Analysis and Design Optimization of Smart Laminated Composite Beams using Layerwise Theory

Many of the developed models for smart laminated composite beams are based on the single-layer theories. Smart laminated composite beams contain strong inhomogenities through the thickness which lead to erroneous results when these beams are analyzed using single-layer theories. However, accurate results can be achieved by using three-dimensional model by setting up computationally expensive refined meshes. It has been demonstrated that layerwise theory can be applied for the analysis of laminated beam with integrated piezoelectric layers as sensors and actuators with acceptable accuracy and computational efforts [

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The present work contains two major aspects; first, a finite element model based on the layerwise theory has been developed to investigate the actuation and sensing mechanism of extensional piezoelectric surfaces bonded and embedded as continuous or discrete patches in a composite laminate. Also the effect of shear piezoelectric patches embedded in a composite laminate has been investigated using the developed layerwise model. The elctro-mechanical coupling effect is included.

The second aspect concerns with design optimization. Most of the developed models of smart laminated composite beams which have been used for optimization are based on single-layer theories. One of the most recent publications in this field has been the work of Soares et al [

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]. From literature survey, it is concluded that smart laminated beam model based on the layerwise theory has not been used for design optimization. In the present work, such a model is developed and used for design optimization. In order to determine the optimal design of the beam for selected purposes, a gradient based optimization procedure, namely, Sequential Quadratic Programming (SQP) is used where the objective is to minimize the mass of the structure while various constraints including layer stress and displacements for static problem as well as frequency constraints for eigenvalue problems are considered. Illustrative examples are given to validate the formulation.