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

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DOI https://doi.org/10.15407/pmach2020.03.060
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. 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.

 

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Received 10 March 2020