The US Department of Defense (DOD), as well as the National Aeronautics and Astronautics Administration (NASA) and the Jet Propulsion Laboratory (JPL) are interested in developing and deploying precise, compliant, light-weight, space-based structures. More specifically, the Air Force’s core competencies ‘Aerospace Superiority’ and ‘Information Superiority’ demand ever-increasing depth and breadth of capability. Whether used for energy transmission or optical reconnaissance, current launch restraints limit rigid space-based optical reflector size. To support this requirement, the Air Force Research Laboratory (AFRL) is developing a large space-based optical membrane telescope. Inflatable reflectors can conceptually break this barrier, but controlling such a compliant structure presents significant problems. While inflatable technology is flight proven, the ability to control the shape of a flexible space structure to optical precision has yet to be demonstrated. A laminate of piezoelectric polymer material can deform a membrane optical surface; however, modeling this system must be improved. Analytic solutions to the beam and axisymmetric membrane models are produced providing insight into resulting behavior of these materials. Based on these results a new mathematical methodology rooted in fundamental perturbation techniques was developed: The Method of Integral Multiple Scales (MIMS). MIMS allows selectable precision when applied to a special class of dynamic systems which can be represented through a Lagrangian. This new method was first applied to a relatively simple linear beam problem for the purpose of illustration. The method is able to integrate spatial and temporal multiple scales directly producing boundary layer solutions. This method is fully realized through the finite element approach, where the solution was shown to be over three orders of magnitude more accurate than a standard finite element result. The finite element methodology is applied to nonlinear beam and axisymmetric circular membrane models producing insight for future design decisions. The results illustrate the capability of such an active membrane to modify a reflected wavefront and provide control for an inflatable optical reflector
