Annotation: The strength of real solids depends essentially on the defect of the structure. In real materials, there is always a large number of various micro defects, the development of which under the influence of loading leads to the appearance of cracks and their growth in the form of local or complete destruction. In this paper, based on the method of singular integral equations, we present a unified approach to the solution of thermal elasticity problems for bodies weakened by inhomogeneities. The purpose of the work is to take into account the heterogeneities in the materials of the elements of the rocket structures on their functionally-gradient properties, including strength. The choice of the method of investigation of strength and destruction of structural elements depends on the size of the object under study. Micro-research is related to the heterogeneities that are formed in the surface layer at the stage of preparation, the technology of manufacturing structural elements. Defectiveness allows you to adequately consider the mechanism of destruction of objects as a process of development of cracks. In studying the limit state of real elements, weakened by defects and constructing on this basis the theory of their strength and destruction in addition to the deterministic one must consider the probabilistic – statistical approach. In the case of thermal action on structural elements in which there are uniformly scattered, non-interacting randomly distributed defects of the type of cracks, the laws of joint distribution of the length and angle of orientation of which are known, the limiting value of the heat flux for the balanced state of the crack having the length of the “weakest link” is determined. The influence of heterogeneities of technological origin (from the workpiece to the finished product) that occur in the surface layer in the technology of manufacturing structural elements on its destruction is taken into account by the developed model. The strength of real solids depends essentially on the defect of the structure. In real materials, there are always many various micro defects, the development of which under the influence of loading leads to the appearance of cracks and their growth in the form of local or complete destruction. In this paper, based on the method of singular integral equations, we present a unified approach to the solution of thermal elasticity problems for bodies weakened by inhomogeneities. The purpose of the work is to take into account the heterogeneities in the materials of the elements of the rocket structures on their functionally gradient properties, including strength. The choice of the method of investigation of strength and destruction of structural elements depends on the size of the object under study. Micro-research is related to the heterogeneities that are formed in the surface layer at the stage of preparation, the technology of manufacturing structural elements. Defectiveness allows you to adequately consider the mechanism of destruction of objects as a process of development of cracks. In studying the limit state of real elements, weakened by defects and constructing on this basis the theory of their strength and destruction besides the deterministic one must consider the probabilistic – statistical approach. With thermal action on structural elements in which there are uniformly scattered, non-interacting randomly distributed defects of the cracks, the laws of joint distribution of the length and angle of orientation of which are known, the limiting value of the heat flux for the balanced state of the crack having the length of the “weakest link” is determined. The influence of heterogeneities of technological origin (from the workpiece to the finished product) that occur in the surface layer in the technology of manufacturing structural elements on its destruction is taken into account by the developed model. The solution of the singular integral equation with the Cauchy kernel allows one to determine the intensity of stresses around the vertexes of defects of the cracks, and by comparing it with the criterion of fracture toughness for the material of a structural element, one can determine its state. If this criterion is violated, the weak link defect develops into a trunk crack. Also, a criterion correlation of the condition of the equilibrium defect condition with a length of 2l was got, depending on the magnitude of the contact temperature. When the weld is cooled, it develops “hot cracks” that lead to a lack of welding elements of the structures. The results of the simulation using singular integral equations open the possibility to evaluate the influence of thirdparty fillers on the loss of functional properties of inhomogeneous systems. The exact determination of the order and nature of the singularity near the vertices of the acute-angled imperfection in the inhomogeneous medium, presented in the analytical form, is necessary to plan and record the corresponding criterion relations to determine the functional properties of inhomogeneous systems.

Annotation: This article analyzes the results of studies, which are based on numerical methods of analysis, of the stress-strain state of thin-walled shell structures. This article also discusses analytical solutions that apply asymptotic approaches and a method of initial parameters in a matrix form for solving a problem of equal stability of reinforced compartments of combined shell systems of the rocket and space technology within the scope of the research being carried out jointly by teams of Yuzhnoye State Design Office and Zaporizhzhya National University. The primary attention is paid to the use of FEM-based direct numerical methods and the research results for which analytical methods can be useful for making a preliminary assessment of the bearing capacity of load-bearing structures, and in some cases for their rational design. This article does not contrast numerical and analytical approaches but about the possibility of using them effectively. The article talks about possible ways of using the up-to-date technique of machine learning (Machine Learning Technology) in the calculation and experimental methods for determining the characteristics of the rocket and space technology.

Annotation: This paper presents the overview and features of the stress-strain state analysis of the multilayer shell structures widely used in the design of the missile compartments. As a result of analysis of the current situation with the stress-strain state studies of the complex configuration shell structures and mathematical support of the load-bearing capacity calculation of the aerospace structures, the following actual research trends can be singled out: 1) improvement of the methods of analytical estimation of the thin-walled structures’ strength and resistance; 2) improvement of the numerical methods of composite materials mechanical properties analysis; 3) development or application of the existing software packages and ADE-systems, automatizing stress-strain state analysis with visualization of the processes under study. One of the most important steps of the third research trend is development of the initial data input media (setting the model parameters) and presentation of analysis results with account of the user interface visualization. The description of the mathematical simulation and experimental studies of the stress-strain state of the interstage bay made of carbon fiber sandwich structure is presented and short description of the structure condition after the tests is provided. Based on the analysis it can be concluded that development of the geometric simulation methods, taking into account the manufacturing deviations, is an independent problem from the point of view of practical applications in the aerospace technology.