Вероятностный коэффициент эффективности материала и пример его применения

Abstract

The paper introduces a mathematical derivation of probability density function for a random variable which is a comparative material's mass or cost efficiency coefficient. At early development stage, the coefficient allows a scientifically based selection of material, taking into account its strength or stiffness, weight or cost characteristics. A distinctive feature of the coefficient is the ability to take into account the effect on material efficiency when the material is applied to a thin-walled body structure of an important technological limitation: the discreteness of the standard range of sheet material thicknesses. This function makes it possible to determine with high accuracy the probability of the deviation of the considered random variable from its expectation not further than the limits of a given interval. The use of this function leads to a significant improvement in the developed methodology for selecting an effective material at the development stage of a thin-walled product, the methodology being previously based on the application of Chebyshev's inequality. We give an example of selecting an effective material from the list of materials considered for a cover sheet of a sandwich-panel under buckling condition.