National Aerospace University – Kharkiv Aviation Institute

In aerospace and mechanical engineering, elements that are loaded by periodic loads (periodic function) are used. In problems for a layer with cylindrical inhomogeneities, it is difficult to take such loads into account. Therefore, there is a need to develop a methodology for calculating the stress state for a layer with a cylindrical cavity and taking into account the boundary conditions in the form of a periodic function. In this paper, we propose a solution to the problem of elasticity theory for a layer with a cylindrical cavity within the framework of the generalized Fourier method. Stresses are given at the upper boundary of the layer and on the surface of the cylindrical cavity, and displacements are given at the lower boundary of the layer. The layer and cylindrical cavity are considered in different coordinate systems (Cartesian and cylindrical). The redistribution functions of the generalized Fourier method are applied to the Lamé equations. The problem is reduced to the sum of two solutions – an auxiliary problem and the main problem. Both problems are reduced to infinite systems of linear algebraic equations, which allow the application of the reduction method to them. After finding the unknowns in the auxiliary problem, the stresses at the geometric location of the cavity are found. The main problem is solved for the layer with the cavity, on which stresses obtained from the auxiliary problem are set with the reverse sign. The complete solution consists of the auxiliary and main problems. Having calculated all the unknowns, it is possible to obtain the stress-strain state at any point of the body with a given accuracy. Numerical analysis of the stress state showed high accuracy of the boundary conditions and dependence on periodic loading. Thus, the stresses sx and sz at the upper boundary of the layer have extremes in the places of maximum values sy and their negative values increase at the location of the cavity. At the same time, the stresses sx exceed the specified sy.

A spatial problem of elasticity is solved for a layer with n longitudinal cylindrical cavities, two of which contain thick-walled pipes in smooth contact with the layer. Stresses are given on the surfaces of the layer, the inner surfaces of the pipes, and the cavities. All canonical surfaces do not intersect each other. The material of the layer and cylindrical pipes is homogeneous and isotropic. An analytical and numerical calculation method, which assumes the fulfillment of statics conditions (for the first basic problem of elasticity theory) and is based on the Lamé equation, is proposed. The basic solutions of the Lamé equation are taken in a form that makes it possible to obtain an exact solution for a separate boundary surface in each separate coordinate system. The basic solutions in these coordinate systems (Cartesian for the layer and local cylindrical for the cylindrical inhomogeneities) are interconnected through the mathematical framework of the generalized Fourier method. The fulfillment of boundary conditions on the upper and lower surfaces of the layer, on the inner surfaces of pipes, on cylindrical cavities, as well as the consideration of interface conditions, create an infinite system of integro-algebraic equations, which is reduced to an infinite linear one. In the numerical study, the reduction method is applied to the resulting infinite linear algebraic system of equations. The solution of the system of equations gives the values of the unknown functions. Numerical calculations have shown the rapid convergence of approximate solutions to the exact one. The numerical analysis of the stressed state of the layer and thick-walled pipes showed that the use of polyamide bushings has almost no effect on the stress-strain state of the structure (compared to their absence), the use of steel bushings reduces the stress in the body of the layer in the areas of their location, redistributing the stress to the bushings themselves. The proposed solution method makes it possible to obtain the stress-strain state of structures containing cylindrical cavities and bushings, and the numerical analysis allows to assess the influence of the material on the values of stress distribution in the structures of machines and mechanisms at the design stage.

Problem setting. The article is devoted to the comprehensive study of the role of innovative systems in the formation of legal relations in the field of the environment. In the context of digital transformation, global environmental challenges and the transition to sustainable development, the need for a conceptual understanding of innovative systems and their legal impact on environmental governance is becoming increasingly relevant. The research focuses on defining the essence, structure and functional significance of innovative systems as a basis for the modernization of environmental legal relations. Analysis of recent researches and publications. The issue of legal regulation of environmental relations and innovation processes has been addressed by a number of prominent scholars, including A. P. Getman, G. I. Balyuk, M. V. Krasnova, E. M. Bilousov, V. L. Bredikhina, D. V. Zadykhailo, D. D. Zadykhailo, I. V. Anisimova and others. However, despite the significant scientific achievements, the problem of understanding innovative systems as an integral legal and institutional phenomenon in the environmental sphere remains insufficiently explored. Target of the research. The research is based on general scientific and special legal methods, including systemstructural analysis, formal-legal method, comparative legal approach and interdisciplinary analysis. The study also includes the examination of national environmental legislation, strategic policy documents and international standards in the field of environmental governance and innovation. Article’s main body. The article reveals the concept of an innovative system as a complex of interconnected institutional, technological, legal, economic and communication elements that ensure the creation, dissemination and application of environmental innovations. The functional roles of these components are analyzed in the context of environmental protection, rational use of natural resources and sustainable development. It is substantiated that the interaction of these elements forms a new model of environmental legal relations based on digital technologies, environmental monitoring systems, open data and participatory governance. Particular attention is paid to how innovative systems transform traditional environmental legal institutions, including state supervision, environmental audit, environmental impact assessment and legal liability. The study demonstrates that innovative systems increase transparency, improve access to environmental information, strengthen public participation and enhance the effectiveness of legal enforcement. At the same time, the research identifies key challenges such as insufficient legal regulation of environmental data circulation, lack of technological standardization, cybersecurity risks and unequal access to innovative resources. Conclusions and prospects for development. It is concluded that innovative systems are a determining factor in the evolution of environmental legal relations and the formation of a modern model of environmental governance based on integration, openness and technological efficiency. Their further development requires systematic improvement of legislation, harmonization with international and European standards, creation of a clear terminological framework and strengthening of institutional capacity. The integration of innovative systems into environmental governance should be comprehensive, combining legal, technological, economic and social instruments in order to ensure effective environmental protection and sustainable development.

When determining the development strategy of a construction organization in the dynamics of the implementation of the production program is the determination and assessment of the dynamics of the development of its production capacity. Today, the issue of calculating production capacity is relevant, since existing methods are outdated and do not correspond to reality. The classical algorithm for calculating production capacity is based on adjusting the actual volume of work through the coefficients of use of machine and labor resources. However, this approach has significant limitations: it does not take into account changes in the structure of work, the relationship between the use of machines and labor, as well as the impact of inflation and instability of contract prices. The article proposes a "MULTI-RESOURCE MODEL", which takes into account complex production processes and leading resources - machine, labor, material - taking into account their natural and cost indicators. The model is based on the methods of discrete parametric linear programming, which allows you to take into account the contract prices of projects and the effect of synergy between customers and the use of production capacity. The problem of determining the terms and costs of construction of objects at a given level of project quality is solved in conditions of contradiction between the probabilistic nature of the manifestation of negative risk factors and specific volumes of resources. To eliminate risks, they must be considered in the form of safety reserves. In practice, when forming and implementing the production program of a construction organization, a low level of justification of the necessary financial and other resources is noted. This leads to an increase in the cost and terms of construction projects, freezing of fixed and working capital and requires measures to minimize risks during construction. Such circumstances determine the relevance of theoretical research and the development of methodological recommendations for a comprehensive assessment of the structure and impact of organizational and technological risks on the efficiency of the construction organization based on the creation of system models. This will allow the contractor to objectively assess the risks, prepare documents for the tender and further substantiate the annual program of the construction organization. The risks of changes in the implementation of a construction project are considered, among which organizational and technological ones, which depend on the construction enterprise, require special attention.

The article is devoted to the development of a conceptual model for the digital transformation of the transport infrastructure of the Republic of Kazakhstan, aimed at increasing the efficiency, sustainability and competitiveness of the country’s transport and logistics complex. An analysis of the current state of the transport infrastructure is carried out and the key challenges for its development are identified, taking into account global digitalization trends and the requirements of the Industry 5.0 concept. The key areas of digital transformation are formulated, including infrastructural and technical, operational and logistical, project coordination, personnel management, and innovation and technology. The proposed conceptual model integrates strategic planning, digital technology implementation tools and a system for evaluating the effectiveness of changes and defines the place of digital transformation in the strategic management of projects and programs for the development of the transport and logistics complex. The results obtained have scientific novelty as a basis for further development of methodological foundations, system, optimization and simulation models of transport and logistics complex management, as well as practical significance for the formation of state and corporate programs for the digital modernization of the transport sector.