On probabilistic methods application to solving aircraft strength inverse coefficient problems

Aeronautical and Space-Rocket Engineering

Strength and thermal conditions of flying vehicles

DOI: 10.34759/vst-2019-4-42-50


Valitova N. L., Kostin V. A.*

Kazan National Research Technical University named after A.N. Tupolev, KNRTU-KAI, 10, Karl Marks str., Kazan, 420111, Russia

*e-mail: VAKostin@kai.ru


Solving problems of static strength, fatigue resistance, and aeroelasticity can be performed in both deterministic and probabilistic formulation. Deterministic approach for aircraft strength computing is adopted as the basic one both in this country and abroad. Aircraft safety requirements increasing leads to the necessity of considering probabilistic safety criteria and development of normative standards for them.

The article deals with solving the inverse strength problems in a probabilistic setting in a general form. In the most general case, the elements of the “output”, as well as parameters of the structure under study, characterized by a certain operator, are stochastic. It is assumed that the probabilistic measure of the “output” is known and can be defined in the form of theoretical distribution law. In this case, the inverse strength problem in probabilistic setting is reduced to either determining the probabilistic measure of parameters of the “input” (at the determined parameters of the “object”), or to determining the probabilistic measure of the “object” parameters. It is assumed initially, that the problems under consideration are quasi-static, and unique deterministic dependence between the “input” and the “output” is known.

Examples of linear transformations for random variables are given when determining probability characteristics of load restoration and identification of structures for the two models, namely a beam and a thin-walled Odinokov’s structure.

Further, the article presents methods for analyzing static systems with random parameters. The real structural elements parameters randomness is being caused by the external environment disturbing effects, unavoidable technological production errors etc. It manifests in the form of cracks, starved spots, initial irregularities and other factors, which may affect the structure behavior in various ways. In particular, destruction may be associated with a large number of dislocations and stresses redistributions. This allows expecting non-linear manifestations in the structure material behavior in the form of hysteresis loops, leading in general case to non-Gaussian distribution of random values.

When considering static systems hereafter, an internal random value (e.g. crack) is being interpreted as an additional random impact at the deterministic system input. This affects the system behavior and leads to natural mixing of random output processes while their transformation in the system, i.e. the effect of natural formation of mixture of distributions.

The examples of determining the probability density for the potential energy dissipation of the rod deformation at random thermal effects, as well as functions of the mixture density in the presence of the internal defect in the beam were considered.

The obtained material can be recommended for developing a base of standards on mixtures’ references necessary for the purposes of structures diagnostics.


random values, random phenomena mixing, stiffness properties


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