Brief communications

Large deflections of viscoelastic panels

R. A. Kayumov^ab, B. F. Tazyukov^c, I. Z. Muhamedova^a, F. R. Shakirzyanov<sup>a

a</sup> Kazan State University of Architecture and Engineering, 1 Zelenaya str., Kazan, 420043 Russia
^b Kazan National Research Technical University named after A.N. Tupolev, 10 K. Marks str., Kazan, 420111 Russia
^c Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia

Abstract: We investigate the problem of large, including supercritical, deflections of viscoelastic panels loaded with a transverse distributed load or a concentrated force, including panels obtained by pre-bending the plates by compressing them. In addition to bending deformations, transverse shear is taken into account. The system of static and kinematic relations in the elastic formulation is reduced to a single resolving nonlinear equation with respect to the deflection, examples of numerical calculations are given. Taking into account the fact that in fibrous materials the creep of the material is manifested mainly in shear, the solution obtained is generalized to the case of linearly viscoelastic panels.

Keywords: composite, panel, buckling, shear, supercritical bending, nonlinear equation, viscoelasticity.

UDC: 539.5

Received: 17.06.2019
Revised: 17.06.2019
Accepted: 19.06.2019

DOI: 10.26907/0021-3446-2019-11-80-86

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2019, 63:11, 71–76

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