# PSI - Issue 50

I.G. Emel’yanov et al. / Procedia Structural Integrity 50 (2023) 57–64 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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with lodgement-type supports. During the operation of such structures under variable thermomechanical loads, a process of accumulation of irreversible changes in the pipe material occurs, leading to the formation of macrocracks and destruction, Manai and Al-Emrani (2019), Nguyen (2021), Abdullah (2021). The problem of evaluating the service life of such structures is an urgent technical and economic problem that can not only prevent man-made and environmental disasters, but also save material. When evaluating the service life of such pipelines, fatigue theory is usually used, the methods of which are based on the empirical approximation of experimental curves for various materials, Manson (1966), Tretyachenko (1989), Troshchenko (1994), Gusenkov and Kotov (1988). When designing metal structures, the hypothesis of linear summation of damages is usually used due to the simplicity of its applicability. However, this hypothesis is not sensitive to the rearrangement of cycles and rare peak overloads. Even though this hypothesis has existed since the middle of the 20th century, work is still underway to refine it, Li (2021), D'Angela and Ercolino (2021), Wang (2020). The aim of the work is to determine the service life of a multi-span pipeline based on the previously solved problem of determining the contact stresses for a cylindrical shell in the zone of contact with the support. The paper uses a modified method for calculating fatigue, based on a change in the tensile strength of the specimen material as damage accumulates in it. As initial stresses for calculating the fatigue problem, the solution of the contact problem of a shell lying on a rigid foundation is presented. When solving the problem, contact stresses are determined, on the basis of which the estimated service life is calculated. 2. Solution of a boundary value problem for a shell in contact with a lodgement-type support Consider a pipe loaded with an external static load in the form of a transverse force P ex and an internal dynamic load in the form of a pulsating pressure p . The pipe rests on a rigid support (Fig. 1). The reactive load (contact pressure) from the rigid support will cause a stress concentration for the shell. Therefore, this area of the connection between the pipe and the support during operation must be calculated for fatigue, since the service life of the pipe will depend on it. This problem models the determination of the stress-strain state of the gas pipeline ground part, which lies on rigid supports, and the assessment of its performance. As mentioned above, the failure of a structure usually occurs as a result of a gradual accumulation of damage of various nature and orientation. Therefore, it is necessary for each moment of operation time t to determine the area of contact, the contact pressure on the pip.

Fig.1 A pipe lying on a lodgement type support.

A thin-walled pipe is a shell of revolution with variable geometric and mechanical parameters along the generatrix. Let's connect the middle surface of the shell with curvilinear orthogonal coordinates s , θ , γ where s are meridional coordinates, θ are circumferential coordinates, and the coordinate γ is measured in the direction of the outer normal to the shell surface.

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