Shape Control of Composite Plates and Shells with Embedded Actuators. II. Desired Shape Specified

Abstract

The changes in shapes of fiber-reinforced composite beams, plates and shells affected by embedded piezoelectric actuators were investigated. An analytical method was developed to determine the voltages needed to achieve a specified desired shape. The method is formulated on the basis of mathematical models using two-dimensional, linear, shallow shell theory including transverse shear effects which are important in the case of sandwich construction. The solution technique is a minimization of an error function which is a measure of the difference between the deformed shape caused by the application of voltages and the desired shape. A computationally efficient, user-friendly computer code was written which is suitable for performing the numerical calculations. The code, designated as SHAPE2, gives the voltages needed to achieve specified changes in shape. To validate the method and the computer code, results generated by the code were compared to existing analytical and experimental results. The predictions provided by the SHAPE2 code were in excellent agreement with the results of the other analyses and data.

Smart Composite Plate Shape Control Using Piezoelectric Materials II. Optimization

“…where 77 are the master element coordinates. The coordinates x and y can be transformed to the master element as: z=zo +a/2; y=K+7012 (8) where (x,,y,) are the plate centroid coordinates, and (a,b) are its dimensions. By substituting equation (8) in equations (1) and (2) the actual and the desired shape equations take the form: zo = 10 +4; + (.…”

“…Koconis et. al [8], developed analytical method to determine the voltages needed to achieve a specified desired shape. Based on Koconis method, a new model is developed using the finite element method to determine the voltage applied to the piezoelectric actuator to get minimum error between the desired shape and the actual shape with a prescribed actuator (s) placement.…”

Active shape control of composite structures under thermal loading

“…So far, piezoceramic materials have been the most widely used smart material to control the shape of a structure. Koconis, Kollar, and Springer [1,2] were among the first ones to investigate the change in shape of composite beams, plates and shells by embedded piezoelectric actuators. Studies on determining the optimal length, actuator locations and applied voltage have been reported by Agrawal and Treanor [3], Bruch et al [4], Sun and Tong [5] and different optimization techniques have been proposed.…”

Static and dynamic analysis of laminated composite plates with integrated piezoelectrics

“…Several analysis and numerical models have been developed to analyze t he laminated composite plates with integrat ed piezoelectric sensors and act uato rs . The often used model is the equivalent single layer model, which includes the Classical Plate Theory ( CPT) [3], [7], [9] or First-order Shear Deformation Theory (FSDT) [4], [10] or High-order Shear Deformation Theory (HSDT) [5], [8] . For thick laminated composites structures, [6] show that Layerwise Theo ry has some advantages .…”