Numerical instability investigations for thin membranes

• Main Author: Zhou, Yang
• Format: Doctoral Thesis
• Language: English
• Published: KTH, Strukturmekanik 2017
• Subjects: Applied Mechanics; Teknisk mekanik
• Online Access: http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-209155

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. === <p>QC 20170616</p>