Engineering Transactions, 19, 2, pp. 309–326, 1971

Lepkoplastyczne Płynięcie Powłoki Walcowej przy Warunku Plastyczności Hubera-Misesa

A. Pabjanek
Instytut Podstawowych Problemów Techniki, Warszawa

In this paper a thin cylindrical shell is considered, loaded by an axially-symmetrical uniformly distributed external pressure, constant in time and greater than the limiting load capacity of the shell. Rigid visco-plastic incompressible material of the shell and the Huber-Mises yield condition are assumed.
A quasi-static state of equilibrium is established for the load grcater than the limiting load capacity in the shell, the forces of inertia being disregarded.
The problem of quasi-static flow of the shell is described by a non-linear set of ordinary differential equations of the first order which have been solved numerically. The calculations are carried out for several values of load and geometrical parameters of the shell. The two-point differential problem obtained here is reduced to Cauchy's problem with the use of Newton's method of solving a set of implicit algebraic equations. The Cauchy problem was solved by the Runge-Kutta method.
The solutions for an «exact» surface of flow of the shell (for the Huber-Mises condition) and its approximation are discussed and compared. The high compatibility of both solutions is shown.
The influence of the geometrical shell parameter on the magnitude and character of the solution of the problem has been investigated.

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