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The mixed formulation of the finite element method for the problems of the Toupin–Mindlin gradient theory of elasticity is justified. This theory permits accounting for scale effects stemming from the material microstructure dimensions, particularly in problems with the limitations of classical elasticity. The variational formulation of the boundary problem is examined where strains, stresses, and their gradients enter into the variational equations along with displacements as equivalent arguments. The key feature of these equations is that they involve only the first-order partial derivatives of displacements, in contrast to the differential equations of the classical problem formulation that involve the derivatives of displacements to the fourth order inclusive, and the Lagrange variational equation in displacements, which incorporates their double differentiation. Their solution based on the mixed finite element method greatly simplifies the choice of approximation functions since there is no need to use finite elements that ensure the continuity of the first displacement derivatives at the element boundaries. This formulation based on a separate approximation of displacements, strains, stresses, and their gradients, is applied to solving the boundary problems of elasticity theory, where the strain gradient is included. For the mixed-method variational equations, the condition is formulated so as to ensure the uniqueness of the solution and stability of the mixed approximation for gradient elasticity theory problems. This condition is defined with the orthogonal projection operator that establishes a one-to-one correspondence between the classical and mixed approximation of strain distributions. A well-suited formulation for the practical application of variational equations for displacements and strains is proposed with the weakest requirements for mixed approximation stability. [ABSTRACT FROM AUTHOR]

The application and comparison of different fracture mechanics concepts are discussed to be used in computing stress intensity factors (SIF) from the numerical solutions of model crack theory problems with a mixed scheme of the finite element method. Approximation of displacements rests on piecewise-linear interpolation functions with triangular elements, and strain and stress distributions are approximated by the linear combination that includes the piecewise-linear interpolation and interior bell function. The latter ensures the stability and convergence of the approximate discrete problem solution. The solution results for linear elastic and elastoplastic model plane central mode I crack-strip tension problems under different loading and plane strain state conditions are presented. Elastoplastic calculations were made with an ideal elastoplastic material model. The application of the energy balance and G-integral concepts to the calculation of the specific work of fracture at the stationary crack tip is substantiated. It is shown that on condition of uniform plate partition in the vicinity of the crack tip, the application of those concepts to SIF calculation for one loading stage is consistent with the Irwin plastic zone correction, maintaining this approach in further mesh thickening. Elastoplastic calculations on repeated loading demonstrated that tensile stresses ahead of the crack tip were about the same as on the initial one, but the opening at the crack tip on the former was larger than on the latter, and this effect was most pronounced for the first half of active loading values. Several aspects of SIF calculations on repeated loading are presented. [ABSTRACT FROM AUTHOR]

The influence of the properties of the profile of a radial static electric field E(r) on the evolution of an unstable ion temperature–gradient (ITG) drift wave in a nonuniformly rotating plasma column in a magnetic field is studied. The effect of symmetry on the decrease in the level of turbulent fluctuations, which are associated with the limiting state of the ITG wave during its destruction, is discussed. The level of turbulence is estimated in the framework of approximation of finite amplitudes depending on the electric field structure. It is shown that the maximum decrease in the level of fluctuations occurs with a symmetrical configuration of the radial electric field. [ABSTRACT FROM AUTHOR]

The paper presents the results of a computational assessment of the shape change of the WWER-1000 reactor core baffle using modern approaches to modeling the processes of radiation swelling, radiation creep, and subcritical damage of irradiated metal by the mechanism of ductile fracture. To simulate radiation effects, mathematical models are used that consider the influence of the stress state and accumulated irreversible deformation on the swelling and creep of austenitic steels exposed to neutron irradiation and elevated temperature. The increased volume concentration of ductile fracture pores in the irradiated metal is considered using the modified Huang equation and the proposed equation derived from Kachanov's solution for a spherical cavity in an unbounded elastic-plastic medium. The determination of the stress-strain state of the WWER-1000 reactor cavity and the inner vessel shaft is based on solving a nonlinear boundary value problem of thermomechanics, which allows describing the kinetics of the coupled processes of elastic-plastic deformation, radiation swelling, radiation creep, contact interaction, and subcritical damage of irradiated metal depending on the accumulated dose of neutron irradiation. The computational analysis is based on a mixed finite element method scheme that provides a continuous approximation for both displacements and stresses and strains, which makes it possible to determine the shape change of the shielding with a high degree of accuracy. The calculation was performed in a two-dimensional formulation for the cross-section of the shielding with the maximum height of the damaging dose and irradiation temperature under the condition of generalized plane deformation. The calculation results were obtained using the median parameters of the temperature-dose dependence of free swelling of austenitic steel 08Kh18N10T. Based on the calculated data, the influence of radiation effects and metal damage according to the ductile fracture models on determining the shape change of the WWER-1000 reactor baffle under conditions of long-term operation was analyzed. [ABSTRACT FROM AUTHOR]

The validity conditions for nonlinear problems of inelastic deformation mechanics, which consider the growth of the volume of nucleated pores in the material exposed to neutron irradiation, are investigated. The porosity analysis of the irradiated material is based on the Rice–Tracey–Huang (RTH) equations and Kachanov's solution for a spherical cavity. The generalized equation combines the classical RTH equations and includes the modified Huang's equation, in which an additional continuous function greater than zero is introduced, which depends on the stiffness of the stress state and has a nonnegative derivative. This modification of the classical Huang's equation improves the properties of the governing equations of the irradiated porous material, which contributes to the weakening of the limitations of the initial data associated with the stiffness of the stress state. The RTH equations are considered to model the growth of the volume concentration of pores in a rigid-plastic material. For the analysis of porosity in an ideal elastic-plastic material, it is proposed to use the solution obtained by Kachanov for a spherical cavity. Applying Kachanov's solution to the simulation of the pore concentration growth allows one to consider the radiation creep in the elastic region of the deformation diagram of the irradiated material in contrast to the classical RTH equations, in which the elastic region is not considered. Modern models of radiation swelling and radiation creep are used, considering the damaging dose, irradiation temperature, and the effect of stress state and accumulated irreversible deformation on the processes of swelling and creep of irradiated material. To analyze the behavior of irradiated porous material, radiation creep equations are used, in which irreversible deformations include instantaneous plastic, radiation swelling, radiation creep, and structural volume deformations that consider the concentration of pores in the material. The analysis of the properties of the governing equations allowed us to establish the conditions under which the dissipation power and the power developed by the additional stresses on the additional deformations caused by them do not decrease during the loading of the irradiated porous material. Based on the obtained energy inequalities that generalize Drucker's postulate, the conditions are established that ensure the correctness of the governing equations of radiation creep, which consider the growth of the pore volume according to the generalized RTH equation and Kachanov's solution for a spherical cavity. According to the results of the analysis, irradiation contributes to the growth of the pore volume in the material, and the limitation of the maximum values of the stiffness parameter of the stress state, taking into account the obtained a priori estimates, contributes to the stability and convergence of the computational processes for solving the boundary value problem. [ABSTRACT FROM AUTHOR]

Applying the Rice–Tracey–Huang models and Kachanov's equilibrium solution of a spherical cavity to the analysis of the ductile fracture pore concentration growth in a material subjected to neutron irradiation is considered. The generalized equation combines the classical Rice–Tracey–Huang equations and includes the modified Huang equation, in which an additional continuous function greater than zero is introduced, which depends on the stiffness of the stress state and has a nonnegative derivative. With this modification of the classical Huang equation, the properties of the governing equations for the analysis of the porosity of irradiated material are improved, which contributes to the weakening of the limitations of the initial data associated with the stiffness of the stress state. The generalized Rice–Tracey–Huang equation is considered to model the process of pore concentration growth in a rigid-plastic material. The equation derived from Kachanov's solution for a spherical cavity is proposed to analyze the porosity in an elastic-plastic material with radiation creep. The application of Kachanov's solution to model the growth of pore concentration allows us to consider the radiation creep in the elastic region of the strain diagram of the irradiated material, in contrast to the classical Rice–Tracey–Huang equations, in which the elastic region is not considered. Taking into account this factor affects the results of the analysis of the behavior of porous material, since with increasing radiation dose, radiation hardening occurs, which leads to a decrease in the plasticity of the material, and therefore, under prolonged neutron irradiation, the role of elastic strain and radiation creep in the elastic region of the strain diagram increases. Based on the obtained relations, which follow from Kachanov's solution, the equation to describe the growth of the volume concentration of pores in the material depending on the increments of instant plasticity and radiation creep strains is formulated. Modern models of radiation swelling and radiation creep are used, which take into account the damaging dose, irradiation temperature, the influence of the stress state and the accumulated irreversible strain on the processes of swelling and creep of the irradiated material. [ABSTRACT FROM AUTHOR]

Kinetic approach to simulation of ion velocity (and energy) distribution function in the process of Z-pinch neck implosion, along with the energy spectrum of ions leaving the neck, are analyzed. A combination of acceleration in a magnetic field growing with time, Coulomb collisions, and losses determine the formation of ion spectrum within the framework of the kinetic Fokker–Planck equation. [ABSTRACT FROM AUTHOR]

The validity conditions of nonlinear problems of mechanics of elastic-plastic deformation, which take into account the evolution of the growth of the volume of nucleated pores in the material based on the generalized Rice–Tracey–Huang equation, are investigated. This equation combines the classical Rice–Tracey–Huang equations, in which an additional continuous function greater than zero is introduced, which depends on the stiffness of the stress state and has a nonnegative derivative. With this modification of the classical Huang equation, the properties of the governing equations for the analysis of the porosity of irradiated material are improved, which contributes to the weakening of the restrictions on the initial data associated with the stiffness of the stress state. Using the generalized Rice–Tracey–Huang equation, the governing equations of material behavior are formulated to describe the nonisothermal processes of elastic-plastic deformation, taking into account the increase in the concentration of ductile fracture pores in the material. The loading process is divided into separate calculation stages, and for each of them, the plastic flow equation and the generalized Rice–Tracey–Huang equation are integrated for the loading stage. Due to integration, the governing equations for the full stress and strain components are obtained, which allows us to describe the processes of active loading, unloading, and reloading. Irreversible deformations in these equations include accumulated plastic deformations and structural volumetric deformations that take into account the concentration of pores in the material. The conditions are formulated under which the dissipation power and the power developed by the additional stresses on the additional deformations caused by them do not decrease in the process of loading the porous material. On the basis of the obtained energy inequalities, which generalize the postulate of Drucker's strengthening in relation to the porous material, the conditions are established that ensure the correctness of the formulated plasticity equations, which take into account the growth of pore concentration in the material on the basis of the generalized Rice–Tracey–Huang equation. [ABSTRACT FROM AUTHOR]

Validity conditions in nonlinear problems of elastic-plastic deformation mechanics, taking into account the process of nucleated pore volume growth in the material via Huang's equation, are investigated. The constitutive equations of material behavior are formulated, making it possible to describe nonisothermal processes of elastic-plastic deformation, considering the growth of viscous fracture pore concentration. The loading process is subdivided into separate computational steps; for each, the plastic flow equation and Huang's equation are integrated over the loading step. The constitutive equations for the total stress and strain components are derived through integration to describe the processes of active loading, unloading, and reloading. The irreversible strains in these equations include accumulated plastic strains and structural bulk strains, which account for the concentration of pores in the material via Huang's equation. The performed analysis of the properties of the constitutive equations made it possible to formulate conditions under which the dissipation power and the power developed by the additional stresses on the additional deformations caused by them do not decrease during the porous material loading. Based on the obtained energy inequalities generalizing Drucker's postulate of hardening for porous materials, this study established the conditions ensuring the validity of the formulated equations of plasticity, which take into account the pore volume growth via Huang's equation. [ABSTRACT FROM AUTHOR]

The conditions that ensure the validity of nonlinear problems of elastic-plastic deformation mechanics, taking into account the growth of nucleated pore volume in the material via the Reiss–Tracey model, are investigated. Using this model, the determinants of material behavior are formulated, making it possible to describe nonisothermal processes of elastic-plastic deformation considering the increased concentration of viscous fracture pores. The loading process is broken down into separate computational stages, within which the plastic flow equation and pore concentration growth equations via the specified model are integrated over the loading stage. Through integration, the constitutive equations for the full stress and strain components are derived, allowing one to describe the active loading, unloading, and re-loading processes. The irreversible strains in these equations include accumulated plastic strains and structural bulk strains, which account for the pore concentration in the material via the Reiss–Tracey model. The solution of practical problems via the formulated equations promotes the persistence of computational processes, making it possible to use extended loading stages in calculations. At the same time, the analysis of properties of the obtained determinative equations is simplified in comparison with the equations of plasticity in finite increments. Conditions are formulated, in which the dissipation power and the power developed by additional stresses and stress-induced on additional strains do not drop during the loading of porous materials. On the basis of the obtained energy inequalities, which generalize Drucker's postulate with respect to the porous material, conditions are established that ensure the correctness of the formulated plasticity equations, which take into account the pore volume growth via the Reiss–Tracey model. [ABSTRACT FROM AUTHOR]

Methods of elastic solutions and interchangeable elasticity parameters for solving nonlinear boundary value problems of mechanics are considered, making it possible to describe non-isothermal processes of inelastic deformation with account of radiation swelling deformations and radiation creep of irradiated material. For modeling the processes of radiation swelling and radiation creep, modern approaches are used, which take into account the damaging dose, irradiation temperature, and the effect of the stress state on the material swelling and creep. Generalized and modified methods of elastic solutions and interchangeable elasticity parameters are investigated and applied to the solution of nonlinear boundary value problems of radiation creep. It is taken into account that the construction and investigation of the properties of iterative methods for solving the equations of radiation creep is complicated due to the fact that, in order to prove the convergence and estimate the accuracy of successive approximations, it is necessary to consider a rather rigid restriction due to the asymmetry of the operator, which relates the errors of the iteration process for two successive approximations. Under such conditions, traditional approaches to investigating the convergence of elastic solution methods and interchangeable elasticity parameters taking into account the properties of self-adjoint operators will prove to be unacceptable. In addition, the standard equation symmetrization procedure for successive approximations leads to excessively conservative estimates of the convergence of iterative processes, and therefore the optimization of their convergence rate has a rather approximate character. This problem is decoupled through a thorough study of the properties of the constitutive equations of radiation creep and the application of a special norm to the analysis of the convergence of successive approximations, which made it possible to construct modified iterative processes and prove the local convergence of elastic solution methods and interchangeable elasticity parameters for the general case of radiation creep equations. The properties of nonlinear operators of generalized and modified processes are studied in detail. On this basis, a priori estimates of the convergence rate of iterative methods for different models of compressed swelling are obtained. Using the obtained a priori estimates, optimization approaches for modified methods of elastic solutions and interchangeable elasticity parameters for solving nonlinear problems of radiation creep have been formulated. [ABSTRACT FROM AUTHOR]

The paper presents the results of the application of the refined calculation guidelines to the analysis of the stress-strain state and fracture resistance of the equipment elements of the NPP primary circuit system with WWER reactor, in particular, the cylindrical part and the zone of the reactor pressure vessel inlet nozzle, coolant collector welded joint in a steam generator, baffle, and reactor internals' shaft under the operating and emergency modes of thermomechanical loading. The calculation methodology is based on the use of the modern models and methods of solution to the nonlinear boundary tasks of non-isothermal thermal viscoplasticity and tasks of fracture mechanics using the refined mixed schemes of the finite element method with increased accuracy. They allow one to obtain reliable solutions to the tasks considering the deformation history of thermomechanical loading, modern concepts of fracture mechanics and approaches to the modeling of brittle-viscous fracture defects, irradiation swelling and creep of metal, as well as as the structural elements, under the conditions of elevated temperature, intensive neutron irradiation and nonstationary modes of thermomechanical loading. The authors obtained and analyzed the calculation results for the cylindrical part and zone of the inlet nozzle of the WWER-1000 reactor pressure vessel, coolant collector welded joint in a steam generator, baffle, and reactor internals' shaft using the proposed guidelines. The results imply the possibilities of the proposed recommendations and make it possible to analyze some general tendencies and features of the application of the refined calculation models to justify the strength and life extension of the NPP structural elements under investigation. [ABSTRACT FROM AUTHOR]

The peculiarities of the calculated assessment of the stress-strain state and the shape change of the WWER-1000 reactor core baffle under the design and long-term operation conditions are considered. The computational analysis results of the baffle and internals using modern approaches to modeling the processes of radiation swelling and radiation creep of austenitic steels, which are under the effect of neutron irradiation and elevated temperature, are presented. Basic principles of stress-strain calculations of baffle and shaft concerning conditions of their contact interaction are formulated. Calculations are performed in the two-dimensional formulation for a cross section of the baffle with the maximum over-height damaging dose and irradiation temperature under the condition of generalized plane deformation. The data concerning the change in shape of the baffle are obtained from the solution of a coupled contact problem of heat transfer and radiation creep in dependence of the accumulated damaging radiation dose. Calculations of the temperature field and the stress-strain state are performed, taking into account temperature redistribution through the violation of design conditions of coolant flow in the area of the baffle-shaft contact. It is found that taking into account radiation creep contributes to a decrease in the stress level but increases swelling and displacement, which adds conservatism to the predicted estimate of the change in shape of the baffle in comparison with data without taking into account creep. Results of calculations are received using median and conservative parameters of the temperature dependence of free swelling of 08Kh18N10T austenite steel. Obtained results allow one to analyze some general tendencies and peculiarities of applying modern models of radiation swelling and radiation creep to determine stress-deformed mill and change in shape of baffle, taking into account contact interaction with shaft depending on accumulated irradiation dose. [ABSTRACT FROM AUTHOR]

The paper presents the results of an analysis of the correctness of constitutive equations of irradiation creep, which describe non-isothermal processes of inelastic deformation, taking into account the irradiation swelling and irradiation creep of material under the conditions of neutron irradiation, high temperatures, and damaging dose. Current models of irradiation swelling and irradiation creep, which take into account the damaging dose, irradiation temperature, and the effect of stress state and accumulated irreversible strain on the processes of swelling and creep of material, are considered. The conditions under which dissipation power and the power developed by additional stresses on additional deformations do not decrease during loading under neutron irradiation conditions have been studied. On the basis of the obtained energy inequalities, which generalize Drucker's postulate for the irradiated material, the conditions that ensure the correctness of the formulated creep equations have been determined. The results of an analysis of the correctness conditions for irradiation creep equations showed that taking into account accumulated irreversible strain in the confined swelling model contributes to the relaxation of restrictions on the possible swelling of the material and initial data, which ensure the correctness of the constitutive equations of irradiation creep. [ABSTRACT FROM AUTHOR]

The results of an analysis of the correctness of constitutive equations of irradiation creep which describe non-isothermal processes of inelastic deformation taking into account radiation swelling and radiation creep of material under the conditions of neutron irradiation, high temperatures and damaging dose, are presented. Modern models of radiation swelling and radiation creep, which take into account the damaging dose, irradiation temperature, and the influence of stress state on the processes of swelling and creep of irradiated material are considered. Using these models, constructive equations are formulated, which allow the processes of inelastic deformation to be described taking into account the radiation swelling and radiation creep strains of the material. The conditions under which the equations of radiation creep are consistent with the principle of irreversibility of inelastic deformation power increment are investigated. Based on the results of the analysis of the properties of constitutive equations, the necessary and sufficient conditions under which the power of dissipation and the power which is developed by additional stresses on additional deformations do not decrease during the loading of the irradiated material have been determined. On the basis of the obtained energy inequalities, which generalize Drucker's postulate concerning the irradiated material, and the general results of the analysis of the properties of nonlinear operators, the conditions that ensure the correctness of the formulated creep equations have been determined. It was found that taking into account radiation creep strains contributes to the relaxation of restrictions on the initial data, which ensure the correctness of the constiyive equations. According to the a priori estimates obtained, the duration of loading stages is determined not only by the data on the convergence and accuracy of the solution of creep equations, which describe the process of deformation of irradiated material, but also by the conditions under which they can be solved. We present a priori estimates of the maximum permissible value of the damaging dose for austenitic 08Kh18N10T steel at different irradiation temperatures. In strength calculations, such estimates are useful at the stage of problem statement to analyze the adequacy of initial data. [ABSTRACT FROM AUTHOR]

An alternative approach is proposed and applied to solve boundary value problems within the strain gradient elasticity theory. A mixed variation formulation of the finite element method (FEM) based on the concept of the Galerkin method is used. To construct finite-dimensional subspaces separate approximations of displacements, deformations, stresses, and their gradients are implemented by choosing the different sets of piecewise polynomial basis functions, interrelated by the stability condition of the mixed FEM approximation. This significantly simplifies the pre-requirement for approximating functions to belong to class C1 and allows one to use the simplest triangular finite elements with a linear approximation of displacements under uniform or near-uniform triangulation conditions. Global unknowns in a discrete problem are nodal displacements, while the strains and stresses and their gradients are treated as local unknowns. The conditions of existence, uniqueness, and continuous dependence of the solution on the problem’s initial data are formulated for discrete equations of mixed FEM. These are solved by a modified iteration procedure, where the global stiffness matrix for classical elasticity problems is treated as a preconditioning matrix with fictitious elastic moduli. This avoids the need to form a global stiffness matrix for the problem of strain gradient elasticity since it is enough to calculate only the residual vector in the current approximation. A set of modeling plane crack problems is solved. The obtained solutions agree with the results available in the relevant literature. Good convergence is achieved by refining the mesh for all scale parameters. All three problems under study exhibit specific qualitative features characterizing strain gradient solutions namely crack stiffness increase with length scale parameter and cusp-like closure effect. [ABSTRACT FROM AUTHOR]

Modern models of irradiation swelling and irradiation creep are considered, in which the damaging dose, irradiation temperature, and influence of stress state on swelling and creep of irradiated material are taken into account. Using these models, constitutive equations of material behavior are formulated, which makes it possible to describe the non-isothermal processes of inelastic strain, taking into account irradiation swelling and irradiation creep strains. The loading process is broken down into separate computational stages, and for each of them the equations of plastic flow and irradiation creep are integrated within the loading stage. Through integration, constitutive equations for the full stress and strain components are derived, which allows the processes of active loading, unloading, and reloading to be described. The irreversible strains in these equations include accumulated plastic strains, irradiation swelling, and irradiation creep strains. The derived equations are treated as constitutive equations for irradiation creep, in which creep strain is defined as strain that includes instantaneous plastic strain and creep strain. Elastic-plastic strain curves that take into account the accumulated damaging dose and irradiation temperature are transformed into a functional dependence that describes the strain of irradiated material depending on the intensity of irradiation creep strain growth during the loading stage. The application of the formulated equations to the solution of practical problems contributes to the persistence of computational processes that makes it possible to use extended loading stages for calculations. At the same time, the study of the properties of the obtained constitutive equations is considerably simplified in comparison with the analysis of plasticity and creep equations in finite increments. Initial prerequisites for the formulation of constitutive equations of irradiation creep based on the full model of swelling, which takes into account the accumulated irreversible strain, are outlined. [ABSTRACT FROM AUTHOR]

Sources of fusion neutrons with an energy of about 10 MeV can be a driver in hybrid fusion–fission reactor. They can be used for the disposal of radioactive wastes involved in the closure of the nuclear fuel cycle. Currently, the projects of such systems rely on the use of the D–T reaction and the production of tritium in the blanket. In terms of availability of fuel components, the D–D reaction is attractive. The energy of the neutrons produced in the D–D reaction directly is not high enough, but fast neutrons of 14 MeV are produced by the burning of the tritium produced in the D–D reactions. The possibilities of using a D–D plasma confined in a magnetic trap to generate fast neutrons are analyzed. To increase the reaction rate, a powerful heating by injection of neutral deuterium atoms is considered. Under such conditions, a significant population of fast deuterons is maintained. The requirements on the parameters of the plasma and the magnetic trap are discussed to present the possible concept of a fusion neutron source based on deuterium plasma. [ABSTRACT FROM AUTHOR]

The paper presents the results of the calculated estimate of the critical pressure level in the oxidant tank of the launch vehicle using generalized diagrams of elastic-plastic deformation of the aluminum alloy AMg6. These diagrams consider the anisotropy of the physical and mechanical properties of the material. The calculation of the stress-strain state is performed using the simplified calculation scheme for the specified structural element of the tank depending on the internal pressure in the axisymmetric statement considering the elastic-plastic deformations. The calculation analysis is based on the mixed scheme of the finite element method, which provides the continuous approximation of displacements and stresses. It allows one to determine the stress-strain state of the tank element with high accuracy. It is implied that the maximum values of stresses and strains occur in the area of the fillet region connecting the ring with the cylindrical shell of the tank. Complying with the obtained data, the calculation of the stress-strain state of the tank element using generalized deformation diagrams, taking into account the anisotropy of physical and mechanical properties and the nature of the load of aluminum alloy AMg6, leads to a more conservative estimate of the critical pressure level as compared with the standard calculation based on the uniaxial tensile diagram. [ABSTRACT FROM AUTHOR]

Special features of computational assessment of dimensional change of WWER-1000 reactor core baffle during the reactor operation are discussed. The paper gives results of computational analysis of a change in shape of core baffle, which was performed by applying up-to-date approaches of modeling the irradiation-induced swelling of constrained austenitic steels under the action of neutron irradiation and elevated temperatures. The results have been obtained by using median and conservative values of parameters of the temperature and dose dependence of free swelling of austenitic steel Kh18N10T. The authors have set out the fundamental principles of elastic-plastic stress-strain analysis of the reactor core baffle and core barrel, taking into account the irradiationinduced swelling deformation and contact interaction conditions. The finite-element analysis is based on a FEM mixed scheme that ensures a continuous approximation both for displacements as well as stresses and strains, thus providing a high-accuracy determination of the stress-strain state. The calculations were carried out in the two-dimensional definition for the baffle cross-section with the maximum damaging dose and irradiation temperature in the baffle height, assuming a generalized plane-strain deformation. The calculated results are given for the reactor full-power operation and scheduled shutdown for re-fueling at the end of the charge life. According to the calculation data, disregarding the irradiation-induced swelling deformation leads to an incorrect assessment of the change in shape of the core baffle during its operation, while the use of the accepted free swelling model gives too conservative results on the shape change, even within the designed lifetime. The influence of the mean normal stress on the irradiation-induced swelling of metal makes the principal contribution to the change in shape of the core baffle. During the reactor operation beyond the designed lifetime there occurs a local contact between the core baffle and the core barrel in the zone of the largest-diameter circular opening of the longitudinal cooling channel and the port channel for coolant flow between the baffle and the barrel. The paper gives results of the analysis of the change in shape of the baffle in modeling of the contact conditions taking into consideration the temperature re-distribution due to deviation from the design coolant passage conditions in the zone where the baffle is in contact with the barrel. In the case of using the median dependence of the free swelling, no loss of the nominal gap between the core baffle and the core barrel is observed within the designed lifetime. The computational assessment using the conservative parameters of the irradiation-induced swelling leads to a distinct decrease of the gap between the core baffle and the core barrel and a local contact between them at the end of the designed lifetime. The residual gap between the spacer grids of edge fuel assemblies and the baffle faces is ensured in the case of the median and conservative dependence of the irradiation-induced swelling. [ABSTRACT FROM AUTHOR]

The paper provides results of the study of correctness of the mathematical model that includes the influence of stresses on irradiation-induced swelling of metal in the problems of elastic-plastic deformation mechanics. The present-day approaches to modeling irradiation-induced swelling, which take into account a damaging dose, irradiation temperature, and the effect of the stress state on the swelling deformation, are discussed. The constitutive equations that describe the elasticplastic deformation processes allowing for the influence of a stress mode on the irradiation-induced swelling in metal are put forward. Analysis of these equations has made it possible to find the conditions that ensure correctness of the plasticity equations considered and to make a lower-bound estimate of the maximum permissible value of free swelling and irradiation dose. A priori estimates of the maximum permissible value of free swelling and damaging dose are given for 08Kh18N10T steel under various irradiation temperatures. In the practice of strength design such estimates are needed at the stage of problem formulation in order to analyze adequacy of input data, for they enable one to assess a prior the possibility of solving the problem for a given temperature and irradiation dose. The boundary-value problem that describes non-isothermal processes of elasticplastic deformation including swelling strains has been defined in the form of a nonlinear operator equation. Based on the findings regarding the correctness of the constitutive equations, we have established the existence and uniqueness of the generalized solution and its continuous dependence on applied loads, thermal strains and swelling strains. The convergence of the method of elasticity solutions and the method of variable elasticity parameters has been studied as applied to a thermoplasticity problem including irradiation-induced swelling strains. [ABSTRACT FROM AUTHOR]

Methods for calculating the heat and neutron transport in structural elements of nuclear and fusion power devices are considered in the framework of statistical modeling and physical neutron kinetics based on the cross sections of interaction of neutrons with matter. Statistical modeling makes it possible to establish the nature of the neutron transport and energy in matter. In the extreme cases, within the framework of this approach, the diffusion and ballistic regimes are realized. In the calculation of heat transfer, the heat release associated with gamma quanta is also taken into account. The possibilities of these methods for estimation of the joint thermal effects of these factors are shown. [ABSTRACT FROM AUTHOR]

The main methodological principles and the procedure of the refined calculation of the stress-strain state and fracture strength of the branch pipe zone of the reactor vessel under thermal shock have been formulated. A mixed scheme of the finite element method was taken as a basis of finite element analysis; it ensures continuous approximation both for displacements and for stresses and strains, which allows the fracture mechanics parameters to be determined with a high degree of accuracy. The paper presents the results of an elastic-plastic analysis of the fracture strength of the inlet branch pipe zone with an underpad crack in the simulation of the typical emergency core cooling conditions of a WWER-1000 reactor. The location and orientation of the postulated crack are substantiated to obtain the most conservative estimate of the fracture strength of the branch pipe. The calculations were performed with including the postulated crack in the finite element model of a fragment of the inlet branch pipe zone using the procedure of successive mesh thickening in the crack region. To determine the allowable critical temperature of brittleness of the branch pipe base metal, the tangent point, thermal crimping and descending branch approaches were used. According to the obtained results, the elastoplastic deformation of the metal and stress history affect the calculated estimate of the fracture strength of the branch pipe zone of the reactor vessel. It has been shown that the traditional linear elastic calculation, which is used to evaluate the fracture strength of the branch pipe, does not have sufficient degree of conservatism, which results in an exaggerated estimate of its strength. [ABSTRACT FROM AUTHOR]

Correction to: Validity analysis of elastic-plastic deformation mechanics problems considering the growth of pores in the material via the Rice-Tracey-Huang models. Chirkov should read: "Validity analysis of elastic-plastic deformation mechanics problems considering the growth of pores in the material via the Rice-Tracey-Huang models. In Strength of Materials, 54, No. 5, 767-775 (2022), the title of the paper "Validity analysis of elastic-plastic deformation mechanics problems considering the growth of pores in the material via the Reiss-Tracey-Huang models. [Extracted from the article]

Electromagnetic drift instabilities are studied in the conditions of a field reversed configuration (FRC). Dispersion equation is based on the set of Vlasov–Maxwell equations taking into account nonadiabatic responses both of ions and electrons. Considered drift instabilities are caused by density and temperature gradients. It is assumed that magnetic field of the FRC is purely poloidal. Two kinds of magnetic field nonuniformity are considered: (i) perpendicular gradient due to high β values (β is the plasma pressure/magnetic pressure) and (ii) curvature of magnetic lines. There is low frequency drift instability existing for high-β regimes. Modes of such instability can propagate transversally to the unperturbed magnetic field lines. [ABSTRACT FROM AUTHOR]

The problem of slow dynamic contact interaction of a system of punches remote from each other with an elastic half-space surface in the absence of friction is studied under the assumptions that the diameters of the contact areas are smaller than the minimum distance between the punches and the time required for the shear wave to travel the distance equal to the punch diameter is comparable to the time scale of the process. A first-order asymptotic model is constructed. As an example, the case of steady-state vibrations of a system of two punches is considered. [ABSTRACT FROM AUTHOR]

We consider mixed variational formulations and the application of the mixed approximations of the finite element method to the solution of problems on natural vibrations of elastic bodies. To solve the generalized spectral problem, three forms of the mixed variational formulations are proposed. The correctness and stability of mixed variational formulations for displacements, strains and stresses are investigated. Matrix equations of the mixed method are given whose solution is performed using the modified algorithm of the steepest descent method. The results of calculations for natural frequencies of free vibrations of a straight and a circular beam are presented that are obtained in the solution of the problem in a two-dimensional formulation based on the classical and mixed finite-element method approaches. [ABSTRACT FROM AUTHOR]

A mixed projection-mesh scheme for solving a boundary-value problem of thermal plasticity is formulated in a quasi-static statement when the process of non-isothermal elastoplastic deformation of a body is a sequence of equilibrium states. In this case, the stress-strain state depends on the loading history, and the process of inelastic deformation is to be observed over the whole time interval under study. The correctness and convergence of the mixed approximations for stresses, strains and displacements are investigated as applied to the solution of nonlinear boundary-value problems that describe the non-isothermal processes of active loading taking into account the initial strains dependent on the history of deformation and heating. The properties of the projecting operators are studied in detail, and on this basis, the condition that ensures the existence, uniqueness and stability of solution is formulated. The results of the analysis of special formulas of the interpolation-type numerical integration are presented, the use of which considerably simplifies the computation procedure for solving equations of the mixed method. The convergence and accuracy estimations are based on the results of the theory of the generalized boundary-value problems and methods of the functional analysis. According to the estimations obtained, the accuracy of solution of a finite-dimensional problem at the initial stages of loading should be sufficient to avoid the effect of increase of the first coefficients in the expansion of the total error on the accuracy of solution of the elastoplastic problem at the subsequent stages of loading. [ABSTRACT FROM AUTHOR]

The influence of weak electrostatic perturbations on the trajectories of circulating particles in a tokamak magnetic field is analyzed. The parameters of the trajectories calculated in the drift approximation allow one to determine the spatial scale of diffusion. The resonant interaction between particles and waves is considered. The possibility of the emergence of collisionless diffusion in the strong turbulence regime is analyzed. © 2004 MAIK “Nauka / Interperiodica”. [ABSTRACT FROM AUTHOR]

To solve a problem on bending of a plate, a special three-node triangular finite element has been constructed on the basis of Zienkiewicz's triangle. A mixed approximation is used for the plate deflection and turning angles. The numerical solution is shown to converge to an exact one with a decrease in the triangle dimensions. The results of the numerical analysis of the convergence and accuracy of the solution of a number of test problems are presented. [ABSTRACT FROM AUTHOR]

Results of a numerical analysis of the interaction between plasma particles and the wave packets of electrostatic fluctuations are presented. The influence of the dynamic parameters of the particles and packets on the particle scattering is studied. It is shown that, in general, the electron scattering by such a kind of fluctuations differs qualitatively from the ion scattering. Estimates of the parameters of collisionless diffusion are proposed. [ABSTRACT FROM AUTHOR]

Polyhedrons in which every integral point belonging to them is a vertex are studied. [ABSTRACT FROM AUTHOR]

For the solution of two-dimensional boundary-value problems of the elasticity theory, a triangular finite element, ensuring stability and convergence of mixed approximation, is proposed. The system of resolving equations of the mixed method is derived with account of strict satisfaction of static boundary conditions at the surface. To solve matrix equations of the mixed method, various algorithms of the conjugate-gradient method with the pre-conditional matrix have been considered. Numerical data on convergence and accuracy of the solution for a number of test problems of the elasticity theory and fracture mechanics are given. The results obtained by the conventional and mixed finite-element method approaches are compared. [ABSTRACT FROM AUTHOR]

A mixed projection-mesh scheme for solving the boundary-value problems of the elasticity theory has been formulated. Correctness and convergence of the mixed approximations for strains and displacements are studied. Application of the numerical integration has been analyzed, and the obtained results are given. The theory of generalized functions and the functional analysis methods have been used for the convergence and accuracy estimates. Iteration algorithms for solving the discrete problems have been proposed. [ABSTRACT FROM AUTHOR]

A study is made of the dynamics of particles interacting with electromagnetic field fluctuations in a plasma in the presence of a magnetic field. Possible mechanisms for the onset of anomalous transport and its suppression by applying a radial electrostatic field are analyzed. Estimates of the diffusion coefficient are proposed based on the calculations of particle trajectories. © 2002 MAIK “Nauka / Interperiodica”. [ABSTRACT FROM AUTHOR]

The possibility of implementing a highly efficient low-radioactive thermonuclear fuel cycle using deuterium as the raw material (primary fuel) is justified. The energy production is ensured mostly by the D-³He reaction, with ³He obtained in the course of the reactor operation. It is shown that, under certain conditions, neutrons account for only ∼5% of the total thermonuclear output power and the neutron power flux to the first wall is q[sub n] < 0.5 MW/m². [ABSTRACT FROM AUTHOR]

Kinetics of the D-T, D-³He, and D-D (catalyzed) fuel cycles in an ambipolar reactor were analyzed. The plasma characteristics and the plasma confinement system parameters necessary for the effective energy production in the ambipolar reactor operated with these fuels were calculated. [ABSTRACT FROM AUTHOR]

The paper describes the effect of the addition of alumina nanofibers on the mechanical properties of the epoxy resin. Alumina nanofibers functionalized with epoxypropyl functional groups are used in this work. The dependence of the mechanical characteristics on the amount of the additive, as well as the features of its distribution in the material, is investigated. In the work, nanocomposites were obtained, which are epoxy resin with aluminum oxide nanofibers. The mechanical properties of the samples were studied by bending tests and differential mechanical analysis (DMA). It has been shown that the addition of alumina nanofibers leads to an increase in ultimate flexural strength. The maximum of this increase is near the percolation threshold of alumina nanofibers in epoxy resin. With the addition of 0.2% alumina nanofibers, the ultimate flexural strength increases from 41 to 71 MPa. It is shown that after exceeding the percolation threshold of nanofibers, the ultimate strength decreases. In this case, the elastic modulus increases from 0.643 to 0.862 GPa. DMA is shown that the glass transition temperature decreases with increasing amount of the additive. This indicates a decrease in the molecular weight of the polymer. By implication, this suggests that the hardener connects the epoxypropyl functional groups on the nanofibers and the epoxy groups in the resin, and as a result of this process, the nanofibers become natural polymer chain length limiters. The data obtained from mechanical testing and differential mechanical analysis can be used to strengthen epoxy resins in polymer composite materials and molding compositions. [ABSTRACT FROM AUTHOR]

The article considers the current problem of helium-3 supply constraints for industry and science. The projected 3He shortage is approximately 55000 liters (at 1 atm and 20°С) in the world production market. Tritium is the only industrial 3He source. Alternative sources of 3He are discussed in this paper. Between 25 and 50% of the 3Не shortage could be addressed with natural gas extraction. To obtain high purity 3He gas, low-temperature methods of separation (superfluid filtration, rectification and adsorption) are promising. The 3He lunar mining operation could cover the entire worldwide shortage, but this is not a perspective over the next fifteen-twenty years. The controlled thermonuclear fusion is both an energy source and a new 3He production alternative source. Between 10 and 25% of the 3He shortage could be covered with this technology. The high molar concentration of 3He in the obtained mixtures will make it possible to extract the rare isotope by the method of low-temperature adsorption with subsequent enrichment by the method of low-temperature rectification. [ABSTRACT FROM AUTHOR]

The content and profile distribution of 137Cs in iron-illuvial dwarf and shallow-podzolic podzols (Albic Podzols) under bilberry-lichen and green-lichen-bilberry pine forests in the located near the Kola Nuclear Power Plant have been analyzed. The pollution density (reserve) of 137Cs in the root-inhabited layer (0–30 cm) in the studied soils was significantly lower than the established control level of 37 000 Bq/m2 and amounts to 530–2459 Bq/m2. A significant part of 137Cs (60 to 90%) was concentrated in mineral horizons. It has been shown that the pollution density of 137Cs in the observation zone of a nuclear power plant was mainly due to global fallout. The greatest influence on 137Cs accumulation in the studied soils was exerted by the organic matter reserve. [ABSTRACT FROM AUTHOR]

Results of numerical analysis of stress intensity factors KI for semielliptical surface cracks in the WWER-1000 reactor pressure vessel by emergency cooling simulation with known engineering procedures, the equivalent spatial integration and direct methods are presented. Engineering procedures employ the results of numerical solution of axially symmetric boundary value problems of thermoelasticity based on the mixed mesh-projection scheme of the finite element method implemented in the RELAX software. The three-dimensional KI computations were performed with the SPACE software. [ABSTRACT FROM AUTHOR]