Точное решение задачи расчета деформаций и напряжений композитного обтекателя конической формы при температурном и силовом нагружении

Точное решение задачи расчета деформаций и напряжений…

Инженерный журнал: наука и инновации

# 6



2016

Exact solution to the problem of computing strains

and stresses for a conical composite fairing subjected

to temperature and force loads

Bauman Moscow State Technical University, Moscow, 105005, Russia

Problems connected with analysis of temperature fields, stresses, and critical force loads

arise during the process of designing structural elements for aircraft of various designa-

tions. Employing contemporary finite element software to solve such problems involves

a labour-intensive process of selecting the right type of finite element, preparing and in-

putting initial data, and analysing the result obtained. However, analytical computation

techniques are still valid. This article presents an analytical technique for calculating pa-

rameters of a fairing, one of the most widespread structural elements. A fairing is a thin-

walled conical rotational shell. This structural element is subjected to force and tempera-

ture loads, the heat field varying along the generatrix and across the thickness of the

shell. The analytical solution for the problem of computing the parameters of a fairing

made out of a composite material amounts to solving an inhomogeneous Bessel equation

with respect to a complex function, the order of which is determined by the elastic moduli

ratio of the material in two perpendicular directions. The method of finding a solution to

this equation that involves using a solution based on momentless theory as a particular

solution is approximate. Therefore the question arises if the solutions found by this meth-

od are acceptable. This article presents an exact solution to the Bessel equation, obtained

by the method of variation of parameters. We analyse the exact solution for a specific

case and compare the approximate and exact solutions. Studying the exact solution helps

to avoid errors related to employing the momentless theory. The method under consid-

eration may be used to increase the correctness of estimating the components of the

stress-strain state of the fairing.

Keywords

: composite, conical shell, non-uniform heating, exact analytical solution, fai-

ring, inhomogeneous Bessel equation.

REFERENCES

[1]

Sarbaev B.S.

Nauka i obrazovanie: nauchnoe izdanie MGTU im. Baumana —

Science and Education: Scientific Edition of Bauman MSTU

, 2015, no. 4,

pp. 58–72. DOI: 10.7463/0415.0765910

[2]

Biderman V.L.

Mekhanika tonkostennykh konstruktsiy. Statika

[Thin Shell

Structure Mechanics. Statics]. Moscow, Mashinostroenie Publ., 1977, 488 p.

[3]

Weicheng Cui, Junhou Pei, Wei Zhang.

Computers and Structures

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pp. 265–279. DOI: 10.1016/S0045-7949(00)00139-5

Sarbaev B.S.

, Dr. Sci. (Eng.), Professor, Department of Spacecraft and Launch Vehicles,

Bauman Moscow State Technical University. Author of over 40 scientific publications in

the fields of composite mechanics, plasticity theory, non-linear deformation of composite

materials and structures. e-mail:

bssarbayev@mail.ru

Razhev V.V.

, student of the Department of Applied Mechanics, Bauman Moscow State

Technical University. e-mail:

125_00@mail.ru