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.
Highlights
Despite development of numerical methods, such as a finite-element method, analytical methods of task solutions and calculations on their basis are still relevant.One of the most widespread classes of tasks are central symmetric [1; 2] and the axisymmetric tasks [3,4,5] differing generally in some coefficients while general structure of the resolving equations is preserved.There are numerous researches on determination of the deflected mode of cylindrical objects under the influence of external pressure and temperature [6]
The above-mentioned property can be used for solving the inverse mechanical problems: determining such a law of the modulus of elasticity change of material of a structure and its elements that would make it equal in tension and strength [7,8,9]
We consider a thick-walled shell with inner radius a and outer radius b, experiencing the inner pressure pa and outer pressure pb (Fig. 1)
Summary
Despite development of numerical methods, such as a finite-element method, analytical methods of task solutions and calculations on their basis are still relevant. There are numerous researches on determination of the deflected mode of cylindrical objects (pipes, reservoirs) under the influence of external pressure and temperature [6]. The change of physical and mechanical parameters of a material under the influence of temperature isn't always taken into account. The above-mentioned property can be used for solving the inverse mechanical problems: determining such a law of the modulus of elasticity change of material of a structure and its elements that would make it equal in tension and strength [7,8,9]
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