Optimization of thick-walled spherical shells at thermal and power influences

Abstract

The problem of optimization for thick-walled shell, experiencing temperature and power feedback. Under the influence of temperature field the properties of material of an object can change. That allows to manage the deflected mode of such objects while achieving a certain law of radial change of physical and mechanical parameters. A centrally symmetric problem of elasticity theory is studied. As a result we received a law of variation of Young's modulus, in which a spherical dome is equally stressed according to the simplified theory of Mohr. The problem was reduced to a Bernoulli differential equation. This equation was solved numerically using Runge-Kutta method of fourth order.