Nonlinear axisymmetric response of orthotropic thin spherical caps on elastic foundations

Dumir, P.C.

doi:10.1016/0020-7403(85)90007-4

Cited by 25 publications

(10 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A nonlinear performance of the critical geometry is revealed where we can observe, for example, the effect of the limits of connectivity for stiffness extrema. We constrained our investigations to closed shells consisting of isotropic materials with external connections at the edge, but point out possible extensions for more complex constitutive laws [21,22], support conditions [23,24] or geometries [25] (e.g. polar-orthotropic annuli on elastic foundations).…”

Section: Introductionmentioning

confidence: 99%

Effects of boundary conditions on bistable behaviour in axisymmetrical shallow shells

Sobota¹,

Seffen²

2017

Proc. R. Soc. A.

View full text Add to dashboard Cite

Multistable shells are thin-walled structures that have more than one stable state of self-stress. We consider isotropic axisymmetrical shallow shells of arbitrary polynomial shapes using a Föppl-von Kármán analytical model. By employing a Rayleigh-Ritz approach, we identify stable shapes from local minima in the strain energy formulation, and we formally characterize the level of influence of the boundary conditions on the critical geometry for achieving bistable inversion-an effect not directly answered in the literature. Systematic insight is afforded by connecting the boundary to ground through sets of extensional and rotational linear springs. For typical cap-like shells, it is shown that bistability is generally enhanced when the extensional spring stiffness increases and when the rotational spring stiffness decreases, i.e. when boundary movements in-plane are resisted but when their rotations are not; however, for certain other shapes and large in-plane stiffness values, bistability can be enhanced by resisting but not entirely preventing edge rotations. Our predictions are furnished as detailed regime maps of the critical geometry, which are accurately correlated against finite-element analysis. Furthermore, the suitabilities of single degree-of-freedom models, for which solutions are achieved in closed form, are evaluated and compared to our more accurate predictions.

show abstract

Section: Introductionmentioning

confidence: 99%

Effects of boundary conditions on bistable behaviour in axisymmetrical shallow shells

Sobota¹,

Seffen²

2017

Proc. R. Soc. A.

View full text Add to dashboard Cite

show abstract

“…Karman -Donnell nonlinear terms as [9,10] The strains across the shell thickness at a distance z from the mid-plane are…”

Section: Fundamental Relations and Governing Equationsmentioning

confidence: 99%

“…Nonlinear free vibration response, static and the maximum transient response under uniformly distributed load of orthotropic thin spherical caps on elastic foundation have been obtained by Dumir [9].…”

Section: Introductionmentioning

confidence: 99%

The nonlinear stability of axisymmetric functionally graded material annular spherical shells under thermo-mechanical load

Anh¹,

Duc²

2016

Mechanics of Advanced Materials and Structures

View full text Add to dashboard Cite

This paper investigates the nonlinear stability of axisymmetric functionally graded (FGM) annular spherical shells with temperature-dependent material properties subjected to thermo-mechanical loads and resting on elastic foundations. Equilibrium and compatibility equations are derived by using the classical thin shell theory in terms of the shell deflection and the stress function. Approximate analytical solutions are assumed to satisfy simply supported boundary conditions and Galerkin method is applied to obtain closed -form of load -deflection paths. An analysis is carried out to show the effects of material and geometrical properties and combination of loads on the stability of the shells.

show abstract

“…Eqs. (19) and (20) are the basic equations used to investigate the nonlinear buckling and postbuckling of FGM annular spherical shells resting on elastic foundations. These are nonlinear equations in terms of two dependent unknowns w and F .…”

Section: Fundamental Relations and Governing Equationsmentioning

confidence: 99%

“…Shen [19] studied post-buckling of shear deformable FGM cylindrical shells surrounded by an elastic medium. Nonlinear free vibration response, static response under uniformly distributed load, and the maximum transient response under uniformly distributed step load of orthotropic thin spherical caps on elastic foundation have been obtained by Dumir [20].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear post-buckling of thin FGM annular spherical shells under mechanical loads and resting on elastic foundations

2014

View full text Add to dashboard Cite

This paper presents an analytical approach to investigate the nonlinear buckling and post-buckling of thin annular spherical shells made of functionally graded materials (FGM) and subjected to mechanical load and resting on Winkler-Pasternak type elastic foundations. Material properties are graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. Equilibrium and compatibility equations for annular spherical shells are derived by using the classical thin shell theory in terms of the shell deflection and the stress function. Approximate analytical solutions are assumed to satisfy simply supported boundary conditions and Galerkin method is applied to obtain closed-form of load-deflection paths. An analysis is carried out to show the effects of material and geometrical properties and combination of loads on the stability of the annular spherical shells.

show abstract

Nonlinear axisymmetric response of orthotropic thin spherical caps on elastic foundations

Cited by 25 publications

References 11 publications

Effects of boundary conditions on bistable behaviour in axisymmetrical shallow shells

Effects of boundary conditions on bistable behaviour in axisymmetrical shallow shells

The nonlinear stability of axisymmetric functionally graded material annular spherical shells under thermo-mechanical load

Nonlinear post-buckling of thin FGM annular spherical shells under mechanical loads and resting on elastic foundations

Contact Info

Product

Resources

About