On the Theory of Smart Composite Structures

Abstract

The present paper is concerned with the basic aspects of a newly suggested theory of smart composite structures based on the continuum mechanics approach. The governing equations describing the behavior of a smart composite structures incorporating sensors and actuators are derived, and the basic optimization problems in the design of these controllable structures are formulated. This theory deals mainly with the extremal features of the controllable smart structures. The objective of modeling is to determine limiting properties of the smart structure. This also allows to determine whether the properties of the presently existing materials, sensors and actuators are sufficient for the optimal design of smart structure, or the development of some new materials, sensors or actuators is required.

The basic optimization problems for the smart composite structures are illustrated by three examples in which the three main sources of control are emphasized. These are the residual strains, material properties, and the geometry of a structure. In the first example, we derive the optimal residual stress in an actuator which provides the minimum deflection of a composite cantilevered beam under static loading. It is shown that the effect of actuator allows to reduce the maximum deflection by 28 times compared with the same beam without active control. The second example is concerned with the optimal design of the controllable Winkler’s foundation in the problem of vibration damping for a simply supported beam under the dynamic loading. The controllable property here is a rigidity of foundation. It is shown that by using the optimally designed controllable foundation, the maximum deflection of a beam can be reduced by about 8 times. The third example deals with the optimal design of an actuator for a smart composite beam. The objective is to reduce the maximum deflection by applying a constant residual strain to the actuator. It is shown, in particular, that for the strains which exceed the obtained critical value, the optimal length of the actuator is smaller than the length of the beam, and it diminishes up to zero with the growth of the applied strain.