Symmetry aspects in stability investigations for thin membranes

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.

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