Modeling of Creep of a Closed Cylindrical Shell Under Hydrostatic Pressure

Objective. The paper presents general equations of the moment theory of a shell of zero Gaussian curvature taking into account creep deformation. The problem of the stress-strain state of a shell is considered, with the boundary conditions: rigidly fixed at the base and free edge at the top. The cylinder is subject to internal hydrostatic pressure. A resolving linear inhomogeneous differential equation of the fourth order with respect to deflection is obtained. The solution is given numerically analytically in the MATLAB software package. The nonlinear Maxwell-Gurevich equation is used as an equation of state between creep deformations and stresses. Method. To determine creep deformations, a linear approximation of the first derivative with respect to time was used, in other words, the Euler method. To verify the solution to the problem, a shell made of secondary PVC was calculated using the grid method [1]. The technique was tested by comparing the solution with the calculations of other well-known researchers. Result. A program for calculation in the MATLAB package with the ability to vary the initial data and output a graph of the dependence of displacements and stresses on time has been developed. As a result of the solution, it was found that during creep in the shell, circumferential stresses increase by 14.7%. Conclusion. The proposed approach can be applied to the analysis of the stress-strain state and bearing capacity of a reinforced concrete shell as well. There are no restrictions on boundary conditions and the type of loading, and the beam material can be not only polymers and composites for construction purposes, but also concrete. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.