0
Research Papers

Topology Optimization for Static Shape Control of Piezoelectric Plates With Penalization on Intermediate Actuation Voltage

[+] Author and Article Information
Zhan Kang1

State Key Laboratory of Structural Analysis for Industrial Equipment,  Dalian University of Technology, Dalian 116024, Chinazhankang@dlut.edu.cn

Xiaoming Wang

 National Engineering Laboratory for System Integration of High Speed Train, CSR Qingdao Sifang Locomotive & Rolling Stock Co., Ltd., Qingdao 266111, China

Zhen Luo

 School of Electrical, Mechanical and Mechatronic Systems, Faculty of Engineering and Information Technology, University of Technology, Sydney, NSW 2007, Australia

1

Corresponding author.

J. Mech. Des 134(5), 051006 (Apr 25, 2012) (9 pages) doi:10.1115/1.4006527 History: Received June 01, 2011; Revised March 28, 2012; Published April 24, 2012; Online April 25, 2012

This paper investigates the simultaneous optimal distribution of structural material and trilevel actuation voltage for static shape control applications. In this optimal design problem, the shape error between the actuated and the desired shapes is chosen as the objective function. The energy and the material volume are taken as constraints in the optimization problem formulation. The discrete-valued optimization problem is relaxed using element-wise continuous design variables representing the relative material density and the actuation voltage level. Artificial interpolation models which relate the mechanical/piezoelectrical properties of the material and the actuation voltage to the design variables are employed. Therein, power-law penalization functions are used to suppress intermediate values of both the material densities and the control voltage. The sensitivity analysis procedure is discussed, and the design variables are optimized by using the method of moving asymptotes (MMA). Finally, numerical examples are presented to demonstrate the applicability and effectiveness of the proposed method. It is shown that the proposed method is able to yield distinct material distribution and to suppress intermediate actuation voltage values as required.

Copyright © 2012 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Schematic illustration of a laminated plate with a host layer and two piezoelectric surface layers

Grahic Jump Location
Figure 2

Eight-node laminated plate element for the considered configuration

Grahic Jump Location
Figure 3

Flowchart of the optimization procedure

Grahic Jump Location
Figure 4

Design domain of a clamped square plate

Grahic Jump Location
Figure 5

Deformation before shape control (displacement scale factor: 25)

Grahic Jump Location
Figure 6

Optimal material layout (obtained with pm = pp = pv = 3)

Grahic Jump Location
Figure 7

Optimal distribution of actuation voltage (V) (obtained with pm = pp = pv = 3): (a) distribution of positive actuation voltage; (b) distribution of negative actuation voltage

Grahic Jump Location
Figure 8

Deformation after shape control (displacement scale factor: 25)

Grahic Jump Location
Figure 9

Optimal material layout (obtained with pm = pp = 3,pv = 1)

Grahic Jump Location
Figure 10

Optimal distribution of actuation voltage (V) (obtained with pm = pp = 3,  pv = 1): (a) distribution of positive actuation voltage; (b) distribution of negative actuation voltage

Grahic Jump Location
Figure 11

Iteration histories for both sets of penalty factors

Grahic Jump Location
Figure 12

Design domain of a clamped square plate (discretized with 24×24 eight-node elements)

Grahic Jump Location
Figure 13

Optimal material layout

Grahic Jump Location
Figure 14

Optimal distribution of actuation voltage (V): (a) distribution of positive actuation voltage; (b) distribution of negative actuation voltage

Grahic Jump Location
Figure 15

Iteration history

Grahic Jump Location
Figure 16

Comparison between the desired shape and the actuated shape: (a) desired shape (displacement scale factor: 10); (b) actuated shape in the optimal design (displacement scale factor: 10)

Grahic Jump Location
Figure 17

Optimal distribution of piezoelectric material

Grahic Jump Location
Figure 18

Optimal distribution of actuation voltage (V): (a) distribution of positive actuation voltage; (b) distribution of negative actuation voltage

Grahic Jump Location
Figure 19

Iteration history

Grahic Jump Location
Figure 20

Comparison between the desired shape and the actuated shape: (a) third mode shape; (b) actuated shape in the optimal design (displacement scale factor: 25)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In