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Numerical instability investigations for thin membranes
KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.ORCID iD: 0000-0002-3875-927X
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: urn:nbn:se:kth:diva-209155OAI: oai:DiVA.org:kth-209155DiVA: diva2:1110338
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
List of papers
1. Instability of thin circular membranes subjected to hydro-static loads
Open this publication in new window or tab >>Instability of thin circular membranes subjected to hydro-static loads
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.

Keyword
Thin membrane, Large deformation, Deformation dependent loading, Bifurcation, Parameter dependence
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-176059 (URN)10.1016/j.ijnonlinmec.2015.06.010 (DOI)000362135600015 ()2-s2.0-84963717204 (ScopusID)
Note

QC 20151029

Available from: 2015-10-29 Created: 2015-10-29 Last updated: 2017-06-16Bibliographically approved
2. Multi-parametric stability investigation for thin spherical membranes filled with gas and fluid
Open this publication in new window or tab >>Multi-parametric stability investigation for thin spherical membranes filled with gas and fluid
2016 (English)In: International Journal of Non-Linear Mechanics, ISSN 0020-7462, E-ISSN 1878-5638, Vol. 82, 37-48 p.Article in journal (Refereed) Published
Abstract [en]

The instability behavior of spherical membranes completely or partially filled with fluid, also with internal gas over-pressure, placed on a friction-less rigid plane was investigated. The two-parameter Mooney-Rivlin model was used for material description. A third order penalty function was used to describe the rigid support. Different problem settings were considered, and different instability responses were observed. For the partially fluid-filled membrane, a multi-parametric problem was defined and analyzed. Augmenting equations were introduced to impose control constraints on variables chosen. These equations also affect the instability analysis. A generalized eigenvalue analysis was used for the stability conclusions. Numerical simulations showed that appropriate control constraints are of essence to interpret the instability conclusions. Fold line evaluations were performed to analyze the dependence of the instability behavior on the parameters. A solution surface algorithm was utilized to analyze and visualize the mechanical responses to multi-variable loading.

Place, publisher, year, edition, pages
Elsevier, 2016
Keyword
Augmenting equations, Fold lines, Generalized eigenproblem, Multi-parametric stability, Solution surfaces
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-186959 (URN)10.1016/j.ijnonlinmec.2016.02.005 (DOI)000375818900005 ()2-s2.0-84960402068 (ScopusID)
Note

QC 20160527

Available from: 2016-05-27 Created: 2016-05-16 Last updated: 2017-06-16Bibliographically approved
3. Multi-parametric stability investigation for thin membranes with contacts
Open this publication in new window or tab >>Multi-parametric stability investigation for thin membranes with contacts
(English)Manuscript (preprint) (Other academic)
National Category
Applied Mechanics
Research subject
Engineering Mechanics
Identifiers
urn:nbn:se:kth:diva-209208 (URN)
Note

QC 20170616

Available from: 2017-06-16 Created: 2017-06-16 Last updated: 2017-06-16Bibliographically approved
4. Instability investigation for rotating thin spherical membranes
Open this publication in new window or tab >>Instability investigation for rotating thin spherical membranes
(English)Manuscript (preprint) (Other academic)
National Category
Applied Mechanics
Research subject
Engineering Mechanics
Identifiers
urn:nbn:se:kth:diva-209211 (URN)
Note

QC 20170616

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

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