Snap-through buckling of eccentrically stiffened shallow spherical caps

Simitses, George J.; Blackmon, C.

doi:10.1016/0020-7683(75)90046-3

Cited by 16 publications

(4 citation statements)

References 25 publications

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“…Shilkrut [15] for a recent survey. However, most of the literature is for shells of uniform thickness [16,17,18,19] or specific, engineered non-uniformities [20]; those with a thickness profile similar to that expected for evaporating droplets have not been investigated. Furthermore, the rich array of deformed shell profiles observed in experiments [3,4,5,6,7] has not, to the best of our knowledge, been systematically quantified as a function of the shell parameters, even for uniform shells.…”

Section: Introductionmentioning

confidence: 99%

Modeling the elastic deformation of polymer crusts formed by sessile droplet evaporation

Head

2006

Phys. Rev. E

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Evaporating droplets of polymer or colloid solution may produce a glassy crust at the liquidvapour interface, which subsequently deforms as an elastic shell. For sessile droplets, the known radial outward flow of solvent is expected to generate crusts that are thicker near the pinned contact line than the apex. Here we investigate, by non-linear quasi-static simulation and scaling analysis, the deformation mode and stability properties of elastic caps with a non-uniform thickness profile. By suitably scaling the mean thickness and the contact angle between crust and substrate, we find data collapse onto a master curve for both buckling pressure and deformation mode, thus allowing us to predict when the deformed shape is a dimple, mexican hat, and so on. This master curve is parameterised by a dimensionless measure of the non-uniformity of the shell. We also speculate on how overlapping time-scales for gelation and deformation may alter our findings.

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Section: Introductionmentioning

confidence: 99%

Modeling the elastic deformation of polymer crusts formed by sessile droplet evaporation

Head

2006

Phys. Rev. E

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“…Following the previous approach to the analysis of shallow spherical caps (Huang 1964, Simitses andBlackmon 1975), the meridional curve of the unloaded cap is approximated by a quadratic function…”

Section: Governing Equationsmentioning

confidence: 99%

“…The approach taken here is based on the theory developed by Simitses and Blackmon (1975) for axisymmetric buckling of shallow reinforced caps. The contribution of the stiffeners is incorporated into the piezo-coupled formulation using the technique of smeared stiffeners.…”

Section: Introductionmentioning

confidence: 99%

Application of piezoelectric actuators to active control of composite spherical caps

Birman¹,

Knowles²,

Murray³

1999

Smart Mater. Struct.

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Dynamics of reinforced shallow spherical caps is considered in this paper. The cap is subjected to a uniform dynamic pressure that results in a globally axisymmetric motion. The reduction of amplitudes and stresses is achieved by using pairs of piezoelectric actuators bonded to the meridional stiffeners (one of the actuators can be bonded to the inner surface of the skin). These pairs of actuators produce dynamic couples that can reduce the amplitude of motion. The analysis is based on the theory of shallow shells (Donnell-Mushtari-Vlasov theory) using a smeared stiffeners technique. The analytical solution is generated for a cap clamped along the boundary using the approximation of the meridional curve suggested by Huang. Numerical results illustrate the feasibility of a significant reduction of deflections and stresses using piezoelectric actuators with weight and energy consumption acceptable in practical design.

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“…In [66] the influence of rib eccentricity on the critical pressure of these shells was investigated. In [2,3,7], using the basic equations of linear theory, when the shell is regarded as sloping within the limits of the axisymmetrie dent, analogously to the procedure outlined in [13] for a smooth shell, the solution of the stability problem for a shell with the above-noted reinforcement under static and pulsed external pressure was constructed.…”

Section: + 3 \ Jj (5)mentioning

confidence: 99%

Stability of spherical reinforced shells

Amiro¹,

Grachev²

1986

Soviet Applied Mechanics

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Spherical shells, together with shells of other forms, are widely used in various branches of mechanical engineering and the construction trades; see [35, 39, 73, etc]. The advantages of these structures include the fact that they give maximum useful volume, assigning universality in their use to the construction, they have great strength under various perturbations, and they are simultaneously supporting and enclosing structures.As is known, the stability of thin-walled structures is often the criterion determining their carrying capacity. The first investigations of the stability of smooth spherical shells with static loading by an external pressure appeared around 70 years ago; see [13], for example. Since then, very many works have considered the stability of unreinforced spherical shells. The results of these investigations have been outlined in detail and analyzed in a series of reviews, of which the most complete (at the corresponding time period) are [13-15, 28, 65, 68].The critical external pressure found in most experimental works (see the review [28]) was 2-4 times lower than the theoretical value obtained from the well-known classical formula of upper critical pressure. It also follows from experimental results that the development of stability loss of thin-walled spherical shells compressed by an external pressure is very diverse. Therefore, the construction of a universal mathematical model covering various variants of stability loss is a problem that remains to be solved. The use of traditional methods for investigating combined variants of buckling is also associated with great difficulty. Note that, as a result of experimental investigation of the stability of smooth shells on carefully prepared (by the method of sputtering in vacuum) samples [8,41], the validity of the classical formula has been established [13], and the strong influence of initial imperfections on the critical load has been shown [28]. The trend to increase in level of critical load (which corresponds to decrease in weight of shell structures) stimulated research on ribbed shells. For spherical shells, these investigations began in [63,64], where the stability of hollow spherical shells was considered. Theoretical investigations on the basis of an approximate scheme which reduces the calculation of a ribbed shell to the consideration of a smooth shell with reduced rigidity characteristics (a structurally orthotropic shell) have been complemented by experimental investigations of the stability of metallic reinforced shells.In [63], which began the investigation of spherical reinforced shells, an empirical formula of the following form was proposed for determining the critical external pressure, on the basis of analyzing experimental dataIn Eq. (I), the following notation is used: ~ is the semivertex angle of the shell; h is the thickness of the covering; R is the radius of curvature of the shell; E is the elastic modulus of the material; also ~0 is the semivertex angle of the insert in the strip; d is the diameter of the sup...

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Snap-through buckling of eccentrically stiffened shallow spherical caps

Cited by 16 publications

References 25 publications

Modeling the elastic deformation of polymer crusts formed by sessile droplet evaporation

Modeling the elastic deformation of polymer crusts formed by sessile droplet evaporation

Application of piezoelectric actuators to active control of composite spherical caps

Stability of spherical reinforced shells

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