AN EXTENDED BEAM THEORY FOR SMART MATERIALS APPLICATIONS - PART II - STATIC FORMATION PROBLEMS

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 part icular emphasis on applications of the model in formation theory [11], [12]. We begin with formal development of the equilibrium equations o f static formation theory in the context of the extended Timoshenko mo del, giving a rigorous discussion of existence, uniqueness, and regula rity of weak solutions with appropriate assumptions on the coefficient s. We continue to obtain the fundamental duality relationship in the c ontext of weak solutions and indicate its usefulness in investigations of approximate formability. Optimal formation problems and correspond ing necessary conditions for optimality are discussed. We conclude wit h a discussion of a particular problem of joint optimization of contro ls and actuator densities in the context of a prismatic extended Timos henko beam and we present the results of some computational studies.