Analysis of the dependence of the optimal location of the supports along the length of the plate on the ratio of the sides

DOI: 10.37153/2618-9283-2024-6-73-81

Authors:  
Rubric:     Theoretical and experimental studies   
Key words: rectangular plate, elasticity, deflection, optimal location, strength, analysis, dependencies, side relations, performance
Annotation:

Introduction. Thin-walled structures consisting of thin rods, plates and shells are widely used in modern construction, mechanical engineering, shipbuilding, aircraft manufacturing and other fields.

In the field of engineering structures, there are problems of strength under the action of normal distributed loads on a rectangular plate [6, 7, 8, 9]. In modern structures, elastic isotropic plates under an arbitrary distributed load are of great practical application [10, 11, 12]. In the field of studying the strength and stability of a rectangular plate, it is worth noting the works of S.P. Timoshenko [1], S.A. Ambartsumyan and others. In the field of optimal design of thin-walled structural elements, namely in problems of plate bending, the issues of determining the optimal location of supports have not been sufficiently studied. These issues are considered in the works of V.Ts. Gnuni and A.V. Eloyan [2, 3, 4, 5].

Purpose. The purpose of the work is to determine the optimal location of supports for an elastic rectangular plate in bending problems providing the lowest values of the maximum deflection of the plate.

Materials and methods. An analysis of the dependence of the effect of the optimal location of supports along the length of the plate on the aspect ratio of the plate is presented.

Results. Based on the results obtained, it is possible to significantly improve the performance characteristics of isotropic plates.

Conclusions. Determining the optimal location of supports is of particular interest for studying the strength of structures.

Used Books:

1.    Timoshenko S.P., Voinovsky-Kreger S. Plates and shells. Moscow: Fizmatgiz. 1963, 635 p.

2.    Gnuni V.Ts. Optimal choice of support location in problems of bending, vibrations and stability of an elastic beam. In the collection. Yerevan State University. 1997, pp.114–117.

3.    Gnuni V.Ts., Eloyan A.V. Optimal choice of support arrangement in the problem of bending a rectangular plate made of a composite material. Izvestiya NAS RA. 2002, vol. 55, no. 2, pp. 8–13.

4.    Eloyan A.V. Optimal choice of the location of supports in an elastic isotropic rectangular plate under the influence of transverse load and temperature field. Izvestiya NAS RA. 2013, vol. 66, no. 4, pp. 17–22.

5.    Eloyan A.V., Karapetyan J.K., Matevosyan G.M., Vardanyan V.A. Optimal choice of support location in the problem of stability of a rectangular plate under the influence of a temperature field. Bulletin of the Scientific Research Center “Construction”. 2022, no. 3(34), pp. 45–54.

6.    Optimal design of structures. Bibliographic Index / Compilers; Vakulenko L.D., Mazalov V.P. Novosibirsk, 1975. Part I, pp.1–121, Part II, pp. 222–472.

7.    Obraztsov I.F., Vasiliev V.V. Optimal design of plates and shells made of reinforced plastics. In the book; Theory of plates and shells, Moscow: Science. 1971, pp. 204–215.

8.    Grigoryan S.A. On an optimization problem for a round plate. Izvestiya NAS RA, 1989, vol. 42, no.6, pp. 50–53.

9.    Zhu S.Ya., Prager W. Recent advances in optimal design of structures. Mechanics, collection. 1969, no. 6, pp.129–143.

10.                       Teters G.A., Rickards R.B., Narusberg V.L. Optimization of shells made of layered composites. Riga: Zinatne, 1978, 238 p.

11.                       Niordson F.I., Pedersen P. Review of research on optimal design of structures. Mechanics, collection. 1973, no. 2, pp. 136–157.

12.                       Wasintyski Z., Brand A. The Present state of Knowledge in the Field Optimum Design of Strictures. Apple. Mech. Rew., 1963, vol.16, no. 5, pp. 344–350.