Buckling of circular plates with an internal ring support and elastically restrained edges

Wang, C.Y.; Wang, C. M.

doi:10.1016/s0263-8231(01)00031-3

Cited by 31 publications

(12 citation statements)

References 6 publications

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“…Therefore, when the boundary departs from such realistic situation, an elastically restrained edge must be considered. [36][37][38][39] Main intention of this work is therefore to study the effect of weakening of thin plate along concentric circle due to crack and the plate being elastically restrained along the outer edge against translation and rotation using exact method of solution approach. The natural frequencies of circular plate for varying values of translation restraint and rotational restraint along the plate periphery, along with the variations in the radius of weakened circle, Poisson's ratio and rotational restraint with hinge of cracked region are obtained for a wide range of non-dimensional parameters.…”

Section: Introductionmentioning

confidence: 99%

Exact Closed-Form Solution of Vibrations of a Generally Restrained Circular Plate with Crack and Weakened Along an Internal Concentric Circle

Rao¹,

Rao²

2017

IJAV

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A thin circular plate with generally restrained periphery and weakened along an internal concentric circle due to a crack, is considered in this paper for studying its vibration characteristics. The frequency for first six modes of plate vibration is computed for varying values of radius of crack, elastic rotational and translational restraints, and the extent of weakening duly simulated by considering the crack as a rotational restraint on the plate. From the results obtained, it is observed that for a plate with translation and rotational restraints, the internal weakening decreases the fundamental frequency by around 31 per cent.

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Section: Introductionmentioning

confidence: 99%

Exact Closed-Form Solution of Vibrations of a Generally Restrained Circular Plate with Crack and Weakened Along an Internal Concentric Circle

Rao¹,

Rao²

2017

IJAV

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“…This uncertainty occurs because, in many practical applications, the edge of the plate is not clamped, free, or simply supported. When the plate's boundary conditions depart from classical cases, elastic translational and rotational restraints should be considered [29,30]. To the best of the authors' knowledge, there Is no other research paper addressing the general boundary conditions with linear translational restraint at the plate edge.…”

Section: Introductionmentioning

confidence: 99%

Frequencies of Circular Plates Weakened Along an Internal Concentric Circle and Elastically Restrained Edge Against Translation

Rao

Rao²

2012

Journal of Applied Mechanics

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The present study deals with the derivation of an exact solution for the problem of obtaining the natural frequencies ofthe vibration of circular plates weakened along an internal concentric circle due to the presence of a radial crack and elastically restrained along the outer edge of the plate against translation. The frequencies of the circular plates are computed for varying values ofthe elastic translational restraint, the radius ofthe radial crack, and the extent ofthe weakening duly simulated by considering the radial crack as a radial elastic rotational restraint on the plate. The results for the first six modes ofthe plate vibrations are computed. The effects of the elastic edge restraint, the radius of the weakened circle, and the extent of the weakening represented by an elastic rotational restraint on the vibration behavior of thin circular plates are studied in detail. The internal weakening due to a crack resulted in decreasing the fundamental frequency of the plate. The exact method of solution and the results presented in this paper are expected to be of specific use in analyzing the effect of a radial crack on the fundamental natural frequency ofthe circular plate in the presence of a translational restraint existing along the outer edge of the plate. These exact solutions can be used to check the numerical or approximate results.

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“…Besides the discontinuity of material and dimension error, the elastoplastic buckling and post-buckling may be the important factors. The buckling problem has been widely studied for plates [7][8] , cylinder shells [9][10] and films [11] . For near hemispherical diaphragm, the bucking problem is more obvious [12] .…”

Section: Introductionmentioning

confidence: 99%

Asymmetric deformation of near hemispherical diaphragm under uniform surface load

Zhang

Tang

et al. 2011

J. Shanghai Jiaotong Univ. (Sci.)

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The asymmetric deformation and eccentricity problems of near hemispherical diaphragm under the uniform surface load are quantitatively characterized in the paper. The analysis is based on a 3D finite element analysis (FEA) model established according to elastic-plasticity and large displacement nonlinear finite element method. Besides, the deformation experiments are taken to validate the reliability of FEA model which shows that the simulation results are in good agreement with the experimental results. Then, three angle parameters, deflection angle β, circumvolving angle θ and distributing angle γ, are introduced and expressed to characterize the asymmetric deformation and eccentricity quantitatively. According to the angle parameters, the inversion processes of uniform thickness diaphragm and varying thickness diaphragm are calculated respectively. The inversion process of varying thickness diaphragm is much steadier than that of uniform thickness diaphragm. The present results show that the asymmetric deformation process can be characterized by curve of three angle parameters (β, θ, γ) exactly, the degrees of eccentricity can be indicated by the final value of deflection angle and the eccentricity position can be characterized by the final values of the three angle parameters.

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Buckling of circular plates with an internal ring support and elastically restrained edges

Cited by 31 publications

References 6 publications

Exact Closed-Form Solution of Vibrations of a Generally Restrained Circular Plate with Crack and Weakened Along an Internal Concentric Circle

Exact Closed-Form Solution of Vibrations of a Generally Restrained Circular Plate with Crack and Weakened Along an Internal Concentric Circle

Frequencies of Circular Plates Weakened Along an Internal Concentric Circle and Elastically Restrained Edge Against Translation

Asymmetric deformation of near hemispherical diaphragm under uniform surface load

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