Polynomial Approximation-Based Optimal Design of Structures Interacting with an Aggressive Environment by the Random Sea
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POLYNOMIAL APPROXIMATION-BASED OPTIMAL DESIGN OF STRUCTURES INTERACTING WITH AN AGGRESSIVE ENVIRONMENT BY THE RANDOM SEARCH METHOD G. V. Filatov
UDC 539.4
The optimal design of structures that interact with an aggressive environment is considered on the example of a thin-walled shell exposed to the internal pressure of the aggressive gas. The simplicity of the above research object is related to quite simple equations describing the stress-strain state (SSS) of the structure. Any mathematical model simulating the corrosion damage process includes empirical coefficients characterizing the degree of influence of certain factors on the corrosion rate. Some coefficients (mainly those describe the corrosive environment behavior, which controls the temperature, concentration of certain substances, etc.) are constant, while others that describe the SSS effect on the corrosion damage rate of the structure, according to earlier findings of the author, vary during the optimal design procedure, significantly affecting the final design results. It should be noted that the proposed method should be applied not at the operation stage of the structure but at its design stage. To define the coefficients of the mathematical model of corrosion damage, a numerical method for multiple identifications of the mathematical model based on experimental data was proposed. This method gives satisfactory results but is quite cumbersome and time-consuming. The analytical method of polynomial approximation gives results comparable in efficiency but is more flexible and fast. Two modifications of the method of polynomial approximation to define the “optimal” set of coefficients of mathematical models of corrosion damage are developed. Numerical simulations are performed for the optimal design of a thin-walled cylindrical shell exposed to an aggressive environment. Keywords: optimal design, stress state, mathematical modeling, polynomial approximation, corrosion damage of structures. Notations d
– current value of the corrosion depth
t
– corrosion time
ei
– strain intensity
si
– stress intensity
s lim
– stress limit value, below which the SSS effect on the corrosion process rate is absent
a
– corrosion rate of unstressed material
Ukrainian State University of Chemical Technology, Dnipro, Ukraine ([email protected]). Translated from Problemy Prochnosti, No. 5, pp. 74 – 83, September – October, 2020. Original article submitted February 20, 2019. 0039–2316/20/5205–0753 © 2020 Springer Science+Business Media, LLC
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f
– operator, which is a function of stress and strain intensities
d ej
– experimental depth of corrosion damage
b- , b+
– lower and upper limits of the change in the parameter of the SSS influence on the rate of corrosion – process, respectively
x i- , x i+
– lower and upper limits of the control variables, respectively
r
– number of constraints
m
– number of control variables
A
– current value of the cross-sectional area of the shell, which is being optimized
h
– shell wall thickness
R
– radius of t
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