Efficiency evaluation of one analytical solution of the elasticity theory problem in the study of thermal stress state of a thin-walled structure made of layered material

Аuthors

Hoa V. D.^*, Mironova L. I.^**

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

*e-mail: dong.hoavan@yandex.ru
**e-mail: mironova_lub@mail.ru

Abstract

The results of study of thermal stress state of a real thin-walled clad structure experiencing temperature effects during the finishing technological operation of manufacturing are presented. A two-layer narrow strip of great length, rigidly fixed along the long side, was adopted as the calculation model. The response of a thin rectangular strip to the effect of temperature field was considered in the formulation of elasticity theory plane problem. The iterative-asymptotic Saint-Venant–Picard–Banach method was adopted as the research method, development of which has currently expanded the boundaries of its applicability in solving elasticity problems. Method includes operating with a small thin-wall parameter. The main results obtained relate to solving mechanics problems, where the models are a narrow strip, a plate and a shell. The proposed mathematical apparatus is used in studying the stress-strain state of thin-walled isotropic and anisotropic bodies. The analytical solution in the final form is found on the relations of lower dimension for new main unknowns of the problem. The transition to them is carried out through the reconstruction of the original system of equations to the form of the operator of the method of simple iterations. Its action is approximate expressions of stress-strain state components through a smaller number of unknowns - functions of lower dimension. The appearance of the latter is not associated with the introduction of hypotheses, but is a consequence of the form of operator containing integration arbitrariness (these functions). Reolving relations for them are found by fulfilling the boundary conditions by approximate expressions of the components of the stress-strain state. The equations can be solved analytically, including with the involvement of the apparatus of asymptotics. The purpose of the work was to evaluate the efficiency of using the analytical solution obtained on the basis of this method in substantiating the strength of real tech nical structures using the example of a membrane panel of incinerator furnace. The obtained calculated values of temperature deformations caused by heating the front surface to the corresponding temperature of the technological process are confirmed by the results of modeling in ANSYS software package and are comparable with the dimensional deviations of the panel during the finishing technological operation. Relative deviations of the calculated and actual values do not exceed, in general, 10%.

Keywords:

plane problem, multilayer strip, thermally stressed state, iterations, Saint-Venant–Picard–Banach method

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