Nonlinear deformation of a thin spherical shell under pressure

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...