The Mylar Balloon Revisited

Mladenov, Iväılo M.; Oprea, John

doi:10.2307/3647797

Cited by 23 publications

(28 citation statements)

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“…The isotensoid was first derived by Taylor (1963) using a direct equilibrium formulation and later by Paulsen (1994) and Mladenov and Oprea (2003) using variational calculus.…”

Section: Lobe Cutting Patternsmentioning

confidence: 99%

Buckling pressure of “pumpkin” balloons

Pagitz¹,

Pellegrino²

2007

International Journal of Solids and Structures

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This paper presents a computational study of the critical buckling pressure of pumpkin balloons, which consist of a thin, compliant membrane constrained by stiff meridional tendons. The n-fold symmetric shape of a pumpkin balloon with n identical lobes is exploited by adopting a symmetry-adapted coordinate system, which leads to the tangent stiffness matrix in an efficient block-diagonal form; the smallest eigenvalue of a particular block leads to the buckling pressure for the balloon. Two different types of balloon design are considered. Extensive results are obtained for the buckling pressures of a set of 10 m diameter experimental balloons and also for an 80 m diameter flight balloon. The key findings are as follows: the same type of buckling mode, forming four circumferential waves is critical for most of the balloons that have been analysed; balloons with flatter lobes are more stable, and the buckling pressure varies with an inverse power-law of the number of lobes; increasing the Young's modulus, the Poisson's ratio of the membrane, or the diameter of the end fitting has the effect of increasing the buckling pressure; but increasing the axial stiffness of the tendons has the effect of decreasing the buckling pressure.

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“…The isotensoid was first derived by Taylor (1963) using a direct equilibrium formulation and later by Paulsen (1994) and Mladenov and Oprea (2003) using variational calculus.…”

Section: Lobe Cutting Patternsmentioning

confidence: 99%

Buckling pressure of “pumpkin” balloons

Pagitz¹,

Pellegrino²

2007

International Journal of Solids and Structures

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“…Tension field theory, the minimal mathematical framework to address this problem, has been developed to predict the general shape of initially flat structures. While solutions have been found for axisymmetric convex surfaces (11)(12)(13) and polyhedral structures (14,15), predictions in a general case remain an open issue and have been addressed numerically in the computer graphics community (16). In a seminal paper, Taylor (17) described the shape of an axisymmetric parachute with an unstretchable sail, a solution also appearing in recent studies on the wrapping of droplets with thin polymeric sheets (18-20).…”

mentioning

confidence: 99%

Programming curvilinear paths of flat inflatables

Siéfert

Reyssat

Bico

et al. 2019

Proc. Natl. Acad. Sci. U.S.A.

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Inflatable structures offer a path for light deployable structures in medicine, architecture, and aerospace. In this study, we address the challenge of programming the shape of thin sheets of high-stretching modulus cut and sealed along their edges. Internal pressure induces the inflation of the structure into a deployed shape that maximizes its volume. We focus on the shape and nonlinear mechanics of inflated rings and more generally, of any sealed curvilinear path. We rationalize the stress state of the sheet and infer the counterintuitive increase of curvature observed on inflation. In addition to the change of curvature, wrinkles patterns are observed in the region under compression in agreement with our minimal model. We finally develop a simple numerical tool to solve the inverse problem of programming any 2-dimensional (2D) curve on inflation and illustrate the application potential by moving an object along an intricate target path with a simple pressure input.

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“…which implies the equivalence of the constructability of M * from M and the claimed property of q. The second equation of the theorem follows immediately from (14).…”

Section: Theorem 310mentioning

confidence: 73%

“…Despite the simple definition, there is surprisingly little known about surfaces with constant κ 1 /κ 2 , except for κ 1 /κ 2 = ±1, i.e., the sphere and minimal surfaces. Another known case is an ideal Mylar balloon (see e.g., [14,15]) which is obtained by gluing two equally sized discs of flexible, but inextensible, foil along their common border, and blowing it up. This particular surface of revolution has a constant ratio of principal curvatures of κ 1 /κ 2 = 2.…”

Section: Previous Workmentioning

confidence: 99%

Discretizations of Surfaces with Constant Ratio of Principal Curvatures

Jimenez

Müller

Pottmann

2019

Discrete Comput Geom

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Motivated by applications in architecture, we study surfaces with a constant ratio of principal curvatures. These surfaces are a natural generalization of minimal surfaces, and can be constructed by applying a Christoffel-type transformation to appropriate spherical curvature line parametrizations, both in the smooth setting and in a discretization with principal nets. We link this Christoffel-type transformation to the discrete curvature theory for parallel meshes and characterize nets that admit these transformations. In the case of negative curvature, we also present a discretization of asymptotic nets. This case is suitable for design and computation, and forms the basis for a special type of architectural support structures, which can be built by bending flat rectangular strips of inextensible material, such as sheet metal.

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The Mylar Balloon Revisited

Cited by 23 publications

References 0 publications

Buckling pressure of “pumpkin” balloons

Buckling pressure of “pumpkin” balloons

Programming curvilinear paths of flat inflatables

Discretizations of Surfaces with Constant Ratio of Principal Curvatures

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