Equilibrium and stability of deployable membrane structures

Abstract:

The objective of this thesis is to investigate the equilibrium and stability of deployable membrane structures.  These structures behave differently to conventional rigid structures and they require an alternative analytical approach.

This thesis introduces a methodology for examining the stability of membrane structures in the fully-deployed configuration.  The enforcement of the equilibrium requirement is an important and powerful part of this methodology.  This requirement is repeatedly invoked to simplify the analysis.  The stability is then examined by calculating potential energy changes between configurations.

The methodology is employed to analyse three examples.  These examples serve to elucidate the methodology and they also reveal some interesting features related to the stability of membrane structures.

The first example is a simple two-dimensional system with multiple lobes.  This system is shown to have multiple equilibrium configurations but only one stable configuration.  The second example is a membrane cylinder with circumferential lobes.  This system is stable if certain conditions are fulfilled.  It is possible to analyse this system using either the energy approach or an equivalent stiffness and it provides an insightful comparison with the energy approach.

The third example is a spheroidal structure with longitudinal lobes separated by load bearing meridians.  This system adopts a Taylor profile as its configuration.  The shape of the meridians is described by elliptic functions and the membrane spans between the meridians.  This system is stable for the deformation mode examined and two alternative modes are suggested for further study.