Longitudinal and Transverse Bending on the Cylindrical Shape of a Sandwich Plate Reinforced with Absolutely Rigid Bodies in the Front Sections
I.B. Badrieva* , M.V. Makarova** , V.N. Paimushinb***
aKazan Federal University, Kazan, 420008 Russia
bTupolev Kazan National Research Technical University, Kazan, 420111 Russia
E-mail: *ildar.badriev1@mail.ru,**makarovmaksim@mail.ru, ***vpajmushin@mail.ru
Received April 11, 2016
Abstract
A geometrically nonlinear problem of longitudinal and transverse bending on the cylindrical shape of a sandwich plate with transversally soft core reinforced in the front sections by absolutely rigid bodies intended to ensure the transfer of load to the carrier layers when they interact with other structural elements has been considered. The equations of the refined geometrically nonlinear theory, which allow one to describe the process of their precritical deformation and to reveal all possible buckling forms of the carrier layers (in-phase, antiphase, mixed bending and mixed bending-shear, and also arbitrary, including all of the above) have been used. These equations have been derived by introducing the contact forces of the interaction of the outer layers with the filler, as well as those of the outer layers and the filler with the reinforcing bodies at all points of the surfaces of their conjugation, as unknown parameters. A numerical method for solving the formulated problem has been developed. The method has been constructed by preliminary reduction of the problem to a system of integro-algebraic equations solved with the help of the finite-sum method. A method has been developed for studying the precritical geometrically nonlinear behavior of the plate as a result of its front compression through a reinforcing body. The results of the numerical experiments have been presented and analyzed.
Keywords: sandwich plate, transversely soft core, contour reinforcing body, middle plate bending, refined model of core, contact stresses, integro-algebraic equations, finite sums method, geometrically nonlinear deformation, precritical behavior
Acknowledgments. The study was performed as part of the state task of the Ministry of Education of the Russian Federation (task no. 9.5762.2017/VU, project no. 9.1395.2017/PCh (setting objectives, performing numerical experiments and analyzing their results) and partially supported by the Russian Science Foundation (project no. 16-11-10299 (numerical method development).
Figure Captions
Fig. 1. Sandwich plate: loading (a) and fixing (b) schemes.
Fig. 2. Sandwich plate with contour reinforcing beams.
Fig. 3. Deflections of the middle surfaces of the carrier layers w(k), cm.
Fig. 4. Axial displacements of the middle surfaces of the carrier layers u1(k), cm.
Fig. 5. Membrane forces of the carrier layers T11(k), kN/m.
Fig. 6. Transverse tangential stresses in the core q1 , MPa.
Fig. 7. Generalized shear forces of the carrier layers N1(k), kN/m.
Fig. 8. Shear forces of the carrier layers Q1(k), kN/m.
Fig. 9. Transverse tangential stresses in the core q1 , MPa, for two problems.
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For citation: Badriev I.B., Makarov M.V., Paimushin V.N. Longitudinal and transverse bending on the cylindrical shape of a sandwich plate reinforced with absolutely rigid bodies in the front sections. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2017, vol. 159, no. 2, pp. 174–190. (In Russian)
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