Probabilistic Material Efficiency Coefficient and Application Example

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

References

[1] Orlov L.N. Otsenka passivnoy bezopasnosti, prochnosti kuzovnykh konstruktsiy avtomobiley i avtobusov [Passive safety assessment and strength of automobile and bus bodies]. Nizhny Novgorod, NGTU Publ., 2005.

[2] Zuzov V.N., Ziyad A.D. Search for optimum solution for track frame on base of refined finite element models. Izvestiya vysshikh uchebnykh zavedeniy. Mashinostroenie [Proceedings of Higher Educational Institutions. Маchine Building], 2005, no. 12, pp. 46--66 (in Russ.).

[3] Voronkov O.V., Peskov V.I. Coefficient of material real mass efficiency and application methods. Trudy NGTU im. R.E. Alekseeva [Transactions of NNSTU n. a. R.E. Alekseev], 2016, no. 3, pp. 105--112 (in Russ.).

[4] Voronkov O.V., Peskov V.I. Effective combination of materials selection method for bus structure sandwich panel. Zhurnal AAI, 2010, no. 5, pp. 8--13 (in Russ.).

[5] Voronkov O.V., Peskov V.I. Snizhenie massy avtobusnogo kuzova za schet ispol’zovaniya trekhsloynykh paneley [Reduction of bus body mass using sandwich panels]. Nizhny Novgorod, Pero Publ., 2015.

[6] Gmurman V.E. Teoriya veroyatnostey i matematicheskaya statistika [Theory of probability and mathematical statistics]. Moscow, Yurayt Publ., 2014.

[7] Toray carbon fibers America, Inc. Quality carbon fiber, 2017.

[8] GOST 28007-88. Nit’ i zhgut SVM vysokomodul’nye tekhnicheskie. Tekhnicheskie usloviya [State standard 28007--88. High-modulus industrial jarn and tow "СВМ". Specifications]. Moscow, Izdatel’stvo standartov Publ., 1989.

[9] Nozdrina L.V., Korotkova V.I., Beyder E.Ya. Termoplasticheskie polimery dlya konstruktsionnykh kompozitnykh materialov (obzor) [Thermoplastic polymers for structural composites (review)]. Tekhnologiya. Ser. Konstruktsii iz kompozitsionnykh materialov [Technology. Constructions from Composite Materials], 1991, no. 1, pp. 3--10 (in Russ.).

[10] Epoxy and infusion matrix T-26: technical characteristics. inumit.ru: website. Available at: http://www.inumit.ru/img/file/tds_t_26.pdf (accessed: 15.05.2019).

[11] Kishkina S.I., Fridlyander I.N. Aviatsionnye materialy. T. 4. Alyuminievye i berillievye splavy. Ch. 1. Deformiruemye alyuminievye splavy i splavy na osnove berilliya. Kn. 1 [Aviation materials. Vol. 4. Aluminum and beryllium alloys. P. 1. Deformable aluminum and beryllium alloys. Book 1]. Moscow, ONTI Publ., 1982.