Static shape control of composite plates using a curvature-displacement based algorithm

Abstract An intuitive algorithm for the determination of voltage distribution in the application to shape control of smart structures using piezoelectric actuators is presented here. This approach uses curvature as the fine-tuning criteria on top of the common displacement-based shape control, and is an extension of the slope–displacement method developed by the same authors. The algorithm called the perturbation buildup voltage distribution (PBVD) is based on an iterative approach inspired by a previous algorithm BVD on displacement control. This method aims to provide a means of targeting the desired shape of a structure by using a higher level shape attribute, in this case curvature. Intuitive iterative parameters of the PBVD method allow the user to have better control over the degree of conformity of the structure’s shape. A natural consequence of this method is the smoothing of the resultant shape. Results show that the slopes and curvatures of the structure can be improved but at a tolerable expense of the displacement criteria. Another result of practical interest is the reduction of internal stresses compared to cases using pure displacement shape control.

[1]  Manfred Hertwig,et al.  Shape Control of an Adaptive Mirror at Different Angles of Inclination , 1996 .

[2]  Dimitris A. Saravanos,et al.  Coupled Layerwise Analysis of Composite Beams with Embedded Piezoelectric Sensors and Actuators , 1995 .

[3]  Buckling of Generally Anisotropic Shallow Sandwich Shells , 1990 .

[4]  M. C. Natori,et al.  Active Shape Control of a Deployable Space Antenna Reflector , 1996 .

[5]  L. Kollár,et al.  Shape Control of Composite Plates and Shells with Embedded Actuators. II. Desired Shape Specified , 1994 .

[6]  Chien-Chang Lin,et al.  Shape Control of Composite Plates by Bonded Actuators with High Performance Configuration , 1997 .

[7]  Raphael T. Haftka,et al.  Selection of actuator locations for static shape control of large space structures by heuristic integer programing , 1985 .

[8]  Grant P. Steven,et al.  A buildup voltage distribution (BVD) algorithm for shape control of smart plate structures , 2000 .

[9]  Peter M. Bainum,et al.  OPTIMAL LINEAR QUADRATIC GAUSSIAN DIGITAL CONTROL OF AN ORBITING TETHERED ANTENNA/REFLECTOR SYSTEM , 1994 .

[10]  Grant P. Steven,et al.  Static shape control of composite plates using a slope-displacement based algorithm , 2000 .

[11]  Moshe Eisenberger,et al.  Shape control of non-symmetric piezolaminated composite beams , 1997 .

[12]  D. H. Robbins,et al.  Analysis of piezoelectrically actuated beams using a layer-wise displacement theory , 1991 .

[13]  H. Tiersten.  Linear Piezoelectric Plate Vibrations: Elements of the Linear Theory of Piezoelectricity and the Vibrations Piezoelectric Plates , 1969 .

[14]  K. Chandrashekhara,et al.  Adaptive Shape Control of Laminated Composite Plates Using Piezoelectric Materials , 1998 .

[16]  R. Christensen,et al.  A HIGH-ORDER THEORY OF PLATE DEFORMATION, PART 1: HOMOGENEOUS PLATES , 1977 .

[17]  Grant P. Steven,et al.  A mixed model for adaptive composite plates with piezoelectric for anisotropic actuation , 2000 .

[18]  G. Subramanian,et al.  A fast algorithm for the static shape control of flexible structures , 1996 .

[19]  K. Chandrashekhara,et al.  Modeling and Shape Control of Composite Beams with Embedded Piezoelectric Actuators , 1996 .

[20]  László P. Kollár,et al.  Shape Control of Composite Plates and Shells with Embedded Actuators. I. Voltages Specified , 1994 .

[21]  J. Reddy.  A Simple Higher-Order Theory for Laminated Composite Plates , 1984 .

[22]  K. Chandrashekhara,et al.  Adaptive Shape Control of Composite Beams with Piezoelectric Actuators , 1997 .

[23]  Hiroshi Okubo,et al.  Tendon Control System for Active Shape Control of Flexible Space Structures , 1996 .