Опір матеріалів і теорія споруд
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Документ Boundary element approaches to the problem of 2-d non-stationary elastic vibrations(КНУБА, 2020) Vorona, Yu. V.; Kozak, A. A.Two boundary element approaches are used to solve the problem on non-stationary vibrations of elastic solids. The first approach is based on the transition to the frequency domain by means of a Fourier series expansion. The second approach is associated with the direct solution of a system of time-dependent boundary integral equations, with a piecewise constant approximation of the dependence of the unknowns on time. In both cases, a collocation scheme is used to algebraize the integral equations, and the difficulties associated with the calculation of singular integrals are overcome by replacing the kernels with the initial segment of the Maclaurin series. After such a replacement, the kernels take the form of a sum, the first term of which is the corresponding fundamental solution of the statics problem while other terms are regular. Since integration of static kernels is not difficult the problem of calculating the diagonal coefficients of the SLAE turns out to be solved. The developed techniques are compared in the process of dynamics analysis solving of elastic media with two cylindrical cavities. The boundary of one of the cavities is subjected to a radial impulse load, which varies according to the parabolic law. Both approaches have shown the similar effectiveness and qualitative consistency.Документ The parametric oscillations of rotating rods under action of the axial beat load(КНУБА, 2020) Nedin, V. O.The paper presents the results of investigation of the axial beat loads’ influence on the transverse rotating rods’ oscillations and their stability. The perforator's long drills are considered as objects of investigation. The analysis of different author’s papers that are studded the dynamics of oscillations of shafts and rotating rods is carried out. The relevance of the research topic is substantiated. The model of the considered dynamic system is described and equations of oscillations in space are given. The technique for investigation is presented. This technique is based on search for new bend forms of rotating rod by solving the equations of oscillations with using the Hubbolt time integration method and the polynomial functions (splines) that are described the current bend form. In it, the spline functions are found by current bend form approximation where each of the found functions is responsible to certain point of rod elastic line and describes the position of nearby points. Described technique was realized in a computer program with graphic user interface that is developed by author. Program allows to monitor for dynamics of the oscillatory motion of the modeled system in real-time by calculating and drawing the current band forms of the rotating rod during the oscillation. Diagrams with regions of stable and instable motion of the rods, that were found by different parameters and boundary conditions are shown. The analysis of the results is obtained and the conclusion about possibility of operating the equipment in certain frequency ranges is done. The space oscillating process of rotating rods is considered with account of the gyroscopic loads and geometric nonlinearity.Документ Thermoelasticity of elastomeric constructions with initial stresses(КНУБА, 2020) Bazhenov, V. A.; Kozub, Yu. G.; Solodei, I. I.The article presents an algorithm for solving linked problems of thermoelasticity of elastomeric structural elements on the basis of a moment scheme of finite elements. To model the processes of thermoelastic deformation of structures with initial stresses the incremental theory of a deformed solid is used. At each step of deformation, the stiffness matrix is adjusted using an incremental geometric stiffness matrix. The use of triple approximation of displacements, deformations and volume change function allows to consider the weak compressibility of elastomers. The components of the stress tensor are calculated according to the Duhamel-Neumann law. To solve the problem of thermal conductivity, a thermal conductivity matrix considering the boundary conditions on the surface of a finite element is constructed. A sequential approximation algorithm is used to solve the thermoelasticity problem. At each stage of the solution, the characteristics of the thermal stress state are calculated. Based on the obtained components of stress and strain tensors, the intensity of internal heat sources is calculated as the dissipative energy averaged over the load cycle. To calculate the dissipative characteristics of the viscoelastic elastomer the parameters of the Rabotnov’s relaxation nucleus are used. Solving the problem of thermal conductivity considering the function of internal heat sources allows you to specify the heating temperature of the body. At each cycle of the algorithm, the values of the physical and mechanical characteristics of the thermosensitive material are refined. This approach to solving thermoelastic problems is implemented in the computing complex "MIRELA+". Based on the considered approach, the solutions of a number of problems are obtained. The results obtained satisfactorily coincide with the solutions of other authors. Considering the effect of preload and the dependence of physical and mechanical properties of the material on temperature leads to significant adjustments to the calculated values.Документ Basic relationships for physically and geometrically nonlinear problems of deformation of primatic bodies(КНУБА, 2020) Maksimyuk, Yu. V.; Pyskunov, S. O.; Shkril, A. A.; Maksimyuk, O. V.The initial relations of thermo elastic-plastic deformation of prismatic bodies are given in the paper. The basic concepts, indifference of deformation tensors, with the condition of energy conjunction in description of the shaping process are laid out on the basis of classical works.Документ Application of stiffness rings for improvement of operating reliability of the tank with shape imperfections(КНУБА, 2020) Lukianchenko, O. O.An efficiency of using of two stiffness rings for improvement of operating reliability of the tank with real shape imperfection at the action of combination load was evaluated. The computer model of the tank was constructed in the form of the thin cylindrical shell by of the program complex of finite element analysis. The tank stability problem under separate and joint action of surface pressure and axial compression was solved by the Lancosh method in linear formulation and as a nonlinear static problem by the Newton-Raphson method. The region of the tank failure-free work, which has the graphical presentation, confirmed the improvement of the tank wall stability due to the use of stiffness rings, especially in the area of surface pressure action.Документ An improved gradient-based method to solve parametric optimisation problems of the bar structures(КНУБА, 2020) Peleshko I. D.; Yurchenko V. V.The paper considers parametric optimisation problems for the bar structures formulated as nonlinear programming tasks. The method of the objective function gradient projection onto the active constraints surface with simultaneous correction of the constraints violations has been used to solve the parametric optimisation problem. Equivalent Householder transformations of the resolving equations of the method have been proposed. They increase numerical efficiency of the algorithm developed based on the method under consideration. Additionally, proposed improvement for the gradient-based method also consists of equivalent Givens transformations of the resolving equations. They ensure acceleration of the iterative searching process in the specified cases described by the paper due to decreasing the amount of calculations. The comparison of the optimisation results of truss structures presented by the paper confirms the validity of the optimum solutions obtained using proposed improvement of the gradient-based method. The efficiency of the propoced improvement of the gradient-based method has been also confirmed taking into account the number of iterations and absolute value of the maximum violation in the constraints.Документ Scientific substantiation of engineering preparation measures due to the influence of construction in the dense building conditions(КНУБА, 2020) Stefanyshyna-Gavryliuk, Yulija D.The method of studying the stress-strain state of reinforcement structures of combined soil massifs has been proposed with the geometric and physical nonlinearity in the formulation of the problem based on the nonlinear theory of elasticity and plasticity of the soil. The study of the stressdeformed state of the computational domain from the standpoint of the mechanics of the deformed solid body had been carried out, using algorithms for solving the problems of the theory of elasticity and plasticity, with the construction of universal computational models of the combined half-space, that allows to determine more reasonably the magnitude of the stress-strain state of complex soil bases in interaction with the reinforcement structures, the surrounding buildings foundations and the whole complex of the surrounding buildings structures. The influence of new construction on the condition of soil bases and foundations of adjacent buildings had been evaluated by determining the change of pressure on the reinforcement structure and determining the stress-strain state change of this structure and the foundation of the existing house. The change in the deformation of the foundation of the existing building, ie the oscillation of the soil foundation and the maximum amplitude of uneven subsidence of the foundations of the existing building have been determined. Each formulation of the problem had to include its own reliability analysis and a specific approach that requires numerical modeling and development of appropriate measures to scientifically substantiate engineering preparation measures in dense building. Further design of protective reinforcement structures for new construction under the conditions of the building reconstruction has carried out considering the impact on the existing buildings and structures and the adjacent soil mass of different stages of construction, begining with the arrangement of protective reinforcement structures, the development of a excavation due to the effect of unloading the foundation, and the sequence of erection of engineering structures.Документ A new approach to the design of suspension roof systems(КНУБА, 2020) Priadko, I. N.; Rudnieva I. N.; Ribakov, Y.; Bartolo H.Over the last century, the suspension roofs design has progressed until the advent of the shells theory in the first half of the 20th century, due to a rapid pace in technological advancement. A paradigm shift emerged with the new trend in structural design towards a new design process that cooperatively integrated economy, efficiency, and elegance. Different approaches in computation, design and reliability assessment of roof structures are discussed in this work to identify the key conditions that have significantly contributed to modern suspension roof design principles. A new algorithm to assess the reliability of suspension roofs at the design stage is proposed and a novel method for computational design and reliability evaluation of suspension roofs is presented in this paper. This method enables to solve some topical issues, such as assignment of initial geometric roof parameters and relevant problems, like numerical determination of reliability indices for statistically non-determined systems of suspension roofs with a big cut on elliptical plan.Документ Mathematical model of the dynamics change departure of the jib system manipulator with the simultaneous movement of its links(КНУБА, 2020) Loveikin, V. S.; Romasevich, Yu. O.; Spodoba O. O.; Loveikin, A. V.; Pochka, К. I.An equation of motion of the manipulator is obtained taking into account the influence of the inertial component of each link of the boom system and the effect of the oscillatory movement of the cargo on the dynamic loads of the metalware elements and hydraulic drive elements. The influence of the simultaneous movement of the first jib section, the second jib section and the telescopic jib section on cargo oscillation, as well as the effect of cargo oscillation on dynamic loads that occur in the boom system and manipulator hydraulic drive elements, is determined.Документ Situation forecasting and decision-making optimization based on using markov finite chains for areas with industrial pollutions(КНУБА, 2020) Getun G. V.; Butsenko Y. A.; Labzhynsky V. A.; Balina O. I.; Bezklubenko I. S.; Solomin A. V.The paper proposes a methodology for modeling engineering-within-nature complex systems (further, “systems”), which will be helpful for researchers and operators of complex technical systems in predicting the emergencies using environmental monitoring systems.