their structural members under strength conditions are submitted.

The problem statement and solution method of creep-damage lifetime prediction for the turbine disk are presented in the paper. The creep-damage calculation results for the disks with constant thickness and variable section are given in the various time moments. The influence analyses of the disk section form on the rupture time have been done.

The paper proposes computer algebra system (CAS) algorithms for computer-assisted derivation of the equations of motion for systems of rigid bodies with holonomic and nonholonomic constraints that are linear with respect to the generalized velocities. The main advantages of using the D’Alembert-Lagrange principle for the CSA-based derivation of the equations of motion for nonholonomic systems of rigid bodies are demonstrated. Among them are universality, algorithmizability, computational efficiency, and simplicity of deriving equations for holonomic and nonholonomic systems in terms of generalized coordinates or pseudo-velocities

The theory behind analytical algorithms for computer-algebra systems is discussed. A computer system is described which is capable of optimizing input data, constructing equations of equilibrium and motion, formulating and solving the basic mechanics problems for a broad class of holonomic systems with elastic and dissipative constraints on the basis of the Lagrange-D'Alembert principle

A method is presented for solving boundary-value elastic problems on the basis of the variational–structural method of R-functions and Reissner's mixed variational principle. A mathematical formulation is given to problems on the deformation of elastic bodies under mixed boundary conditions and bodies interacting with smooth rigid dies. Solutions satisfying all the boundary conditions are proposed. For undetermined components of these solutions, the resolving equations are derived and their properties are studied. A posteriori estimation of numerical solutions is made. As examples, solutions are found to a problem on the stress–strain state of a short cylinder and to a contact problem on a cylinder interacting with a smooth die. A numerical method of solving such problems is analyzed for convergence, and the accuracy of the solutions is estimated.