In the realm of mechanical engineering and construction, a significant advancement has been made that could reshape how we design and analyze structures with cylindrical inclusions, particularly in the energy sector. Oleksandr Yu. Denshchykov, a researcher from the National Aerospace University Kharkiv Aviation Institute, has published a groundbreaking study in the Journal of Mechanical Engineering (Mehanika), titled “First Main Problem of the Theory of Elasticity for a Layer with Two Thick-Walled Pipes and One Cylindrical Cavity.” This research addresses a critical gap in the literature by providing a method to calculate the stress-strain state of structures fixed on cylindrical inclusions, a common feature in machine and aircraft construction.
The study focuses on a model where an elastic homogeneous layer is situated on two thick-walled pipes, with a longitudinal cylindrical cavity parallel to the layer boundaries. “The problem is particularly relevant for structures where the stress values on the inner surfaces of the pipes are known, but accurate calculation methods have been lacking,” Denshchykov explains. This gap has posed challenges in the design and prediction of geometric parameters for such structures.
Denshchykov’s approach involves using two types of coordinate systems: Cartesian for the layer and cylindrical for the pipes and cavity. The basic solutions in these different coordinate systems are given as Lamé equations, which are then combined using transition functions and the generalized Fourier method. This sophisticated mathematical framework allows for the formation of an infinite system of integro-algebraic equations based on boundary conditions and continuity conditions between the layer and the pipes.
The research employs numerical methods to solve these equations with a given accuracy, enabling the determination of the stress-strain state at any point within the elastic body. One of the key findings is that the stresses along the lower and upper surfaces of the layer are not significantly affected by the distance between the thick-walled pipes. However, the stresses along the surface of the pipe and layer junction decrease as the distance between the pipes increases.
This research has profound implications for the energy sector, particularly in the design and analysis of structures involving fibrous composites and other materials with cylindrical inclusions. The ability to accurately predict the stress-strain state of these structures can lead to more efficient and safer designs, ultimately reducing costs and improving performance.
As Denshchykov notes, “The obtained numerical results can be used in the prediction of geometric parameters during the design phase, which is crucial for ensuring the reliability and longevity of structures in the energy sector.” This advancement not only fills a critical gap in the literature but also paves the way for future developments in the field of mechanical engineering and construction.
The study, published in the Journal of Mechanical Engineering (Mehanika), represents a significant step forward in our understanding of the behavior of structures with cylindrical inclusions. As the energy sector continues to evolve, the insights gained from this research will be invaluable in shaping the future of structural design and analysis.