Optimization of Bendable I-Section Elements Subject to Corrosion and Material Damage

image_print
DOI https://doi.org/10.15407/pmach2020.03.060
Journal Journal of Mechanical Engineering – Problemy Mashynobuduvannia
Publisher A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN 0131-2928 (Print), 2411-0779 (Online)
Issue Vol. 23, no. 3, 2020 (September)
Pages 60-67
Cited by J. of Mech. Eng., 2020, vol. 23, no. 3, pp. 60-67

 

Author

Мark M. Fridman, Kryvyi Rih Metallurgical Institute of the National Metallurgical Academy of Ukraine (5, Stephan Tilha St., Kryvyi Rih, 5006, Ukraine), e-mail: mark17@i.ua, ORCID: 0000-0003-3819-2776

 

Abstract

Operation of structures in high temperature conditions and aggressive environments leads to such phenomena as corrosion and material damage. Corrosion leads to a reduction in structural cross-section and, consequently, an increase in stresses. As to material damage, namely, the appearance of micro-cracks and voids resulting from inelastic creep strain, it leads to a deterioration of physical characteristics (for example, the elastic modulus) and a sharp decrease in   the stress values at which structural failure occurs. This paper is a continuation of the research in the field of optimal design of structures operating under conditions of corrosion and material damage (high temperature, aggressive environment, etc.). A first paper in this field was devoted to the optimization of bendable rectangular cross-section elements. This paper considers the optimization of the lengthwise thickness of flanges of bendable I-section elements, using the same principle of equal damage, which was applied to optimize the bendable rectangular cross-section elements. It is assumed that the flange width and web height of an I-section element are fixed. Since, during bending, mainly I-beam flanges work (their moment of inertia is 85% of the moment of inertia of the entire cross-section), the web is not taken into account in the calculation. As an equation of corrosion, V. M. Dolinsky’s model is adopted, taking into account the effect of tension on the corrosion wear of structures. In the model of the kinetic equation that describes the change in material damage, Yu. N. Rabonov’s model is adopted, where the value of damage ω varying from 0 to 1 is taken to be a variable parameter. As the criterion of optimality, the minimum weight of structures is adopted. In conclusion, presented is an algorithm for solving a more complete problem of optimizing the parameters of bendable I-section elements, namely, the web height and the flange width, using the obtained analytical expressions that determine the optimal distribution of the thickness of flanges along the length of the structure.

 

Keywords: corrosion, material damage, optimization.

 

Full text: Download in PDF

 

References

  1. Kachanov, L. M. (1974). Osnovy mekhaniki razrusheniya [Fundamentals of fracture mechanics]. Moscow: Nauka, 308 p. (in Russian).
  2. Kachanov, L. M. (1985). O vremeni razrusheniya v usloviyakh polzuchesti [On the time of fracture under creep conditions]. Izv. AN SSSR. Otd. tekhn. nauk – Proceedings of the USSR Academy of Sciences. Department of Technical Sciences, no. 8, pp. 26–31 (in Russian).
  3. Rabotnov, Yu. N. (1966). Polzuchest elementov konstruktsiy [Creep of structural elements]. Moscow: Nauka, 752 p. (in Russian).
  4. Lemaitre, J. (1984). How to use damage mechanics. Nuclear Engineering and Design, vol. 80, iss. 2, pp. 233–245. https://doi.org/10.1016/0029-5493(84)90169-9.
  5. Chaboche, J.-L. (1981). Continuous damage mechanics – a tool to describe phenomena before crack initiation. Nuclear Engineering and Design, vol. 64, iss. 2, pp. 233–247. https://doi.org/10.1016/0029-5493(81)90007-8.
  6. Golub, V. P. (1996). Non-linear one-dimensional continuum damage theory. International Journal of Mechanical Sciences, vol. 38, iss. 10, pp. 1139–1150. https://doi.org/10.1016/0020-7403(95)00106-9.
  7. Sosnovskiy, L. A. & Shcherbakov, S. S. (2011). Kontseptsii povrezhdennosti materialov [Concepts of material damage]. Vestnik TNTU – Scientific journal of TNTU, Special Issue (1), pp. 14–23 (in Russian).
  8. Travin, V. Yu. (2014). Otsenka povrezhdennosti materiala pri raschete prochnosti i dolgovechnosti elementov korpusnykh konstruktsiy [Assessment of material damage in calculating the strength and durability of elements of hull structures]. Izv. Tul. un-ta. Tekhn. nauki – Izvestiya Tula State University. Series: Technical science, iss. 10, part 1, pp. 128–132 (in Russian).
  9. Volegov, P. S., Gribov, D. S., & Trusov, P. V. (2017). Damage and fracture: Classical continuum theories. Physical Mesomechanics, vol. 20, iss. 2, pp. 157–173. https://doi.org/10.1134/S1029959917020060.
  10. Kostyuk, A. G. (1953). Opredeleniye profilya vrashchayushchegosya diska v usloviyakh polzuchesti [Determination of the profile of a rotating disk under creep conditions]. Prikl. matematika i mekhanika – Journal of Applied Mathematics and Mechanics, vol. 17, iss. 5, pp. 615–618 (in Russian).
  11. Reitman, M. I. (1967). Theory of the optimum design of plastics structures with allowance for the time factor. Polymer Mechanics, vol. 3, iss. 2, pp. 243–244. https://doi.org/10.1007/BF00858872.
  12. Prager, W. (1968). Optimal structural design for given stiffness in stationary creep. Journal of Applied Mathematics and Physics (ZAMP), vol. 19, iss. 2, pp. 252–256. https://doi.org/10.1007/BF01601470.
  13. Nemirovskii, Yu. V. (1971). Design of optimum disks in relation to creep. Strength of Materials, vol. 3, iss. 8, pp. 891–894. https://doi.org/10.1007/BF01527642.
  14. Nemirovsky, Yu. V. (2014). Creep of clamped plates with different reinforcement structures. J. Appl. Mechanics and Techn. Physics, vol. 55, pp. 147–153. https://doi.org/10.1134/S0021894414010179.
  15. Zyczkowski, M. (1971). Optimal structural design in rheology. Journal of Applied Mechanics, vol. 38, iss. 1, pp. 39–46. https://doi.org/10.1115/1.3408764.
  16. Pochtman, Yu. M. & Fridman, M. M. (1997). Metody rascheta nadezhnosti i optimalnogo proyektirovaniya konstruktsiy, funktsioniruyushchikh v ekstremalnykh usloviyakh [Methods for calculating the reliability and optimal design of structures operating in extreme conditions]. Dnepropetrovsk: Nauka i obrazovaniye, 134 p. (in Russian).
  17. Fridman, M. M. & Zyczkowski, M. (2001). Structural optimization of elastic columns under stress corrosion conditions. Structural and Multidisciplinary Optimization, vol. 21, iss. 3, pp. 218–228. https://doi.org/10.1007/s001580050186.
  18. Fridman, M. M. & Elishakoff, I. (2015). Design of bars in tension or compression exposed to a corrosive environment. Ocean Systems Engineering, vol. 5, iss. 1, pp. 21–30. https://doi.org/10.12989/ose.2015.5.1.021.
  19. Fridman, M. M. (2016). Optimalnoye proyektirovaniye trubchatykh sterzhnevykh konstruktsiy, podverzhennykh korrozii [Optimal design of tubular bar structures subject to corrosion]. Problemy mashinostroyeniya – Journal of Mechanical Engineering, vol. 19, no. 3, pp. 37–42 (in Russian). https://doi.org/10.15407/pmach2016.03.037.
  20. Fridman, М. M. (2019). Optimal Design of Bending Elements in Conditions of Corrosion and Material Damage. Journal of Mechanical Engineering, vol. 22, no. 3, pp. 63–69. https://doi.org/10.15407/pmach2019.03.063.
  21. Dolinskii, V. M. (1967). Calculations on loaded tubes exposed to corrosion. Chemical and Petroleum Engineering, vol. 3, iss. 2, pp. 96–97. https://doi.org/10.1007/BF01150056.
  22. Gurvich, I. B., Zakharchenko, B. G., & Pochtman, Yu. M. (1979). Randomized algorithm to solve problems of nonlinear programming. Izvestiya Akademii nauk SSSR. Tekhnicheskaya kibernetika – Bulletin of the USSR Academy of Sciences. Engineering Cybernetics, no. 5, pp. 15–17 (in Russian).

 

Received 10 March 2020

Published 30 September 2020