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Nonlinear Deflection Model for Corner-Supported, Thin Laminates Shape-Controlled With Moment Actuators

[+] Author Affiliations
Jordan E. Massad, Pavel M. Chaplya, Jeffrey W. Martin, Philip L. Reu, Hartono Sumali

Sandia National Laboratories, Albuquerque, NM

Paper No. IMECE2007-43069, pp. 243-252; 10 pages
doi:10.1115/IMECE2007-43069
From:
  • ASME 2007 International Mechanical Engineering Congress and Exposition
  • Volume 10: Mechanics of Solids and Structures, Parts A and B
  • Seattle, Washington, USA, November 11–15, 2007
  • Conference Sponsors: ASME
  • ISBN: 0-7918-4304-1 | eISBN: 0-7918-3812-9

abstract

The shape control of thin, flexible structures has been studied primarily for edge-supported thin-plates. For applications such as electromagnetic wave reflectors, corner-supported configurations may prove more applicable since they allow for greater flexibility and larger achievable deflections when compared to edge-supported geometries under similar actuation conditions. Models of such structures provide insight for effective, realizable designs, enable design optimization, and provide a means of active shape control. Models for small deformations of corner-supported, thin laminates actuated by integrated piezoelectric actuators have been developed. However, membrane deflections expected for nominal actuation exceed those stipulated by linear, small deflection theories. In addition, large deflection models have been developed for membranes; however these models are not formulated for shape control. This paper extends a previously-developed linear model for a corner-supported thin, rectangular laminate to a more general large deflection model for a clamped-corner laminate composed of moment actuators and an array of actuating electrodes. First, a nonlinear model determining the deflected shape of a laminate given a distribution of actuation voltages is derived. Second, a technique is employed to formulate the model as a map between input voltage and deflection alone, making it suitable for shape control. Finally, comparisons of simulated deflections with measured deflections of a fabricated active laminate are investigated.

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