Consistent Equations of Nonlinear Rectilinear Laminated Bars Theory in Quadratic Approximation

V.N. Paimushin^a,b*, S.A. Kholmogorov^b*

^aKazan Federal University, Kazan, 420008 Russia

^bTupolev Kazan National Research Technical University, Kazan, 420111 Russia

E-mail: ^*vpajmushin@mail.ru, ^**hkazan@yandex.ru

Received January 31, 2017

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Abstract

Two versions of one-dimensional equilibrium equations for rectilinear laminated bars on basis of S.P. Timoshenko's model subject to transversal compression for each layer and describing geometrical nonlinear deformation by arbitrary displacements and small strain have been derived. The equations are based on the earlier proposed consistent theory of elasticity relations, the usage of which does not lead to spurious bifurcation solutions. The first version corresponds to contact problem statement, when contact stresses are introduced in the coupling points of layers as unknown parameters. The second version corresponds to preliminary satisfaction to the kinematic coupling conditions of layers with respect to displacements.

Keywords: rectilinear bar, laminated structure, geometrically nonlinearity, arbitrary displacements, small strain, S.P. Timoshenko's model, contact stresses, kinematic coupling conditions

Acknowledgments. The study was supported by the Russian Foundation for Basic Research (project no. 16-38-60068, 17-08-01279) and was performed within the framework of the state task of the Ministry of Education and Science of Russia (project no. 9.1395.2017).

Figure Captions

Fig. 1. Laminated bar (lengthwise section).

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For citation: Paimushin V.N., Kholmogorov S.A. Consistent equations of nonlinear rectilinear laminated bars theory in quadratic approximation. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2017, vol. 159, no. 1, pp. 75–87. (In Russian)

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