# For a calculation of stresses in vessels under unsymmetrical hydraulic-statics pressure and heating

### Mathematics. Physics. Mechanics

### Аuthors

^{1}

^{*},

^{1},

^{2}

^{**}

1. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

2. Progresstech, 2nd Khutorskay St., 38a, 127387, Russia

*e-mail: borisn@km.ru

**e-mail: good-for-you@mail.ru

### Abstract

The problem to be considered in this paper isboundary problemsdevoted toa stress-deformed state of a circle cylindrical shell with varied conditions on the boundaries and with the presence of hydraulic-statics pressure action, which is constant along of an axis, that correspondents to a horizontal position of vessels, which are partially filled by a liquid. Such problem in condition of endshinge joints was solved in the V.Z. Vlasov’s monograph with the help of double trigonometric seriesmethod, in which an axial stress is shown only on the basis of the semi-momentless theory.Since the dry part of the vessels cylindrical shell with no liquid can havethe very high temperature, which can lead to appearance of high thermo-elastic stresses, it is needed to consider a problem of stress-deformed state calculation of cylindrical shells being under action of temperature, which is constant by length and piece – constant along the contour.

The method of asymptotic synthesis (MAS) and ordinary trigonometric series with the method of initial parameters are used for an essential widening of studyingpossibilities for stress-deformed state. An attraction of the MAS is stipulated by necessity to calculate the bending moments in a zone with absence of hinge joints, for example, on the rigidly fixed edges of the shells, where it is impossible to find the bending moments on the basis of the semi-momentless theory, because of algebraic non-differential dependence between the axial and cross bending moments and the radial displacement, as far as the partial derivative of the radial displacement with respect to an axial coordinate is equal to zero; but the radial displacement is equal to zero with the condition of rigidly fixed edges of shells, therefore the bending moments are equal to zero too. But by attracting the MAS the stress-deformed state on the basis of semi-momentless theory equations was supplemented with symmetrical and unsymmetrical edge effects, destined to play an essential role in calculation of stress state on shells rigidly fixed edges.

In this way the submitted here investigations could be interpreted as some generalization of V.Z. Vlasov’s problem in the case of shells witharbitrary boundary conditions under action of both the unsymmetrical hydraulic-statics pressure and piece-constant temperature field.

The MAS in the form of differential equations of the semi-momentless theory and the edge effect theory equations allowed to get the analytical solutions and simple formulae for important unknown quantities of stress-deformed state in the case of circle cylindrical shells with varied conditions on boundaries.

### Keywords:

cylindrical shell, hydraulic-statics pressure, vessel, main stress tate, edge effect, temperature### References

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