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Instability of thin circular membranes subjected to hydro-static loads
KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.ORCID iD: 0000-0002-3875-927X
KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.ORCID iD: 0000-0002-5819-4544
2015 (English)In: International Journal of Non-Linear Mechanics, ISSN 0020-7462, E-ISSN 1878-5638, Vol. 76, 144-153 p.Article in journal (Refereed) Published
Abstract [en]

Membrane structures subjected to hydrostatic load are prone to undergo large deformations and lose stability. This paper investigates different instability phenomena for a thin, circular and initially flat and horizontal membrane. The Mooney-Rivlin hyper-elastic model is used to provide the material description. An axisymmetric and a 3D model have been set up to show the large deformations and instability behavior with different parameter settings. Numerical examples show that the methods developed are capable to describe the deformation dependent loading conditions and the instability phenomena. The numerical simulations show fundamental differences in the response and instability behavior when the horizontal membrane is loaded from above or below. The parameters of fluids and membranes and the means for introducing the pressure are of essence for interpreting the instability behavior.

Place, publisher, year, edition, pages
2015. Vol. 76, 144-153 p.
Keyword [en]
Thin membrane, Large deformation, Deformation dependent loading, Bifurcation, Parameter dependence
National Category
Applied Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-176059DOI: 10.1016/j.ijnonlinmec.2015.06.010ISI: 000362135600015Scopus ID: 2-s2.0-84963717204OAI: oai:DiVA.org:kth-176059DiVA: diva2:865776
Note

QC 20151029

Available from: 2015-10-29 Created: 2015-10-29 Last updated: 2017-12-01Bibliographically approved
In thesis
1. Parametric stability analyses for fluid-loaded thin membranes
Open this publication in new window or tab >>Parametric stability analyses for fluid-loaded thin membranes
2015 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Membrane structures are commonly used in many elds. The studies of thesestructures are of increasing interest. The two projects focus on the evaluations ofequilibrium states for uid-pressurized membranes under dierent loading conditions,and the corresponding instability behavior.The rst part of the current work discusses the instability behavior of a thin,planar, circular and initially horizontal membrane subjected to downwards or upwards uid pressure. The membrane structures exhibit large deformations under uid pressure. Various instability behaviors have been observed for dierent loadingparameters. Limit and bifurcation points have been detected for dierent loadingconditions. Dierent loading parameters have been used to interpret the instabilitybehavior. The eects on instability of parameters, the initial states of the membrane,and the chosen mesh have been discussed.The second part of the current work discusses instability behavior of a thin,spherical and closed membrane containing gas and uid placed on a horizontal rigidand non-friction plane. A multi-parametric loading has been described. By addingthe practically relevant controlling equations, the complex equilibrium paths werefollowed using the generalized path following algorithm, and the stability conclusionswere made dierently, according to the considered load parameters and theconstraints. A generalized eigenvalue analysis was used to evaluate the stabilitybehavior including the constraint eects. Fold line evaluations were performed toanalyze the parametric dependence of the instability behavior. A solution surfaceapproach was used to visualize the mechanical response under this multi-parametricsetting.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2015. xii, 78 p.
Series
TRITA-MEK, ISSN 0348-467X ; 2015:08
Keyword
Membranes, Hydro-static load, Multi-parametric loading, Bifurcations, Generalized path-following, Fold lines, Mesh eects, Augmenting equations, Generalized eigenproblem, Solution surface.
National Category
Applied Mechanics
Research subject
Engineering Mechanics
Identifiers
urn:nbn:se:kth:diva-176030 (URN)978-91-7595-745-6 (ISBN)
Presentation
2015-11-20, lecture hall V1, Teknikringen 76, KTH, Stockholm, 10:30 (English)
Opponent
Supervisors
Note

QC 20151029

Available from: 2015-10-29 Created: 2015-10-28 Last updated: 2015-10-29Bibliographically approved
2. Numerical instability investigations for thin membranes
Open this publication in new window or tab >>Numerical instability investigations for thin membranes
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Membrane structures are commonly used in many fields. The studies of these structures are of increasing interest. The projects in this thesis focus on the evaluations of equilibrium states for pressurized membranes under different problem settings, using finite element methods, and the corresponding instability behaviors.

The first part of the current work discusses the instability behavior of a thin, planar, circular and initially horizontal membrane subjected to downwards or upwards fluid pressure. The membrane structures exhibit large deformations under pressure. The method for evaluating fluid pressure from gravity was developed in finite element context, and used in numerical simulations. Limit and bifurcation points have been detected for different loading parameters and conditions. The effects on instabilities of parameters, the initial states of the membrane, and the chosen mesh are discussed.

The second part of the current work discusses instability behavior of a thin, spherical and closed membrane containing gas and fluid, when placed on a horizontal rigid and non-friction plane. A multi-parametric loading is described. By adding practically relevant controlling equations, different classes of equilibrium paths were followed using a generalized path following algorithm. Stability conclusions were made, according to the considered load parameters and the constraints. A generalized eigenvalue analysis was used to evaluate the stability behavior including the constraint effects. Fold line evaluations were performed to analyze the parametric dependence. A solution surface approach is used to visualize the mechanical response under this multi-parametric setting.

The third part of the current work focuses on instability response of a truncated sphere, containing gas and fluid, and in contact with two vertical rigid and non-friction planes. Different penalty formulations were used and compared. The effects of contact implementations on instability behaviors were investigated. Bifurcation points induced by contacts have been observed. Multi-parametric problems were defined, and generalized paths were followed. The multi-parametric stability was evaluated using generalized eigenvalue analysis, based on the mass and total differential matrices. The effects of augmenting equations on bifurcation points and limit points are discussed.

The fourth part of the current work analyses the instability response of a truncated sphere, completely filled with fluid, placed on a horizontal plane and spinning around the vertical axis. The loads from fluid pressure and the constraints, e.g., fluid volume, were formulated to generate a symmetric differential matrix. Several mesh patterns with different symmetries were used to simulate the model, and the obtained results are compared. Various problem settings were considered, and generalized paths were followed. The effects of symmetry aspects of the chosen meshes on instability behaviors are discussed, as are the effects of parameters.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2017. 29 p.
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-209155 (URN)
Public defence
2017-06-14, Kollegiesalen, Brinellvägen 8, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20170616

Available from: 2017-06-16 Created: 2017-06-15 Last updated: 2017-06-16Bibliographically approved

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