Multi-parametric stability investigation for thin spherical membranes filled with gas and fluid

Zhou, Yang; Nordmark, Arne; Eriksson, Anders

doi:10.1016/j.ijnonlinmec.2016.02.005

Cited by 11 publications

(4 citation statements)

References 32 publications

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“…The stability of thin membrane structures considering fluid and/or gas filling based on the equations in section 4.2 is discussed in a series of papers. [63][64][65][66] A particular emphasis is on bifurcations and various post-buckling resp. post-bifurcation pathes.…”

Section: 32mentioning

confidence: 99%

Some remarks on load modeling in nonlinear structural analysis–Statics with large deformations–Consistent treatment of follower load effects and load control

Schweizerhof,

Konyukhov

2024

Numerical Meth Engineering

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Load modeling in nonlinear statics, particularly incorporating large deformations differs significantly from the treatment in linear analysis. As in structural dynamics masses in a gravity field generate the loading, their location, and their modifications within the deformation process must be considered in a nonlinear simulation. A specific view besides loading by masses is on gas and fluid interaction with structures. In addition, load control using specifically designed algorithms is evaluated with respect to realistic applications. Within the load modeling an unavoidable, however side aspect, is the general discussion about the so‐called follower forces and non‐conservative loading. As an example of real‐world applications, the specifics of inflated rubber dams are presented.

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Section: 32mentioning

confidence: 99%

Some remarks on load modeling in nonlinear structural analysis–Statics with large deformations–Consistent treatment of follower load effects and load control

Schweizerhof,

Konyukhov

2024

Numerical Meth Engineering

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“…A zero eigenvalue indicates that a small perturbation in a specific direction can occur at constant potential energy. The present numerical work has only considered the tangent stiffness matrix in the eigenvalue extraction, but it has been previously noted that at least a simplified mass matrix must be introduced when considering constrained equilibrium formulations resulting from, e.g., two-parameter load descriptions [44].…”

Section: Static Stabilitymentioning

confidence: 99%

“…Loading came from a fluid of density ρ = 1•10 −6 kg/mm 3 ≈ ρ H 2 O , and a gravity acceleration of g = 9.81 m/s 2 . Fluid level Z fluid , measured from the initial horizontal membrane plane was the primary load parameter, but the fluid volume V fluid enclosed by the membrane was seen as a secondary parameter [44].…”

Section: Numerical Modellingmentioning

confidence: 99%

Symmetry aspects in stability investigations for thin membranes

Eriksson

Nordmark

2016

Comput Mech

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Modelling of structural instability problems is considered for thin square membranes subjected to hydrostatic pressure, with a focus on the effects from symmetry conditions considered or neglected in the model. An analysis is performed through group-theoretical concepts of the symmetry aspects present in a flat membrane with one-sided pressure loading. The response of the membrane is described by its inherent differential eigensolutions, which are shown to be of five different types with respect to symmetry. A discussion is given on how boundary conditions must be introduced in order to catch all types of eigensolutions when modelling only a subdomain of the whole. Lacking symmetry in a FEM model of the whole domain is seen as a perturbation to the problem, and is shown to affect the calculated instability response, hiding or modifying instability modes. Numerical simulations verify and illustrate the analytical results, and further show the convergence with mesh fineness of different aspects of instability results.

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“…Three-dimensional elastic membranes such as balloons have various engineering and biomedical applications including parachutes, gas inflated cushion roof panels, air beams, automobile airbags and human brain tissue [1][2][3][4]. Nonlinear inflation of pressurized membranes, especially hyperelastic balloons, is a classical finite deformation problem in continuum mechanics, which has received considerable attention in the past few years [5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Snap-through instabilities of pressurized balloons: Pear-shaped bifurcation and localized bulging

Wang

Huo

et al. 2018

International Journal of Non-Linear Mechanics

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This paper investigates numerically the post-bifurcation evolution of ellipsoidal or spherical balloons subject to internal pressure, where the primary -shaped curves of pressure vs. principal stretch and the corresponding bifurcated branch, i.e. pear-shaped deformation, are captured quantitatively. We quantify and discuss the range of pear-shaped bifurcation intervals of ellipsoids and the associated critical points. For rugby-shaped ellipsoidal balloons, we find that there exists a threshold for the aspect ratio of the major and minor axes that leads to pear-shaped bifurcation, which is detected by the finite element method. When the rugby shape becomes sufficiently slender, the nonlinear response of the ellipsoidal balloons is well approximated by the deformation of a tube with localized bulging instead of pear-shaped configuration. We obtain the nonlinear evolution of the localized bulging of rugby-like ellipsoids numerically. Furthermore, we examine the influence of various aspect ratios for rugby-shaped balloons on the localized bulging response. We find that pumpkinshaped ellipsoids can always bifurcate into pear shape. Lastly, we provide a unified phase diagram on instability mode selection of various aspect ratios of ellipsoidal balloons, with diverse representative deformed configurations.

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Multi-parametric stability investigation for thin spherical membranes filled with gas and fluid

Cited by 11 publications

References 32 publications

Some remarks on load modeling in nonlinear structural analysis–Statics with large deformations–Consistent treatment of follower load effects and load control

Some remarks on load modeling in nonlinear structural analysis–Statics with large deformations–Consistent treatment of follower load effects and load control

Symmetry aspects in stability investigations for thin membranes

Snap-through instabilities of pressurized balloons: Pear-shaped bifurcation and localized bulging

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