Finite Element Formulation for Static Shape Control of a Thin Euler-Bernoulli Beam Using Piezoelectric Actuators


The main component of future space satellites will be an ultra-large, ultra-low mass aperture for high bandwidth communication or high quality imaging from on-orbit. Such an aperture will require an extremely high surface precision tolerance in order to be effective, especially for imaging purposes. Such tight surface precision tolerances dictate the use of an active control scheme to enable tight control of the shape of the aperture. Further, by integrating an active control scheme during the fabrication process, the aperture will become multi-functional and enable many scientific endeavors. One possible method for analyzing ultra-flexible space structures is through the use of the finite element method. Although many commercial packages are available, careful design of a tailored finite element solver can reveal important information about the system, such as where sensors should be placed on the structure. As an illustrative example, this work formulates the weak form of the equation of motion governing the dynamics of a cantilevered, Euler-Bernoulli beam. In particular, static shape control will be implemented on such a beam using a mathematically formulated LQR controller.


Mathematics and Statistics


United States. Air Force. Office of Scientific Research
United States. Defense Advanced Research Projects Agency
National Science Foundation (U.S.)
Virginia Space Grant Consortium

Keywords and Phrases

Euler-Bernoulli beam; finite elements; piezoelectric; static shape control

Document Type

Article - Conference proceedings

Document Version


File Type





© 2004 American Society of Mechanical Engineers (ASME), All rights reserved.

Publication Date

01 Jan 2004