An Extended Beam Theory for Smart Materials Applications Part II: Static Formation Problems |
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Authors: | D Y Gao D L Russell |
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Institution: | (1) Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-123, USA , US |
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Abstract: | In this paper we further develop the theory of the extended Timoshenko beam model, as first introduced in Part I 5] of this
work, with particular emphasis on applications of the model in formation theory 11], 12]. We begin with formal development
of the equilibrium equations of static formation theory in the context of the extended Timoshenko model, giving a rigorous
discussion of existence, uniqueness, and regularity of weak solutions with appropriate assumptions on the coefficients. We
continue to obtain the fundamental duality relationship in the context of weak solutions and indicate its usefulness in investigations
of approximate formability. Optimal formation problems and corresponding necessary conditions for optimality are discussed.
We conclude with a discussion of a particular problem of joint optimization of controls and actuator densities in the context
of a prismatic extended Timoshenko beam and we present the results of some computational studies.
Accepted 14 November 1996 |
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Keywords: | , Elastic beam, Timoshenko beam, Formation theory, AMS Classification, 35J25, 35J50, 35Q72, 49L10, |
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