|Journal||Journal of Mechanical Engineering|
|Publisher||A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
|ISSN||0131-2928 (Print), 2411-0779 (Online)|
|Issue||Vol. 22, no. 3, 2019 (September)|
|Cited by||J. of Mech. Eng., 2019, vol. 22, no. 3, pp. 63-69|
Мark M. Fridman, Kryvyi Rih Metallurgical Institute of the National Metallurgical Academy of Ukraine (5, Stephan Tilho Str., Kryvyi Rih, 5006, Ukraine), e-mail: firstname.lastname@example.org, ORCID: 0000-0003-3819-2776
During operation, many of the critical elements of building and engineering structures are in difficult operating conditions (high temperature, aggressive environment, etc.). In this case, they may be subject to a double effect: corrosion and material damage. Corrosion leads to a reduction in the cross-section of a structure, resulting in stress increase therein. In turn, the damage to the material is accompanied by the appearance of microcracks and voids therein due to inelastic deformation (creep), which leads to a deterioration of physical characteristics of the material (for example, elastic modulus) and a sharp decrease in the stress values at which the structure is destroyed. This paper considers the optimization of bending rectangular cross-section elements operated in conditions conducive to the appearance of both corrosion and material damage. As the equation of corrosion, the model of V. M. Dolinsky is taken. This model takes into account the effect of stresses on the corrosion wear of structures. As a kinetic equation describing the change in material damage, the model of Yu. N. Rabotnov is used. The optimality criterion is the minimum mass of the structure. The height of the rectangular cross-section bending element along its length is optimized using the principle of equal damage at the final moment of the lifetime of the structure. The proposed approach can be used to solve similar problems of the optimal design of structures operating in conditions of corrosion and material damage with the use of both analytical solutions and numerical methods.
Keywords: corrosion, material damage, optimization.
Full text: Download in PDF
- Kachanov, L. M. (1974). Osnovy mekhaniki razrusheniya [Fundamentals of fracture mechanics]. Moscow: Nauka, 308 p. (in Russian).
- 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).
- Rabotnov, Yu. N. (1966). Polzuchest elementov konstruktsiy [Creep of structural elements]. Moscow: Nauka, 752 p. (in Russian).
- 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
- 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
- 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
- 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).
- 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.
- 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
- 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).
- 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
- 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
- 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
- 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
- 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.
- 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
- Fridman, M.M. & Elishakoff, I. (2013). Buckling optimization of compressed bars undergoing corrosion. Ocean Systems Engineering, vol. 3, iss. 2, pp. 123–136. https://doi.org/10.12989/ose.2013.3.2.123
- 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
- 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
- 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
- Gurvich, I. B., Zakharchenko, B. G., & Pochtman, Yu. M. (1979). Randomized algorithm to solve problems of nonlinear programming. Izv. Ac. Sci. USSR. Engineering Cybernetics, no. 5, pp. 15–17 (in Russian).
Received 17 April 2019
Published 30 September 2019