Solution of the Problem of Stressed State for a Closed Elastoplastic Cylindrical Shell Containing a Crack in the Complex Form

• Published in: Journal of mathematical sciences (New York, N.Y.) Vol. 279; no. 2; pp. 213 - 225
• Main Authors: Kostenko, I. S., Nykolyshyn, T. M., Rostun, M. Yo
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.02.2024; Springer Nature B.V
• Subjects: Boundary conditions; Configurations; Crack opening displacement; Cylindrical shells; Elastoplasticity; Mathematics; Mathematics and Statistics; Mechanical properties; Numerical analysis; Plastic zones; Quadratures; Singular integral equations; Thin walled shells; closed elastoplastic cylindrical shell; δ; parabolic crack; fracture criterion; stressed state; model; complex form of equations
• ISSN: 1072-3374; 1573-8795
• DOI: 10.1007/s10958-024-07006-2

To study the stressed state and limit equilibrium of a closed elastoplastic cylindrical shell containing a plane longitudinal internal crack of any configuration, we use an analog of the δ c -model and represent the resolving system of equations of the problem in the complex form. The obtained system of equations is reduced to a system of nonlinear singular integral equations whose solution is constructed by the method of mechanical quadratures with regard for the conditions of plasticity of thin shells, the conditions of boundedness of stresses, and the conditions of uniqueness of displacements. We also perform the numerical analysis of the dependences of the crack opening displacements and the sizes of plastic zones on the boundary conditions imposed on the shell edges, on the configuration of the crack, and on the geometric and mechanical parameters.