Creep of a closed cylindrical tank at hydrostatic pressure

Abstract

Objective. When constructing the resolving relations of the theory of shells, the validity of the basic assumptions about the material of the structure under consideration is assumed, which is considered homogeneous, isotropic and viscoelastic, i.e. obeying the Maxwell-Gurevich law. The subject to study is a polymer cylindrical shell, rigidly clamped at the base and subject to internal hydrostatic pressure. Method. The problem is reduced to an inhomogeneous differential equation of the fourth degree with respect to the displacement of the middle surface w along the z axis. Since the closed form representation of the solution to this equation is extremely difficult, the search for it is presented numerically, in particular, using the grid method. The creep strain components ε*x, ε*θ, γ*xθ were determined as a linear approximation of the velocity by the Runge-Kutta method. Result. In the process of calculating the shell using moment theory, it was found that as a result of shell creep, tangential stresses increased by more than 12 percent. Conclusion. The proposed technique makes it possible to simulate changes in the mechanical properties of the shell (for example, indirect heterogeneity) caused by the influence of physical fields.

Keywords

• closed cylindrical shell
• hydrostatic pressure
• grid method
• resolving equation
• runge-kutta method