Tula State University (TSU) (Russian: Ту́льский госуда́рственный университе́т, ТулГУ) is the largest state university in Tula, Central Russia. Since May 2006, its rector is Mikhail Gryazev, professor, doctor of technical sciences. More than 20,000 students, 400 post graduates, and 600 foreign students[citation needed] study at Tula State University. The university consists of nine faculties (colleges), a medical institute, a center of pre-university studies, a regional center for professional development, and 73 departments (chairs)..
The work is devoted to the development and practical application of a surrogate model of electrochemical machining of the outer workpiece cylindrical surface using a tool-electrode with a partially insulated surface. The model earlier developed by the authors and the method of its numerical solution were used as the original mathematical model. The approximations of the results of numerical simulation of the primary distribution of current density were used. In contrast to the original mathematical model, which requires time-consuming calculations for each set of process parameters (the minimum interelectrode gap, the workpiece radius, the angle of active area of partially insulated tool electrode), the developed surrogate model enables performing all necessary calculations using the analytical dependences. The surrogate model enables more precise determining the rational modes of electrochemical machining, which provide the required compromise between the accuracy and productivity of the process, using significantly lower computational resources.
The method of representing the J-integral during deformation of an elastic-plastic adhesive layer connecting elastic cantilevers using additive components is studied. The additive components of the J-integral are responsible for a specific aspect of deformation: stresses on the end surface of the adhesive layer; the reversible part of the deformations and the irreversible part of the deformations. Two approaches to solving the problems of loading samples connected by overlapping using mixed mode I+II loading of the adhesive layer are analyzed: an analytical solution and the finite element method. The load analysis showed the presence of stress vectors at the boundary of the adhesive layer directly adjacent to the free surface. The results obtained demonstrate a high degree of correspondence in terms of average tangential and diagonal stresses in the elasticity zone, as well as average tangential stresses in the area of elastic-plastic deformation of the adhesive layer. During numerical modeling of problems involving mixed load modes I+II, the components I and II of the J-integral load modes were calculated, and its reversible and irreversible parts were identified. The studies revealed that thinning of the adhesive layer affects all average stresses within the elastic model, as well as the average diagonal components of the stress tensor for elastic-plastic behavior of the layer, with an increase in the length of the zone of irreversible deformations. When the layer thickness is zero, where the J-integral determines the singular stress distribution, a similarity was found between the solutions of problems describing the behavior of a thin adhesive layer in both elastic-plastic and elastic deformation modes.
The paper presents a mathematical description of a group control method based on an analogy with the translational motion of atoms, referred to as the thermal motion equivalent method. The stability of this method is investigated using agent prototypes based on quadcopters. Both field and semi-field experiments conducted to verify the proposed methodology are outlined. The results of experiments involving the launch of two real agents confirmed the need to compensate for turbulent flows created by propulsion systems. The thermal motion equivalent method based on the principles of potential field was adapted to account for the perturbations by adding a force equivalent calculated from the current velocity of the agent. The experiments have demonstrated the effectiveness of this compensation in laboratory conditions. In addition, it was established by semi-full-scale simulation involving two real and two virtual agents that the presence of virtual agents did not harm the stability of a swarm. The findings of this study open up new prospects for the application of group control methods in robotics and unmanned vehicle systems.
The results of a study of the stress-strain state of a two-layer steel-concrete lining of a tunnel constructed in a waterproof rock massif near the boundary of the overlying stratum of aquifers with other physical and mechanical characteristics are presented. Using developed by the authors the computer software being implemented a new analytical solution of the corresponding geomechanics problem, multivariante calculations were performed, which made to be possible to identify the basic dependencies of stress field formation in the "rock mass-lining" system.
A mathematical model for determining the stress-strain state of an orthotropic cylindrical shell with an open profile is proposed, based on the finite element method. The shell is not considered thin or medium-thick, to which the technical hypotheses of Kirchhoff, Timoshenko, Ambartsumyan, or Vlasov do not apply. As an example of model implementation, rigid restraint along the contour of the generatrices is considered. The developed model is based on a three-dimensional stress-strain state and a physically nonlinear approach to accounting for the mechanical properties of materials, associated with their dependence on the type of stress state. In other words, the model is constructed taking into account the structural properties of the materials from which the shell is constructed. These properties manifest themselves in orthotropic composites, where, under loading, the components of the compliance tensor continuously vary from point to point as the ratios between the components of the stress tensor change, which can be interpreted as induced mechanical heterogeneity of the material. The relationship between second-rank tensors is derived from the strain potential formulated in the normalized space of the principal material axes of orthotropy. These features of the problem somewhat complicate the calculations of spatial structures. Therefore, the developed mathematical model is based on isoparametric ten-node finite elements in the form of a tetrahedron with three degrees of freedom per node, the stiffness matrix of which was transformed to account for the mechanical properties of orthotropic materials. Due to the general nonlinearity of the resulting model due to the specific nature of the shell material, its numerical implementation was carried out using an iterative procedure of the variable elasticity method. As a result of implementing the computational model, the required set of parameters for the stress-strain state of the shell was obtained. The calculation results were compared with the characteristics obtained using the best-known equations of state for orthotropic materials with imperfect elasticity. A brief analysis of the obtained quantitative characteristics of shell deformation and its qualitative patterns is provided, taking into account various equations of state.
