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The previous chapter discussed the modeling of beam-like structures with induced-strain actuation. Many practical structures can be simplified and analyzed as beams, but such an assumption is not accurate in a large number of other structures, such as fuselage panels in aircraft, low aspect-ratio wings, and large control surfaces. It is possible to treat such structures as plates and perform a simple two-dimensional analysis to estimate their behavior. Some of the theories discussed in the previous chapter can be extended to two-dimensional plate-like structures. This chapter describes the modeling of isotropic and composite plate structures with induced-strain actuation. It will combine both the actuators and substrate into one integrated structure to model its behavior. The discussion focuses on induced-strain actuation by means of piezoceramic sheets, but the general techniques may be equally applicable to other forms of induced-strain actuation.
Plate analysis, including induced-strain actuation, is based on the classical laminated plate theory (CLPT), sometimes referred to as classical laminated theory (CLT). It is an equivalent single layer (ESL) plate theory in which the effects of transverse shear strains are neglected. It is valid for thin plates that have thicknesses of one to two orders of magnitude smaller than their planar dimensions (length and width). In the CLPT formulation, a plane-stress state assumption is used.
Classical Laminated Plate Theory (CLPT) Formulation without Actuation
A composite laminate consists of a number of laminae or plies, each with different elastic properties.
The twenty-first century could be called the 'Multifunctional Materials Age'. The inspiration for multifunctional materials comes from nature, and therefore these are often referred to as bio-inspired materials. Bio-inspired materials encompass smart materials and structures, multifunctional materials and nano-structured materials. This is a dawn of revolutionary materials that may provide a 'quantum jump' in performance and multi-capability. This book focuses on smart materials, structures and systems, which are also referred to as intelligent, adaptive, active, sensory and metamorphic. The purpose of these materials from the perspective of smart systems is their ability to minimize life-cycle cost and/or expand the performance envelope. The ultimate goal is to develop biologically inspired multifunctional materials with the capability to adapt their structural characteristics (such as stiffness, damping and viscosity) as required, monitor their health condition, perform self-diagnosis and self-repair, morph their shape and undergo significant controlled motion over a wide range of operating conditions.