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Computational Science, Engineering & Technology Series
ISSN 17593158 CSETS: 30
COMPUTATIONAL METHODS FOR ENGINEERING SCIENCE Edited by: B.H.V. Topping
Chapter 13
Numerical Modelling of Thin Pressurised Membranes A. Eriksson
KTH Mechanics, Royal Institute of Technology, Stockholm, Sweden A. Eriksson, "Numerical Modelling of Thin Pressurised Membranes", in B.H.V. Topping, (Editor), "Computational Methods for Engineering Science", SaxeCoburg Publications, Stirlingshire, UK, Chapter 13, pp 331350, 2012. doi:10.4203/csets.30.13
Keywords: space membranes, inflation, compressible medium, quasistatic equilibrium, parameter dependence.
Summary
A large variety of thin threedimensional pressurised structures, balloons,
are used in engineering and medical contexts. These structures show large
displacements and deformations when pressurised. Several analytical and
numerical treatments for more or less general situations are available in
literature, but treatment of these structures also leads to accompanying
aspects, such as the load description, contact formulations, dynamics,
wrinkling under compression, and instability aspects. A particular aspect
is related to the medium used to pressurise the membrane, where fluids and
gases or combinations give different situations of density and
compressibility, significantly affecting the response.
A common assumption in a numerical treatment is that the response can be based purely on the membrane behaviour, avoiding the problems of very thin shell formulations. The problems are, however, both geometrically nonlinear due to finite deformations and materially nonlinear through, e.g., hyperelastic material assumptions. It is common also to only consider quasistatic equilibrium situations, where any combination of pressure and volume can be immediately introduced, without dynamic or thermal effects. The dynamical aspects of the behaviour are in these cases primarily related to the filling processes of the membranes. Instability investigations of any class of optimised structures demand elaborate solution methods. Previous work by the author has described generalised pathfollowing methods for nonlinear quasistatic discretised structural problems, as developments of the equilibrium path methods for loaddisplacement relations. The methods thereby allow the calculation of the parameter dependence in different aspects of structural response, e.g., deflections, stresses, critical loads. The parameter dependence evaluations also go beyond sensitivity investigations. It will be shown how also nonobvious parameters such as the ambient temperature can be used in mechanical response evaluations. The primary objective in using these general paths is the detailed phenomenological description of structural instabilities. Such evaluations are useful tools for understanding the behaviour of many structures, particularly as the quasistatic critical states are often the attractors of dynamic response. From the application viewpoint, the parameterised formulation means that a studied loadcarrying structure is just one instance of a class of similar structures, where different responses are relevant for different instances. The borders between these behaviour regions also provide important results from simulations. An interesting possibility is to use one and twodimensional manifolds for the visualization of response aspects. The presentation will describe a simple finite element model, but primarily the solution methods for parameterised nonlinear equilibrium problems. The pressurised balloon problem is used to demonstrate the generalised setting and applications of these models. purchase the fulltext of this chapter (price £20)
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