PROBLEM OF MULTIPARAMETRIC OPTIMIZATION
OF THE CONSTRUCTION OF THE JOINT BETWEEN THE CERAMIC HULL
AND METALLIC FUSELAGE OF AN AIRPLANE
D. A. Rogov
and P. V. Kovalenko
Translated from Novye Ogneupory, No. 10, pp. 24 – 30, October, 2014.
Original article submitted September 1, 2014.
An approach to the solution of the problem of determining the optimal design of the connector assembly be
tween the ceramic hull of a high-speed airplane and its metallic fuselage is presented. Definitions of the pa
rameters that exert an effect on the bearing capacity of this assembly are given. An example illustrating the so
lution of the problem of finding the optimum of the parameters of a construction for the case of a three-layer
axisymmetric model is presented.
Keywords: ceramic hull, optimization parameter, penalty function, objective function, heat resistance, con-
vective heat exchange, stresses
The designer must often find a compromise between fac-
tors that exert a mutually inverse influence on the decision
process. For example, a variation in some parameter may
have a positive influence on certain properties of a construc-
tion and, at the same time, affect other properties negatively.
In such cases a so-called “golden mean,” or optimum has to
A reliable connection between the ceramic hull of a
high-speed airplane with its metallic fuselage is a complex
construction problem, since it must comply with a number of
requirements. In particular, for constructions with an adhe
sive method of connection between the ceramic and metallic
rings significant heating across the entire connector assem
bly is not acceptable, since, in the first place, advancing ther
mal expansion of the metal leads to the appearance of critical
stresses in the ceramic, and, secondly, the strength of the ad
hesive falls significantly at high temperatures .
The solution of an optimization problem comprises the
following stages: the creation of a mathematical model that
describes the essence of a physical phenomenon;
parameterization of the problem; selection of the objective
function, which generally depends on a large number of vari-
ables; and finding a minimum of the function in a region,
membership to which is specified by a condition according
to which a certain number of constraints (equalities or in-
equalities) is satisfied. The existence of constraints substan-
tially increases the complexity of a minimization problem,
since in the constricted space of the optimized parameters the
extremum of an objective function is not necessarily found at
a point with zero gradient and, as a rule, proves to be at the
boundary of the search domain.
MATHEMATICAL STATEMENT OF PROBLEM
Heat Resistance Problem
Let us model the adhesive joint of a ceramic fairing with
a metallic frame in the form of a three-layer annular con
struction of a given length (Fig. 1). The outer surface of the
ceramic wall interacts with the surrounding medium in the
form of combined convective and radiant heat exchange. On
the inner surface of the metallic ring we limit the discussion
to the case of heat discharge exclusively by radiation. The
side surfaces are assumed to be adiabatic (heat flow through
the surface q = 0). All the required properties of the materials
are known. We will state the problem mathematically.
Under given conditions the temperature in a three-layer
wall will be a function of only a single coordinate r, and the
Refractories and Industrial Ceramics Vol. 55, No. 5, January, 2015
1083-4877/15/05505-0396 © 2015 Springer Science+Business Media New York
GNTs Russian Federation OAO ONPP Tekhnologiya, Obninsk,
Kaluga District, Russia.