Formulation of a Laminated Shell Theory Incorporating Embedded Distributed Actuators

Smart materials have created new paradigms for structural design by introducing new concepts for vibration, damage, and structural control. Shape memory alloy reinforced composites are some of the newest and most versatile of this category of novel materials. They have shown tremendous versatility to adaptively and actively tailor mechanical and physical properties of structures and to perform shape and damage control. Moreover, the have generated new concepts for acoustic and vibration control. However, the unique behavior of the shape memory alloy fibers used as active elements within the composite also poses some difficult and interesting problems for describing the mechanical behavior of SMA reinforced structures. This paper will describe the formulation of a generalized laminate shell theory that incorporates embedded distributed actuators, i.e., shape memory alloy fibers or piezoelectric films. The theories consider the nonlinear strain-temperature-stress coupling for shape memory alloy actuators and the simplifications for analyzing piezoelectric actuators. Some of the computational difficulties of predicting the behavior of SMA reinforced shells will be discussed.