Optimization of composite plates with piezoelectric stiffener-actuators under in-plane compressive loads

Stiffeners which are used to strengthen a plate can be constructed of piezoceramic materials and subsequently used as piezo actuators to improve the load carrying capacity of the plate. In the present study, a fibre composite plate with initial imperfections and under in-plane compressive loads is studied with a view towards minimizing its deflection using the piezo actuators and the fibre orientations. Piezoceramic stiffeners are bonded symmetrically on the top and bottom of the plate and deployed as actuators. Two cases of electric fields, namely, the in-phase and out-of-phase voltages are applied to the actuators. The presence of initial deflections leads to deformation under the in-plane compressive loads which should be less than the critical buckling load. Two cases of initial imperfections are considered, and the first one is the deterministic initial deflections which are known a priori and as such they are given as input parameters for the problem. In the second case the initial deflections are uncertain and they have to be obtained according to a given criterion. In the present study they are determined to produce the least favourable initial deflection (largest deflection) at a given point and the solution is obtained by convex modelling. The effect of the actuators, the ply angles and the voltage are studied and their effects on the transverse deflection are investigated. A performance index involving the L2 norm of the deflections is minimized using the piezo effect and as well as the ply angles the optimal values of which are determined for various problem parameters.