Shape Recovery of Viscoelastic Beams After Stowage

Abstract

The deployment of viscoelastic structures that have been held stowed for a given time duration can be formulated as a viscoelastic boundary value problem in which the prescribed condition switches from constant displacement to constant traction. This paper presents closed-form expressions for the load relaxation and shape recovery of a linear viscoelastic beam subject to such time-varying constraints. It is shown that a viscoelastic beam recovers to its original shape asymptotically over time. The analytical solutions are employed to investigate the effect of temperature and stowage time on the time required to achieve recovery with a specified precision. Based on the time-temperature equivalence principle, the relationship between recovery time and holding duration is concisely presented on a single plot. It is found that recovery time increases with holding duration but with a diminishing effect.

Keywords:

• Deployable structure
• Shape recovery
• Spacecraft structure
• Stowage
• Viscoelasticity

ACKNOWLEDGMENTS

A preliminary version of this paper was presented at the 51st AIAA/ASME/ ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference in Palm Springs in May 2009. The author is thankful to Professor Sergio Pellegrino at the California Institute of Technology for his guidance and use of facilities.

Notes

Communicated by Marco Amabili.