Adaptive Laminated Composite Shells

In this chapter, the transition from voluminous to areal structures, as already prepared in Section 4.4, will be implemented with special regard to laminated composites and adaptive capabilities making use of the piezoelectric effect for actuation as well as sensing. Therefore, a comprehensive constitutive description is developed and appropriate kinematic relations are specified. Afterwards, possibilities of different complexity for the reduction to a less general description are considered in view of specialized application cases. 

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The constitutive relation of an adaptive laminated composite shell is given in Eq. (6.6). Being considered for the thin wall of the beam, the lines, respectively columns, associated with the cross-sectional strain component °(x, s) and bending curvature Ks x,s) can be dropped in accordance with Remark 7.4. To comply with the specification of a prismatic beam in Remark 7.1, also with regard to the material properties, the latter need to be constant along the lengthwise direction and thus the constitutive matrix lK(s) only depends on the cross-sectional coordinate. The constitutive relation of the wall and the corresponding formulation for the beam with the constitutive matrix P then... 

The sequence of theories developed throughout the foregoing chapters, leading the way from piezoelectric composites via adaptive laminated composite shells to adaptive thin-walled beams, allows for examinations of almost arbitrary complexity. The attempt to provide examples for the full spectrum of capabilities will be dropped in favor of an application-oriented approach. Hence, the subsequent investigations will be carried out in view of the integral actuation of structures with certain similarity to helicopter rotor blades. 

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