Influence of transverse loading on the stability of a clamped rectangular plate

Sukhoterin, M. V.; Baryshnikov, Sergey; Knysh, Tatiana; Pizhurina, Natalia

doi:10.1051/matecconf/201823901022

Cited by 5 publications

(6 citation statements)

References 10 publications

(27 reference statements)

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“…However, at present, the behavior of plates and shells of smooth-variable thickness, at a joint account of mentioned important factors, is insufficiently studied and requires further study [17,18].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear parametric oscillations of a viscoelastic shallow shell of variable thickness

et al. 2019

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The problem of parametric oscillations of an isotropic viscoelastic shallow shell of variable thickness under periodic load is considered. It is believed that under the influence of specified load, the shallow shell allows displacements (in particular, deflections), commensurate with its thickness. In a geometrically nonlinear statement, taking into account the viscoelastic properties of material, a mathematical model of the problem has been developed using the classical Kirchhoff-Love hypothesis. Using the Bubnov-Galerkin method based on the polynomial approximation of the deflections, the problem is reduced to the study of the system of integro-differential equations, where time is the independent variable. The solution of the system of integrodifferential equations is determined by the proposed numerical method. Based on this method, a numerical solution algorithm is described. The Koltunov-Rzhanitsyn kernel with three different rheological parameters is chosen as a weakly singular kernel. At the same time, the effect of geometric nonlinearity, viscoelastic properties of material, as well as other physicomechanical and geometric parameters and factors (rheological parameters, thickness, initial shape imperfections, aspect ratios, boundary conditions, excitation coefficient) on the area of dynamic instability is taken into account. The results obtained in this study are in good agreement with the results and data obtained by other authors.

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Section: Introductionmentioning

confidence: 99%

Nonlinear parametric oscillations of a viscoelastic shallow shell of variable thickness

et al. 2019

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“…Now let us compare normal and shear stresses at the critical points of the plate. For this purpose, let us use the results of work [20], which calculates bending moments Mx for the similar Reissner plates.…”

Section: Discussionmentioning

confidence: 99%

“…The problem of determining bending functions w(x, y) and stress functions ψ(x, y) are solved in works [20] using superposition of corrective functions. The required bending and stress functions are represented by the following expressions:…”

Section: Methodsmentioning

confidence: 99%

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Shear stresses in rectangular panels of ship structures in the calculations according to Reissner theory

et al. 2018

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This study calculates and analyzes torsion moments of a rectangular panel with clamped edges as an element of ship structures under the action of uniform pressure with allowance for transverse shear deformation and examines the contribution of the corresponding shear stresses to the general stress state. In order to solve this problem, the method of infinite superposition of corrective functions of bending and stresses is applied. It involves an iterative process of mutually correcting the discrepancies from the said functions while meeting all boundary conditions. A particular solution for the bending function in the form of a quadratic polynomial is chosen as the initial approximation. It is established that torsion moment series diverge at the corner points of the plate going into infinity, which yields infinite values for the shear stresses at these points as well. Results of torsion moment calculation for square plates with different width ratios are provided. A 3D distribution diagram of moments is obtained. The computational experiment confirms the correctness of theoretical conclusions about infinite torsion moments at the corner points of the plate. Comparison with bending moments shows that torsion moments cannot be ignored during the assessment of the stress-strain state. The behavior of torsion moments near the corner points is qualitatively different from the simplified Kirchhoff theory, where they turn into zero.

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“…In dynamic calculation of this type of structures according to the "standard procedure, designers are limited by the possibility of obtaining only the most approximate reliability estimates.The ways to the main reserves of increasing the efficiency of the structureconstructions are unavailable, since these reserves are found only when considering the wave nature of dynamic loads (seismic) and are connected with the necessity of assuming irreversible strains in a structure". To determine the reserve capabilities of water retaining structures in calculations, various linear and nonlinear models are used in a planeor spatial form [1][2][3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%