Abstract
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.
Highlights
Symmetry in structures is often a result from aesthetic considerations or from functional optimization
Double values indicate that the double critical solution was split into two, and (L) that the bifurcation was replaced by a limit solution
The paper has described how symmetry aspects of a structure, and in particular of a discretization mesh on a structure, will affect the results obtained from a numerical simulation
Summary
Symmetry in structures is often a result from aesthetic considerations or from functional optimization. The present work considers the symmetry and regularity aspects in the context of instability analyses of thin pressurized membranes with a highly symmetric shape. This class of simulations is valid for a large variety of thin threedimensional inflatable structures used in several engineering and medical contexts [23,26,29]. An analytical treatment shows how a subdomain modelling can hide or modify instabilities, and how the domain symmetry and accompanying sets of boundary conditions for equilibrium solution and eigenmode extraction affect instability representation and conclusions. A few concluding remarks are given on the effects from symmetry in the modelling of instability affected structures
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