# Equilibrium and stability of deployable membrane
structures

## B. Andrew Lennon

*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.

[Cambridge University | CUED | Structures
Group | Geotechnical
Group]

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This page is maintained by rcb@eng.cam.ac.uk
(last update 4 November 2003)