Stability and Breathing Motions of Pressurized Compressible Hyperelastic Spherical Shells

Akyüz, Uğurhan; Ertepinar, A.

doi:10.1006/jsvi.2001.3730

Cited by 3 publications

(2 citation statements)

References 17 publications

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“…By using the theory of small deformations superposed on large elastic deformations, the stability of the finitely deformed state and small, free, radial vibrations about this state are investigated. Akyüz and Ertepinar (2001) also investigated the stability of homogeneous, isotropic, compressible, hyperelastic, thick spherical shells subjected to external dead-load traction and gave the critical values of stress and deformation for a foam rubber, slightly compressible rubber and a nearly incompressible rubber. Alexander (1971), by using the non-linear analysis, predicted that the axial load had a significant effect on the value of tensile instability pressure.…”

Section: Introductionmentioning

confidence: 99%

Large deformation analysis and stability analysis of a cylindrical rubber tube under internal pressure

Sang

Xing

Liu

et al. 2016

jtam

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Rubber tubes under pressure can undergo large deformations and exhibit a particular nonlinear elastic behavior. In order to reveal mechanical properties of rubber tubes subjected to internal pressure, large deformation analysis and stability analysis have been proposed in this paper by utilizing a modified Gent's strain energy function. Based on the nonlinear elastic theory, by establishing the theoretical model of a rubber tube under internal pressure, the relationship between the internal pressure and circumferential principal stretch has been deduced. Meanwhile stability analysis of the rubber tube has also been proposed and the relationship between the internal pressure and the internal volume ratio has been achieved. The effects on the deformation by different parameters and the failure reasons of the rubber tube have been discussed, which provided a reasonable reference for the design of rubber tubes.

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Section: Introductionmentioning

confidence: 99%

Large deformation analysis and stability analysis of a cylindrical rubber tube under internal pressure

Sang

Xing

Liu

et al. 2016

jtam

View full text Add to dashboard Cite

show abstract

“…Dragoni [27] has proposed an analytical solution for thick tubes of hyperelastic, compressible, and incompressible materials under radial pressure. The stability of homogeneous, isotropic, compressible, hyperelastic, thick spherical shells subjected to external dead-load traction has been investigated by Akyüz and Ertepınar [28].…”

Section: Introductionmentioning

confidence: 99%

Effect of Compressibility on Nonlinear Buckling of Simply Supported Polyurethane Spherical Shells Subjected to an Apical Load

Yildirim

Yükseler

2011

Journal of Elastomers & Plastics

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In this study, the effect of compressibility on the nonlinear buckling of the simply supported polyurethane spherical shells subjected to an apical concentrated load is presented. The problem is strongly nonlinear both physically and geometrically. Since the closed form solution of the corresponding algebraical and differential equations is not possible, numerical methods are used unavoidably. The governing equations of the problem are converted to algebraical difference equations via the finite difference method and the obtained algebraical equations are solved numerically by using the NewtonRaphson method. Several numerical experiments corresponding to the various values of a thickness parameter, a depth parameter and a material constant related with the compressibility of polyurethane are performed and the forceapex deflection curves are drawn. Concluding remarks pertaining to the effect of the variation of the material constant related with the compressibility on the buckling loads and buckling deflections of the simply supported polyurethane

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Combined effect of compressibility, height and thickness on the nonlinear behaviour of polyurethane, simply-supported spherical shells under apical loads

Yildirim¹,

Yükseler²

2014

Bitlis Eren Univ J Sci Technol

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Previously, the effect of compressibility on the nonlinear buckling behaviour of thin, polyurethane, simplysupported spherical shells subjected to apical loads has been presented without considering the orders of the thickness and height of the spherical shells. In the meantime; it has been observed that although the variations of the thickness and height of the spherical shells do not affect the comments made for the effect of the compressibility on the buckling loads, they do affect the comments made for the effect of the compressibility on the buckling deflections considerably. In this study; combined effect of the compressibility, height and thickness on the buckling loads, buckling deflections and the apical loadapical deflection diagrams of polyurethane, thin, simply-supported spherical shells subjected to apical loads is investigated. Comparing the force-deflection diagrams corresponding to various values of the parameters pertaining to the compressibility of the material used, the height and the thickness of the shell; the variations of the buckling loads, buckling deflections and forms of the force-deflection diagrams corresponding to the various combinations of the mentioned parameters are discussed.

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Stability and Breathing Motions of Pressurized Compressible Hyperelastic Spherical Shells

Cited by 3 publications

References 17 publications

Large deformation analysis and stability analysis of a cylindrical rubber tube under internal pressure

Large deformation analysis and stability analysis of a cylindrical rubber tube under internal pressure

Effect of Compressibility on Nonlinear Buckling of Simply Supported Polyurethane Spherical Shells Subjected to an Apical Load

Combined effect of compressibility, height and thickness on the nonlinear behaviour of polyurethane, simply-supported spherical shells under apical loads

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