Refined equations and buckling modes under four-point bending loading of the sandwich test specimen with composite facing layers and a transversely flexible core

V.N. Paimushin^∗ , M.V. Makarov^∗∗

Kazan National Research Technical University named after A.N. Tupolev – KAI, Kazan, 420111 Russia

Kazan Federal University, Kazan, 420008 Russia

E-mail: ^∗vpajmushin@mail.ru, ^∗∗makarovmaksim@mail.ru

Received August 18, 2022

ORIGINAL ARTICLE

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DOI: 10.26907/2541-7746.2022.4.329-356

For citation: Paimushin V.N., Makarov M.V. Refined equations and buckling modes under four-point bending loading of the sandwich test specimen with composite facing layers and a transversely flexible core. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2022, vol. 164, no. 4, pp. 329–356. doi: 10.26907/2541-7746.2022.4.329-356. (In Russian)

Abstract

A refined geometrically nonlinear theory of sandwich plates and shells with a flexible soft core and composite facing layers having low shear and compressive stiffness was introduced. It is based on the refinement of the shear model of S.P. Timoshenko taking into account transverse compression, as well as on the use of simplified three-dimensional equations of the theory of elasticity for a transversely flexible core. By integrating the equations over the transverse coordinate to describe the stress-strain state of the core, two two-dimensional unknown functions were introduced, which are transverse shear stresses, constants by thickness. For describing the static deformation process with high variability of the parameters of the stress-strain state of the core, two variants of two-dimensional geometrically nonlinear equations were derived. In the first one, the geometric nonlinearity was considered in the standard approximation by retaining the terms containing only the membrane forces in the facing layers. In the second variant additional geometrically nonlinear terms of a higher order of smallness were kept. Using the compiled equations, a geometrically and physically nonlinear problem of four-point bending of the sandwich specimen was formulated with regard to the physically nonlinear relationship between the transverse shear stresses and the corresponding shear strains in the facing layers. A numerical method stemming from the finite sum method (integrating matrix method) was developed for its solution and post-buckling behavior of specimen was investigated. It was shown that when the specimens are tested, their failure can be caused by the transverse shear buckling mode of the facing layer near the loading roller.

Keywords: sandwich plates and shells, composite facing layers, transversely flexible core, physical and geometrical nonlinearity, sandwich specimen, four-point bending test, integrating matrices, shear buckling mode, continuation method by shear strain

Acknowledgments. This study was funded by the Russian Science Foundation (project no. 19-79-10018, construction of equations, numerical solution of the problem) and supported by the Kazan Federal University Strategic Academic Leadership Program (PRIORITY-2030, three-point bending tests).

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