Estimated closeness of optimum piecewise constant section width in I-rods with stability or first eigen-frequency limits to the predicted minimum material consumption with regard to strength requirements
https://doi.org/10.31675/1607-1859-2020-22-4-114-125
Abstract
The previous research described estimated closeness of optimum piecewise constant section width in I-rods with stability or first eigen-frequency limits to the predicted minimum material consumption with regard to strength requirements in continuous change in variable rod parameters. It is however known that in construction, rods are generally designed with piecewise constant change in the section parameters. Besides, in another work, the criterion was formulated for assessment of optimum solutions of piecewise constant sections of I-rods with stability or the first eigen-frequency limits, without considering the strength requirements. This paper focuses on a more general problem of estimated closeness of optimum piecewise constant section width in I-rods with stability or first eigen-frequency limits to the predicted minimum material consumption with regard to strength requirements.
About the Authors
L. S. LyakhovichRussian Federation
Leonid S. Lyakhovich, DSc, Professor, Academician RAACS
2, Solyanaya Sq., 634003, Tomsk
P. A. Akimov
Russian Federation
Pavel A. Akimov, DSc, Professor, Academician RAACS;
2, Solyanaya Sq., 634003, Tomsk, Russia
26, Yaroslavskoe Road, 129337, Moscow, Russia
B. A. Tukhfatullin
Russian Federation
Boris A. Tukhfatullin, PhD, A/Professor
2, Solyanaya Sq., 634003, Tomsk, Russia
References
1. Abd Elrehim M.Z., Eid M.A., Sayed M.G. Structural optimization of concrete arch bridges using genetic algorithms. Ain Shams Engineering Journal. 2019. V. 10. I. 3. Pp. 507−516.
2. Afzal M., Liu Y., Cheng J.C.P., Gan V.J.L. Reinforced concrete structural design optimization: A critical review. Journal of Cleaner Production. 2020. V. 260, article 120623.
3. Belardi V.G., Fanelli P., Vivio F. Structural analysis and optimization of anisogrid composite lattice cylindrical shells. Composites Part B: Engineering. 2018. V. 139. Pp. 203−215.
4. Chen L.L., Lian H., Liu Z., Chen H.B., Atroshchenko E., Bordas S.P.A. Structural shape optimization of three dimensional acoustic problems with isogeometric boundary element methods. Computer Methods in Applied Mechanics and Engineering. 2019. V. 355. Pp. 926−951.
5. Khan W., Siraj-ul-Islam, Ullah B. Structural optimization based on meshless element free Galerkin and level set methods. Computer Methods in Applied Mechanics and Engineering. 2019. V. 344. Pp. 144−163.
6. Martin A., Deierlein G.G. Structural topology optimization of tall buildings for dynamic seismic excitation using modal decomposition. Engineering Structures. 2020. V. 216. 110717.
7. Nguyen L.C., Nguyen-Xuan H. Deep learning for computational structural optimization. ISA Transactions. 2020. V. 103. Pp. 177−191.
8. Lyakhovich L.S. Osobye svoistva optimal'nykh sistem i osnovnye napravleniya ikh realizatsii v metodakh rascheta sooruzhenii [Specific properties of optimum systems using methods of structural analysis]. Tomsk: TSUAB, 2009. 372 p. (rus)
9. Lyakyjvich L.S., Akimov P.A., Tukhfatullin B.A. Kriterij ocenki optimal'nyh reshenij pri formirovanii kusochno-postoyannyh uchastkov sterzhnej dvutavrovogo poperechnogo secheniya pri ogranicheniah po ustojchivosti ili velichiny pervoj chastoty sobsvtnnyh colebanij [Assessment criterion for optimum design solutions of piecewise constant sections in rods of I-shaped cross-section with stability or first eigen-frequency limits]. Vestnik Tomskogo gosudarstvennogo arkhitekturno-stroitel'nogo universiteta – Journal of Construction and Architecture. 2020. V. 22. No. 1. Pp. 92–105.
10. Lyakhovich L.S., Akimov P.A., Tukhfatullin B.A. Assessment of the proximity of design to minimum material capacity solution of problem of optimization of the flange width of I-shaped cross-section rods with allowance for stability constraints or constraints for the value of the first natural frequency and strength requirements. International Journal for Computational Civil and Structural Engineering. 2020. V. 16. I. 2. Pp. 71−82.
11. SNiP 16.13330.2017. Stal'nye konstruktsii (aktualizirovannaya redaktsiya SNiP II-23-81*) [Steel structures]. Moscow: Minstroi RF, 2017. 140 p. (rus)
12. Hadley G. Nelineinoe i dinamicheskoe programmirovanie [Nonlinear and dynamic programming]. Moscow: Mir, 1967. 507 p. (transl. from Engl.)
13. Lyakhovich L.S., Akimov P.A., Tukhfatullin B.A. Assessment criteria of optimal solutions for creation of rods with piecewise constant cross-sections with stability constraints or constraints for value of the first natural frequency. Part 1: Theoretical foundations. International Journal for Computational Civil and Structural Engineering. 2019. V. 15. I. 4. Pp. 88−100.
14. Lyakhovich L.S., P.A. Akimov P.A., Tukhfatullin B.A. Assessment criteria of optimal solutions for creation of rods with piecewise constant cross-sections with stability constraints or constraints for value of the first natural frequency. Part 2: Numerical examples. International Journal for Computational Civil and Structural Engineering. 2019. V. 15. I. 4. Pp. 101−110.
Review
For citations:
Lyakhovich L.S., Akimov P.A., Tukhfatullin B.A. Estimated closeness of optimum piecewise constant section width in I-rods with stability or first eigen-frequency limits to the predicted minimum material consumption with regard to strength requirements. Vestnik Tomskogo gosudarstvennogo arkhitekturno-stroitel'nogo universiteta. JOURNAL of Construction and Architecture. 2020;22(4):114-125. (In Russ.) https://doi.org/10.31675/1607-1859-2020-22-4-114-125