FLEXURAL RIGIDITY OF MULTILAYER PLATES
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ural Rigidity of Multilayer Plates N. F. Morozova,b,*, P. E. Tovstika,b,**, and T. P. Tovstikb,*** a b
St. Petersburg State University, St. Petersburg, 199034 Russia
Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, 199078 Russia *e-mail: [email protected] **e-mail: [email protected] ***e-mail: [email protected] Received March 27, 2020; revised April 17, 2020; accepted April 23, 2020
Abstract—The flexural rigidity of a thin elastic multilayer plate with transversely isotropic layers is considered. If the rigidity of the layers is very different, the classical model based on the hypothesis of a straight normal is not applicable and the effect of lateral shear must be taken into account. Two models for taking into account the effect of transverse shear for a multilayer plate are compared. The first of them, based on the distribution of tangential deformations over the thickness of the plate, was proposed in the work of E. I. Grigolyuk and G. M. Kulikov in 1988. The second model uses an asymptotic expansion of the solution of three-dimensional equations of elasticity theory in powers of a small thinwalled parameter. The errors of the models are estimated by comparison with the exact solution of the three-dimensional test problem.
Keywords: multilayer plate, transverse shear rigidity models DOI: 10.3103/S002565442005012X
1. INTRODUCTION The classical Kirchhoff–Love (KL) model, based on the hypothesis of a straight non-deformable normal, is the basic two-dimensional model of the theory of thin plates. The range of applicability of this model is limited to single-layer plates made of homogeneous isotropic material. For anisotropic plates with low transverse shear rigidity, for plates with oblique anisotropy, for multilayer plates with alternating soft and hard layers, the KL model leads to large errors and it becomes necessary to use refined models. For anisotropic plates with low transverse shear rigidity and for multilayer plates with alternating soft and hard layers, the Timoshenko–Reissner (TR) model, which takes into account the transverse shear, leads to a significant improvement in the results compared to the KL model. For multilayer plates, an equivalent single-layer TR plate made of a homogeneous material is introduced [1–8], which simulates a multilayer plate in the study of its deflections, vibrations and stability. If the equivalent bending stiffness and mass density can be found using the same formulas as in the KL model, then the determination of the shear rigidity presents certain difficulties and is discussed in detail below. One of the ways to determine the shear rigidity is the asymptotic expansion of the solution of the three-dimensional problem in a series in powers of a small dimensionless thickness [2–5]. An alternative method is based on the hypothesis of the distribution of transverse shear strains over the plate thickness [6–8]. These methods are discussed using the example of the problem of free vibrations of a multilayer plate with transv
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