Optimization calculation of the geometric parameters of a structure with cardboard filler

F. R. Shakirzyanov ; R. A. Kayumov ; I. M. Zakirov ; G. G. Karimova ; I. Z. Muhamedova ; B. F. Tazyukov

Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 160 (2018) no. 4, pp. 695-708

Résumé

The problem of estimation of the bearing capacity of panels with a folded filler from cardboard has been considered. The strength and stiffness characteristics of the cardboard along and across the fibers have been determined by testing the cardboard samples for tension, compression, three-point bending, and shear. The results of the experiments demonstrate that when the cardboard is deformed after reaching a certain value, the yield surface is observed. This enables us to calculate the structure of cardboard according to the theory of limit equilibrium. A model of deformation of the structure of a core from cardboard has been constructed. A technique for estimating its ultimate load has been developed. Based on the kinematic and static theorems of the theory of limit equilibrium, the maximum load at which the structure collapses is determined. The limiting load has been found using the method of variation of elastic characteristics, which allows to obtain the lower and upper bounds of the limiting load simultaneously. As a criterion for cardboard strength, the Tsai–Wu criterion has been used. To sample the calculation area, the finite element method has been used. The comparative analysis of the numerical calculations with the results obtained from analytical formulas has been carried out. Numerical experiments have been performed. The regularities of the influence of geometrical parameters of the filler on the maximum load of the structure have been revealed. The optimal parameters of the geometry of the aggregate have been determined from the condition of the minimum weight of the structure with its maximum bearing capacity.

Détail

Keywords: limit load, experiment, optimization, finite element method.
Mots-clés : identification

Bibliographie

[1] Zakirov I. M., Karimova G. G., “The effort applied for creasing plates having a clip in a rigid matrix with a groove”, Evraz. Soyuz Uch. (ESU), 2016, no. 2, 60–61 (In Russian)

[2] Zakirov I., Alexeev K., “Sandwich panel featuring chevron cores for airframe and building structures: properties and technology thereof”, SAMPE Europe 29th Int. Conf. and Forum (Paris, 2008), 201–205

[3] Zakirov I. M., Nikitin A. V., Karimova G. G., “Investigation of creasing and cardboard folding operations”, Vestn. KGTU im. A.N. Tupoleva, 2015, no. 5, 76–82 (In Russian)

[4] Alekseev K. A., Zakirov I. M., Karimova G. G., “Geometrical model of creasing roll for manufacturing line of the wedge-shaped folded cores production”, Russ. Aeronaut., 54:1 (2011), 104–107 | DOI

[5] Nagasawa S., Endo R., Fukuzawa Y., Uchino S., Katayama I., “Creasing characteristic of aluminum foil coated paperboard”, J. Mater. Process. Technol., 201:1–3 (2008) | DOI

[6] State Standard 32659-2014. Polymer composites. Testing methods. Determination of interlaminar shear strength by short-beam method, Standartinform, M., 2014, 19 pp. (In Russian)

[7] State Standard 1924-1-96. Paper and board. Determination of tensile properties. Part 1. Constant rate of loading method, Izd. Standartov, M., 1999, 10 pp. (In Russian)

[8] State Standard 13648.2-68. Paper and board. Determination of tensile properties. Part 1. Constant rate of loading method, Izd. Standartov, M., 1999, 4 pp. (In Russian)

[9] Alfutov N. A., Zinov'ev P. A., Popov B. G., Calculation of Multilayer Plates and Shells of Composite Materials, Mashinostroenie, M., 1984, 263 pp. (In Russian)

[10] Alfutov N. A., Zinov'ev P. A., Tairova L. P., “Identification of elastic characteristics of unidirected materials on the basis of testing multilayer composites”, Raschety Prochn., 30 (1989), 16–31 (In Russian)

[11] Kayumov R. A. The extended problem of identification of mechanical characteristics of materials based on the results of testing of constructions, Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, 2004, no. 2, 94–105 (In Russian)

[12] Hahn H. T., Tsai S. W., Introduction to Composite Materials, Technomic Publ. Comp., 1980, 467 pp.

[13] Narayanaswami R., Adelman H. M., “Evaluation of the tensor polynomial and Hoffman strength theories for composite materials”, J. Compos. Mater., 11:4 (1977), 366–377 | DOI

[14] Kayumov R. A., “A method for two-sided limiting load estimation”, Strength Mater., 24:1 (1992), 64–70 | DOI

[15] Kayumov R. A., Shakirzyanov F. R., “Behavior simulation and bearing capacity estimation of a thin-walled structure-soil system with account of soil creep and degradation”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 153, no. 4, 2011, 67–75 (In Russian) | MR

[16] Berezhnoi D. V., Amirova R. M., Balafendieva I. S., Sekaeva L. R., “Calculation of stress-strain and ultimate state of soil in the zone of well drilling and installation”, Proc. XXII Int. Symp. “Dynamic and Technological Problems of Structural Mechanics and Continuous Media” Dedicated to A.G. Gorshkov, v. 1, TR-Print, M., 2016, 42–44

[17] Sultanov L. U., “Calculation of elastic-plastic deformations by FEM”, IOP Conf. Ser.: Mater. Sci. Eng., 158:1 (2016), 012090, 1–5 | DOI | MR