RADIOELECTRONIC AND COMPUTER SYSTEMS

A genetic algorithm for solving the problem of optimal beam material distribution along length at a given restriction on maximum sagging value is suggested. A review of literature sources is conducted and it was shown that existing solutions cover partial cases only in which the position of the point with maximum sagging was defined previously. In the paper presented I-section beam with constant proportions is considered, i.e., beam width, caps, and web thickness are proportional to beam height in the current cross-section. A statically determined beam is being considered. The load applied to a beam can be arbitrary, including cases of non-symmetrical loads and differently oriented ones. The position of point(s) at which beam sagging is maximum are unknown at the beginning of optimization and are found in the process solution. The problem is solved in the linear definition. Beam mass was assumed to be an optimization criterion. The method of finite differences is used for beam sagging finding, i.e., for the solution of the differential equation of the bending beam with a variable cross-section. Discretization allows transforming the problem of design into the problem of beam height determination at a system of reference points. At this stage, found values of beam height must satisfy restrictions on reference point displacements. The suggested technique allows controlling beam displacement quite flexibly because restrictions on point displacement are considered separately and do not depend on each other. The suggested objective function is the linear superposition of beam mass and the possible penalty in case of beam maximum sagging over exceeding predefined values. The application of a genetic algorithm allows getting sets of beam thicknesses those, which guaranty reaching the minimum of the objective function. The model problem is solved. It is shown that the suggested algorithm allows effectively solves problems of optimal design of beams with restrictions on the maximum sagging value. The suggested approach can be developed for strength restrictions, statically undetermined structures, etc.

conditional optimization; method of finite differences; genetic algorithm

Vasiliev, V. V. Optimal Design of a Composite Cylindrical Grid Shell Loaded with External Pressure. Mech. Solids, 2020, no. 55, pp. 303–308. DOI: 10.3103/S0025654420030152.

Kondratiev, A., Gaidachuk, V. Weight-based optimization of sandwich shelled composite structures with a honeycomb filler. Eastern-European Journal of Enterprise Technologies, 2019, vol. 1, no. 1(97), pp. 24–33. DOI: 10.15587/1729-4061.2019.154928.

Misura, S., Smetankina, N., Misiura, I. Optimal Design of the Cyclically Symmetrical Structure Under Static Load. Integrated Computer Technologies in Mechanical Engineering – 2020. ICTM 2020. Lecture Notes in Networks and Systems, 2021, vol. 188, pp. 256-266. DOI: 10.1007/978-3-030-66717-7_21.

Sonmez, F. O. Optimum Design of Composite Structures: A Literature Survey (1969–2009). Journal of Reinforced Plastics and Composites, 2016, vol. 36, no. 1, pp. 1–37. DOI: 10.1177/0731684416668262.

Banichuk, N. V. Vvedenie v optimizaciju konstrukcij [Introduction to Design Optimization]. Moscow, Nauka Publ., 1986. 302 p.

Alekhin, V. V. Design of a transversely layered cantilever of minimum mass under specified maximum-deflection constraint. Journal of Applied Mechanics and Technical Physics, 2007, vol. 48, no. 4, pp. 556-561. DOI: 10.1007/s10808-007-0070-3.

Reitman, M. I. Optimization of Elastic Flexible Bars. Engineering Optimization, 1995, vol. 23, no. 3, pp. 173–186. DOI: 10.1080/03052159508941352.

Gurchenkov, A. A., Vilisova, N. T., German, I. M., Romanenkov, A. M. Uprugie balki minimal'nogo vesa, pri nalichii neskol'kikh vidov izgibayushchikh nagruzok [Elastic beams of minimum weight, in the presence of several types of bending loads]. Inzh. zhurnal: nauka i innovatsii – Eng. journal: science and innovation, 2015, no. 5(41). 9 p.

Zrazhevsky, G., Golodnikov, A. Uryasev, S. Mathematical Methods to Find Optimal Control of Oscillations of a Hinged Beam (Deterministic Case). Cybernetics and Systems Analysis, 2019, vol. 55, no.41, pp. 1009-1026. DOI: 10.1007/s10559-019-00211-x.

Kurennov, S. S. Optimal'noe proektirovanie staticheski opredelimoi balki pri ogranichenii na maksimal'nyi progib [Optimum design of a statically definable beam with limitation on the maximum beam deflection]. Aviacijno-kosmicna tehnika i tehnologia – Aerospace technic and technology, 2020, vol. 1(161), pp. 28-34. DOI: 10.32620/aktt.2020.1.05.

Kushnir, M. Ya., Tokarieva, K. A. Vykorystannya system shtuchnoho intelektu u zadachakh prohnozuvannya finansovykh indeksiv: ohlyad naukovykh dzherel [Artificial intelligence systems in the financial market predictions: literature review]. Radioelektronni i komp'uterni sistemi – Radioelectronic and computer systems, 2020, no. 3, pp. 108–117. DOI: 10.32620/reks.2020.3.11.

Soremekun, G., Gürdal, Z., Kassapoglou, C., Toni, D. Stacking sequence blending of multiple composite laminates using genetic algorithms. Composite Structures, 2002, vol. 56б no. 1, pp. 53–62. DOI: 10.1016/s0263-8223(01)00185-4.

Sjølund, J. H., Peeters, D., Lund, E. Discrete Material and Thickness Optimization of sandwich structures. Composite Structures, 2019, vol. 217, pp. 75–88. DOI: 10.1016/j.compstruct.2019.03.003.

Shi, J.-X., Yoshizumi, K., Shimoda, M., & Sakai, S. Free-form optimization of heteromorphic cores in sandwich structures to enhance their thermal buckling behavior. Structural and Multidisciplinary Optimization, 2021, vol. 64, pp. 1927-1937. DOI: 10.1007/s00158-021-02955-7.

Kashanian, K., Kim, I. Y. A novel method for concurrent thickness and material optimization of non-laminate structures. Structural and Multidisciplinary Optimization, 2021, vol. 64, no. 3, pp. 1421–1437. DOI: 10.1007/s00158-021-02928-w.

Kurennov, S. S. Longitudinal-Flexural Vibrations of a Three-Layer Rod. An Improved Model. Journal of Mathematical Sciences, 2016, vol. 215, no. 2, pp. 159 169. DOI: 10.1007/s10958-016-2829-7.

Kurennov, S. S., Barakhov, K. P., Poliakov, A. G. Stressed State of the Axisymmetric Adhesive Joint of Two Cylindrical Shells under Axial Tension. Materials Science Forum, 2019, vol. 968, pp. 519–527. DOI: 10.4028/www.scientific.net/msf.968.519.