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

F.R. Shakirzyanov^a∗, R.A. Kayumov^a,b∗∗, I.M. Zakirov^b, G.G. Karimova^b∗∗∗, I.Z. Muhamedova^{a∗∗∗∗}, B.F. Tazyukov^{c∗∗∗∗∗}

^aKazan State University of Architecture and Engineering, Kazan, 420043 Russia

^bA.N. Tupolev Kazan National Research Technical University, Kazan, 420111 Russia

^cKazan Federal University, Kazan, 420008 Russia

E-mail: ^∗faritbox@mail.ru, ^∗∗kayumov@rambler.ru, ^∗∗∗kgg 1@mail.ru,

^∗∗∗∗muhamedova-inzilija@mail.ru, ^{∗∗∗∗∗}bulat.tazioukov@kpfu.ru

Received January 22, 2018

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Abstract

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.

Keywords: limit load, experiment, identification, optimization, finite element method

Acknowledgments. The study was performed within the the state assignment of the Ministry of Science and Higher Education of the Russian Federation no. 9.5762.2017/VU (project no. 9.1395.2017/PCh) and supported by the Russian Foundation for Basic Research (project no. 19-08-00349) and by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities (project no. 1.12878.2018/12.1.).

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For citation: Shakirzyanov F.R., Kayumov R.A., Zakirov I.M., Karimova G.G., Muhamedova I.Z., Tazyukov B.F. Optimization calculation of the geometric parameters of a structure with cardboard filler. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2018, vol. 160, no. 4, pp. 695–708. (In Russian)

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