Article

### Cover

### Title

Nonlinear deformation of a thin spherical shell under pressure### Author

^{}R.A. Sabirov

### Organization

Reshetnev Siberian State Aerospace UniversityKrasnoyarsk, Russian Federation

### Abstract

Pressure vessels, including spherical tanks, used in aerospace technology. If not allowed large deformation, then to resolve the issue ensure the integrity of the design is the balance equation of Laplace with the regulatory application of safety factors on purpose. The equations of equilibrium of a spherical shell on the deformed scheme, i.e. taking into account the magnitude of deflection, which increases the initial radius of the shell from the action of pressure. The unknown parameters are the bending and membrane internal stress occurring in the shell. It is believed that the initial amount of shell material during its deformation does not change, so the thickness is a variable. Consideration of these parameters transforms the equation of equilibrium in a nonlinear equation linking the deflection and the magnitude of internal pressure. Constant parameters in this equation include the initial radius, the initial volume of the shell material and the Young's modulus. An example of the deformation of the ball, which examined the relationship of the deflection on the internal pressure, internal volume, pressure and wall thickness assuming incompressibility of the material. Graphs of increase in the internal volume of the balloon, reducing the wall thickness, increase the voltage and change of internal stress. The conclusion is that in the ball thin shell, connected the internal pressure, deflection, internal volume and wall thickness, the pressure increases to a certain value, then it starts to decrease, has led to experimentation with communicating vessels – balloons.### Keywords

calculation of the stress and deformations, large displacements, the pressure in the balloon### References

[1] Van Czi-de. Prikladnaja teorija uprugosti [Applied theory of elasticity]. Moscow : Fizmatgiz, 1959. 400 p.

[2] Vol'mir A. S. Ustojchivost' uprugih sistem [Stability of elastic systems]. Moscow : Fizmatgiz, 1963. 880 p.

[3] Sausvel R. V. [Southwell R. V.] Vvedenie v teoriju uprugosti dlja inzhenerov i fizikov. Gosudarstvennoe izdatel'stvo inostrannoj literatury [An introduction to the theory of elasticity for engineers and physicists]. M., 1948. 675 p.

[4] Timoshenko S. P., Gud'er Dzh. Teorija uprugosti [Theory of elasticity]. Moscow : Nauka, 1975. 576 p.

[5] Modelirovanie sharovogo sosuda po deformirovannoj sheme [Simulation of ball vessel on the deformed scheme] / A. V. Izohvatov, S. A. Polegotchenkov, L. A. Burym, T. V. Dadyko, I. A. Motorkin ; Nauchnyj rukovoditel' – kand. tehn. nauk R. A. Sabirov // Sbornik materialov Mezhdunarodnoj konferencii studentov, aspirantov i molodyh uchjonyh «Prospekt Svobodnyj-2016», posvjashhjonnoj Godu obrazovanija v Sodruzhestve Nezavisimyh Gosudarstv, Sibirskij federal'nyj universitet, 15–25 aprelja 2016, Krasnojarsk, p. 34–38. [Jelektronnyj resurs] http://conf.sfu-kras.ru/mn2016/.