On shells of revolution with the Love-Kirchhoff hypotheses

Wan, Frederic Y. M.; Weinitschke, H. J.

doi:10.1007/bf00058512

Cited by 21 publications

(10 citation statements)

References 106 publications

(181 reference statements)

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“…Energy consumption in the deformation process was long considered a significant factor to measure the deformability of thin shells. Here energy distribution on the external surface was explored using Kirchhoff-Love’s theory based mechanics 34 , which bridges the buckling and post-buckling performance to volume retraction. If the shell thickness t is less than 10% of its radius, the energy consumed in the deformation process can be separated into stretching and bending energies, given as 35 :…”

Section: Resultsmentioning

confidence: 99%

Buckling-induced retraction of spherical shells: A study on the shape of aperture

Lin

Xie

et al. 2015

Sci Rep

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Buckling of soft matter is ubiquitous in nature and has attracted increasing interest recently. This paper studies the retractile behaviors of a spherical shell perforated by sophisticated apertures, attributed to the buckling-induced large deformation. The buckling patterns observed in experiments were reproduced in computational modeling by imposing velocity-controlled loads and eigenmode-affine geometric imperfection. It was found that the buckling behaviors were topologically sensitive with respect to the shape of dimple (aperture). The shell with rounded-square apertures had the maximal volume retraction ratio as well as the lowest energy consumption. An effective experimental procedure was established and the simulation results were validated in this study.

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Section: Resultsmentioning

confidence: 99%

Buckling-induced retraction of spherical shells: A study on the shape of aperture

Lin

Xie

et al. 2015

Sci Rep

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“…Shell deformation is modeled using Reissner's nonlinear shallow shell equations for thin shells of revolution undergoing axisymmetric deformations with small in-plane strains and moderate rotations (Reissner, 1950;Wan and Weinitschke, 1988). Linear elastic isotropic material behavior is assumed.…”

Section: Governing Equations For Axisymmetric Deformations Of a Sphermentioning

confidence: 99%

Snap transitions in adhesion

Springman

Bassani

2008

Journal of the Mechanics and Physics of Solids

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Equilibrium adhesion states are analyzed for nonlinear spherical caps adhered to a rigid substrate under the influence of adhesive tractions that depend on the local separation between the shell and substrate. Transitions between bistable snapped-in and snapped-out configurations are predicted as a function of four nondimensional parameters representing the adhesive energy, the undeformed shell curvature, the range of the adhesive interactions, and the magnitude of an externally applied load. Nonuniform energy and traction fields associated with free-edge boundary conditions are calculated to better understand localized phenomena such as the diffusion of impurities into a bonded interface and the diffusion of receptors in the cell membrane. The linear Griffith approximations commonly used in the literature are shown to be limited to shells with a small height to thickness ratio and short-range adhesive interactions. External loading is found to alter the adhered configurations and the spatial distributions of both adhesive and elastic energies. An important implication of the latter analysis is the theoretical prediction of the pull-off force, which is shown to depend not only on the interface properties, but also on the geometric and material parameters of the shell and on both the magnitude and type of external loading. AbstractEquilibrium adhesion states are analyzed for nonlinear spherical caps adhered to a rigid substrate under the influence of adhesive tractions that depend on the local separation between the shell and substrate. Transitions between bistable snapped-in and snapped-out configurations are predicted as a function of four nondimensional parameters representing the adhesive energy, the undeformed shell curvature, the range of the adhesive interactions, and the magnitude of an externally applied load. Non-uniform energy and traction fields associated with free-edge boundary conditions are calculated to better understand localized phenomena such as the diffusion of impurities into a bonded interface and the diffusion of receptors in the cell membrane. The linear Griffith approximations commonly used in the literature are shown to be limited to shells with a small height to thickness ratio and short-range adhesive interactions. External loading is shown to alter the adhered configurations and the spatial distributions of both adhesive and elastic energies. An important implication of the latter analysis is the theoretical prediction of the pull-off force, which is shown to depend not only on the interface properties, but also on the geometric and material parameters of the shell and on both the magnitude and type of external loading.

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“…Particularly if the nondimensionalized stiffness of the thin layer is on the order of (t/L) À1 , it is known that the interfacial behavior is exactly the same as that of generalized Y-L equation in solids. This section is to examine the subject further, based on the classical Kirchhoff-Love hypothesis of thin shell (see for example, Wan and Weinitschke, 1988), with a focus on the stiffness with magnitudes of higher orders of (t/L) À1 . Here we restrict our attention on the configuration with a planar, curved interface.…”

Section: Interface Stress Model Along a Curved Boundarymentioning

confidence: 99%