Compromise optimization of a composite plate with a given probability of realization

Abstract

A method is proposed for solution of the problem of the compromise optimization of three properties of a composite plate (thermal conductivity, stability, and the probability P^* of design realization), which depend on three initial stochastic data with constant average values, and two variable initial data. The geometry of the domain of plate properties, the curve of optimal Pareto solutions, and the scatter ellipses is determined at four points for a given range of variable parameters. A method of constructing the curves of optimal Pareto solutions for the following assigned probabilities of design realization is proposed and numerically implemented: P^*=0.40, 0.80, and 0.95. The generalized efficiency function Φ_Σ (Φ_Σ → max, 0 ≤ Φ_Σ ≤ 1) of the first two properties decreases from 0.74 to 0.23 as the numerical value of P^* increases from 0.40 to 0.95. A family of isolines Φ_Σ = const is plotted for all three properties investigated, and max Φ_Σ determined as 0.63.