An analytical solution for axisymmetric buckling of annular plates based on perturbation technique

Abolghasemi, Saeed; Eipakchi, Hamidreza; Shariati, Mahmoud

doi:10.1016/j.ijmecsci.2016.12.027

Cited by 8 publications

(3 citation statements)

References 26 publications

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“…Hence, their buckling analysis under different boundary and loading conditions can be found in several papers. 1–8 In the majority of practical cases, the buckling can happen beyond the elastic range. The plastic buckling may occur when the material of plate has a low proportional limit in comparison with the nominal yield stress (e.g.…”

Section: Introductionmentioning

confidence: 99%

A numerical approach to the elastic/plastic axisymmetric buckling analysis of circular and annular plates resting on elastic foundation

Hasrati

Ansari

Rouhi

2019

Proceedings of the Institution of Mechanical Engineers, Part C:

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Presented herein is the elastic/plastic axisymmetric buckling analysis of circular and annular plates resting on elastic foundation under radial loading based on a variational numerical method named as variational differential quadrature. To accomplish this aim, a first-order shear deformable plate model is developed in the context of incremental theory of plasticity (IT) (with the Prandtl-Reuss constitutive equations) and the deformation theory of plasticity (DT) (with the Hencky constitutive equations). It is considered that the material of plates exhibits strain hardening characterized by the Ramberg-Osgood relation. Also, the Winkler and Pasternak models are employed in order to formulate the elastic foundation. To implement the variational differential quadrature method, the matrix formulations of strain rates and constitutive relations are first derived. Then, based upon Hamilton's principle and using the variational differential quadrature derivative and integral operators, the discretized energy functional of the problem is directly obtained. Selected numerical results are presented to study the effects of various parameters including thickness-to-radius ratio, elastic modulus-to-nominal yield stress ratio, power of the Ramberg-Osgood relation and parameters of elastic foundation on the elastic/plastic buckling of circular and annular plates subject to different boundary conditions. Moreover, several comparisons are provided between the results of two plasticity theories, i.e. IT and DT. The effect of transverse shear deformation is also highlighted.

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Section: Introductionmentioning

confidence: 99%

A numerical approach to the elastic/plastic axisymmetric buckling analysis of circular and annular plates resting on elastic foundation

Hasrati

Ansari

Rouhi

2019

Proceedings of the Institution of Mechanical Engineers, Part C:

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show abstract

“…Circular and annular plates are very important structural elements in aerospace, ocean, mechanical and civil engineering applications [1]. There have been many studies conducted on bending, buckling and vibration of circular and annular plates using the finite element method [2,3], differential quadrature method [4], Ritz method [5,6], perturbation method [7], the differential transformation method [8]. However, the finite difference method is rarely adopted for analyses of circular and annular plates.…”

Section: Introductionmentioning

confidence: 99%

Uncovering the finite difference model equivalent to Hencky bar-net model for axisymmetric bending of circular and annular plates

Zhang

Wang

Challamel

et al. 2018

Applied Mathematical Modelling

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As there are a few finite difference models in the literature for axisymmetric bending of plates, only one of these models is equivalent to the Hencky bar-net model (HBM) that comprises a finite number of rigid circular arcs and straight radial segments joined by frictionless hinges with elastic rotational springs. This paper is concerned with uncovering the one finite difference model (FDM) that is equivalent to the HBM. Based on the energy formulation, the governing equation for HBM is derived and it will be used to identify the FDM that has the same discrete set of equations. By using this equivalency between the HBM and the identified FDM, the expressions of edge spring stiffnesses of HBM are derived for various boundary conditions. As illustrative examples, the HBM is used to solve the bending problems of circular plates under uniformly and linearly increasing distributed loads. The analytical solutions of HBM avoids the singularity problem faced in FDM at the plate center. This paper also presents some benchmark bending solutions for annular plates with and without an internal ring support for different boundary restraints by using the HBM.

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“…Analytical solution can be found on axisymmetric plates by adopting a curvilinear coordinate system: in such a context, new analytical solution based on the first order shear theory and on the perturbation technique is presented for the axisymmetric buckling analysis of annular plates in [15]. Analytical solution for buckling of functional graded material truncated conical shells reinforced by orthogonal stiffeners is recently proposed in [16].…”

Section: Introductionmentioning

confidence: 99%

Analytical solution for buckling of Mindlin plates subjected to arbitrary boundary conditions

Ruocco

Mallardo

Minutolo

et al. 2017

Applied Mathematical Modelling

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The study investigates buckling behavior of isotropic plates subjected to axial, biaxial and pure shear loads. The effect of transverse shear deformation is taken into account by adopting the Mindlin first order shear theory. By applying the extended Kantorovich method, an exact solution is presented without any approximation on the boundary conditions. The procedure is proposed at thin, moderately thick and thick isotropic plates. The obtained results are in good agreement with those available in literature and they demonstrate the accuracy of the proposed procedure

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An analytical solution for axisymmetric buckling of annular plates based on perturbation technique

Cited by 8 publications

References 26 publications

A numerical approach to the elastic/plastic axisymmetric buckling analysis of circular and annular plates resting on elastic foundation

A numerical approach to the elastic/plastic axisymmetric buckling analysis of circular and annular plates resting on elastic foundation

Uncovering the finite difference model equivalent to Hencky bar-net model for axisymmetric bending of circular and annular plates

Analytical solution for buckling of Mindlin plates subjected to arbitrary boundary conditions

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