a failure control method for smart composite morphing ... · pdf filea failure control method...

A FAILURE CONTROL METHOD FOR SMART COMPOSITE MORPHINGAIRFOIL BY PIEZOELECTRIC ACTUATOR

Shahin Zareie1, Abolghassem Zabihollah2

1M.Sc, School of Science and Engineering, Sharif University of Technology, Kish Island, Iran

2Faculty, School of Science and Engineering, Sharif University of Technology, Kish Island, Iran

E-mail: [email protected]

Received January 2011, Accepted September 2011No. 10-CSME-74, E.I.C. Accession 3237

ABSTRACT

In this paper, a nonlinear Finite Element (FE) approach based on the layerwise displacementtheory is utilized to obtain the interlaminar stresses due to buckling phenomena in unsymmetriclaminated smart composite morphing structure. An On/Off control strategy is designed tocontrol the snap-through phenomena. Due to cycling nature of applied load on morphing, thesestructures are vulnerable to failure due to fatigue. A failure control mechanism utilizing apiezoelectric actuator is developed to control the failure.

Keywords: smart morphing composite; layerwise displacement theory; nonlinear finite element;failure control.

UNE METHODE DE CONTROLE DE DEFAILLANCE PAR ACTIONNEURPIEZOELECTRIQUE D’UNE SURFACE PORTANTE EN MATERIAU COMPOSITE

RESUME

Dans cet article, une approche par element fini non-lineaire basee sur la theorie dedeplacement par couche, est utilisee afin de determiner la contrainte inter-laminaire desstructures en materiau composite. Le stress inter-laminaire est developpe en raison d’unphenomene appele flambage dans la structure d’un composite lamine asymetrique. Unestrategie de controle on/off est concue pour controler le probleme de snap-through. A cause de lanature cyclique de la charge appliquee, ses structures sont vulnerables a la defaillance due a lafatigue. Un mecanisme de controle a l’aide d’un actionneur piezoelectrique est ainsi developpepour detecter les defaillances.

Mots-cles : materiau composite intelligent; theorie de deplacement par couche; element fininon-lineaire; controle de defaillance.

Transactions of the Canadian Society for Mechanical Engineering, Vol. 35, No. 3, 2011 369

1. INTRODUCTION

The concept of composite smart structures are used in many advanced engineeringapplications [1,2]. The smart composite morphing structure is known as a new class of smartcomposite structure that is recently developed in aerospace and marine industries. A morphingcomposite structure have two or more stable states and morph it’s shape when needed by smallmagnitude of force [3].

Analysis of composite morphing structure is a complicated problem in nature. It is necessary totheorize this mechanism with considering many issues, including, mechanics of compositelaminates, electro-mechanical coupling and non-linear finite element for proper design. Dano andHyer [4] primary studied the multi-stable shapes to investigate the snap-through behavior ofunsymmetric laminates. Interests in using this structure as element of aircraft is grown up [6,7].Nir et al. [4] designed and analyzed a smart fin which is used in airborne vehicles. Excellentcapabilities of adaptive structure led Minnetyana et al. [6] to use this concept to design a C-130flapron. Potential of using bi-stable laminated composite morphing structures for airfoil section isstudied by Diaconu et al. [7] who developed a finite element model for nonlinear static analysis ofa morphing flap-like structure.

In order to commercialize the use of smart morphing structure, the issue of how to force andcontrol/monitor this structure, in the snap-through mechanism must be explored in more detail.This structure needs sensors and actuators to achieve self-controlling and self-monitoring. Thecontrol of snap-through behavior of multistable laminates was studied by Giddings et al. [8].They considered a bistable carbon/fiber composites actuated by a Macro/Fiber piezoelectricactuator. Bowen et al. [9] made unsymmetrical carbon fiber/epoxy composites bonded withpiezoelectric actuator. Using Shape Memory Alloy (SMA) wires to change shape of compositelaminates is studied by Dano and Hyer [10].

On the other hand, studying of back and forth interlaminar stresses in snap-through structure isone of the most vital issue that needs to be considered. When snap-through is occurred, more fatiguein each fiber’s layer is appeared. In a go-back cycle, delamination and failure may occure because offatigue, specially in piezoelectric layer. The problem of interlaminar stresses has been studied bymany researcher, Ramesh et al. [11] used a third-order shear deformation theory to study theinterlaminar stresses. Plagianakos et al. [12] investigated a higher-order layerwise laminated theoryfor this purpose. The research in this field, are mostly based on Equivalent Single Layer (ESL)theories and linear states. However, smart morphing composite with embedded piezoelectric, haveinhomogeneous in material and layup configurations. Requiring advanced theory with higheraccuracy to describe buckling and interlaminate stress with highest accuracy. Mirzababaee andTahani [13] studied the electromechanical coupling effects due to presence of piezoelectric layer onthe interlaminar stresses in composite plate using a layerwise laminate theory.

Changing modes in morphing composites is basically a nonlinear phenomena, requiring anonlinear approach to study the problem. In the present work, an efficient and accurate nonlinearfinite element model is utilized for the analysis of smart composite morphing structures. Then, inorder to monitor and/or failure control due to exitance interlaminar stresses, an On/Off control ofstructure strategy is utilized in which, the interlamniar stresses are measured when necessary,command the actuator to modify the deflection and thus reduce stresses.

2. THE FINITE ELEMENT FORMULATIONThe displacement and electrical field of a smart laminated plate based on Layerwise

Displacement Theory (LDT) is given by [14]:


u x,yð Þ~XN

I~1

Xm

J~1

UIJwI x,yð ÞwJ zð Þ ð1Þ

v x,yð Þ~XN

I~1

Xm

J~1

VIJwI x,yð ÞwJ zð Þ ð2Þ

w x,yð Þ~XN

I~1

Xm

J~1

WIJwI x,yð ÞwJ zð Þ ð3Þ

Q x,yð Þ~XN

I~1

Xm

J~1

QIJwI x,yð ÞwJ zð Þ ð4Þ

where u, v and w are displacements along x, y and z{directions respectively. N is the totalnumber of nodes through the thickness. w(z) is the 1-D Lagrange interpolation function alongthe z{direction which is defined between any two adjacent layers Fig. 1 [14].

The morphing section can be considered a strip of a plate, therefore strain field for a trip ofplate, with considering geometric nonlinearity, is given by [14]:

exx~XN

I~1

LUI

LxwIz

1

2(XN

I~1

LWI

LxwI )(

XN

J~1

LWJ

LxwJ) ð5Þ

ezz~XN

I~1

WI

LwI

Lzð6Þ

Fig. 1. The Layers of composite along z{direction in 3{D.


cxz~XN

I~1

UILwI

LzzXN

I~1

LWI

LxwI ð7Þ

Considering the given strains and proceeding a finite element approach, one may obtain thematrix equation of the laminated strip integrated with piezoelectric actuator as given by [15]:

(½K �z½G�)fWgz½M�f €WWg~½FmzFel� ð8Þ

where ½K �, ½G�, ½M�, Fm and Fel represent stiffness, geometric stiffness, mass matrices, mechanicalforce and electrical force, respectively. The stiffness matrix K is composed of linear and nonlinearterm that are given by [14]:

½K �~½K �Lz½K �NL ð9Þ

where ½K �L is linear stiffness matrix and ½K �NL is nonlinear stiffness matrix [14]. As the mechanicalforce is constant, it is neglected in this paper and electrical force can be given by Fel [14]:

½Fel�~XN

k~1

ðzk

zkz1

½�ee�k½E�kdz ð10Þ

Where fEg represents the electric field, and feg the piezoelectric coupling matrix. For sake ofsimplicity, the thermal effects have been neglected. For more detail on derivation of finite elementequation. One may consult Ref. [14]

Fig. 2. A wing of aircraft has been studied.

Fig. 3. Geometry of smart composite morphing structure.


Due to changing layup angle in the layer changes the global stress-strain relationship. Thetransformed relation of an orthotropic lamina for a plate as derived as [16]:

sxx

szz

txz

26664

37775

k

~

�CC11�CC13 0

�CC31�CC33 0

0 0 �CC55

26664

37775

kexx

ezz

cxz

26664

37775

k

{

0 0 e{13

0 0 e{33

e{15 e{

25 0

26664

37775

kEx

Ey

Ez

26664

37775

k

ð11Þ

where

C{11~C11 cos4 h

C{13~C13 cos4 h

Fig. 4. Layup configurations of morphing composite tail.

Table 1. Grapghite/epoxy(GY-70/934) and Piezoelectric properties and other parameters.

Properties

Grapghite/epoxy(GY-70/934) Piezoelectric

E1(Gpa) 294 86

E2(Gpa) 6.4 66.3

G12(Gpa) 4.9 31

n12 0.23 0.3125

r(kg=m3) 1590 7600

d31mV{1 - {122|10{12

d33mV{1 - 285|10{12

d15mV{1 - 0

G33mV{1 - 11:53|10{9


C{33~C33

e{31~e31 cos2 hze31 sin2 h

e{31~(e31{e24) cos h sin h

e{33~e33

e{31~e15 cos2 hze24 sin2 h

where �CCij are reduced stiffness and �eeij are reduced stiffness electro netostrictive materialcoefficients. fsg represents the stress vecto [16].

3. NUMERICAL EXAMPLE

An aircraft’s wing shown in Fig. 2 is considered. The focus is on the tail of wing that is similarto an arcplate. A small segment of acrplate is selected and shown in Fig. 3, where d is2 cm and r is 20 cm. The composite arcplate is an unsymmetric laminate with layupconfigurations of ½0=0={45=0=45=90=90=0� as given in Fig. 4. The material of this morphingplate is Graphite/Epoxy (GY-70/934) and the actuator element is piezoelectric [17]. The

Fig. 6. Measured internal energy vs. the displacement.

Fig. 5. Measured force vs. displacement.


corresponding material properties are given in Table 1. The thickness of substrate layers andpiezoelectric layer are, respectively, 100 mm and 50 mm.

3.1. Mode change in morphing structureIn order to change the mode of the composite plate, a piezoelectric actuator mounted on the

upper surface is utilized. The piezoelectric actuator is used for the 31 mode, in which the electricfield is applied through the thickness and the displacement is measured along the length of theactuator. Figure 5 illustrates the displacement measured versus the applied load in the center ofthe plate. The snap-thorough is occurred at point A. After point A, the morphing composite plateis switched from the first mode to the second mode. As it is observed the snap-throughphenomena results in changing the internal energy which is shown in Fig. 6. Another importantfeature is that utilizing the multi-stable mode structures may significantly reduce the requiredenergy to switch between the modes for a morphing structures as shown in Fig. 7, providing asignificant energy saving and consequently resulting in better performance during a moreover.

An interlayer stresses of each layer along the thickness is calculated using Eq. (11). Sincethe volume fraction of piezoelectric is small in the structure, the effect of electro-mechanical

Fig. 8. Force vs. voltage using mode d33 of PZT.

Fig. 7. Changing energy mode for conventional and morphing airfoil.


coupling is neglected to obtain the stresses. Preventing failure and/or mismatching thepiezoelectric layer from the substrate in{service is an interesting problem. The piezoelectric(PZT) actuator can apply inverse force on the composite structure after buckling to return thedeflection to allowable region. A piezoelectric actuator is used to apply a load in oppositedirection, modify the displacement after buckling, thus, availing the possibility of failure.

From Fig. 8, one may realize that the the critical point of interlayer stresses occurred at pointC. Therefore, this point is chosen to attach the piezoelectric actuator.

3.2. Failure controlConsidering the inhomogeneity in material and geometric of a composite plate integrated

with piezoelectric material, the problem of delamination, especially at the interfaces ofpiezoelectric and substrate is very severe. Delamination usually starts at the free edge ofpiezoelectric layer. The Fig. 9 illustrates possible delamination surface in multilayeredcomposite morphing structure schematically.

In order to control the response of the structure, an on-off controller is designed by using anopen-loop controller type as shown in Fig. 10. The controller switches to ‘‘On’’ when thedisplacement reaches the point A. The actuator applies force to change mode.

The interlaminar stresses through the thickness for multilayered morphing composite isshown in Fig. 11, in order to mitigate the interlaminar stresses, particulary at the critical point,using piezoelectric actuator, {10N force is applied to the surface.

Fig. 10. The failure controller of smart composite morphing structure is shown schematically.

Fig. 9. A delamination surface may occur, because of fatigue in surface between piezoelectric andgraphite/eopxy.


Similarly, Figs. 12–14 illustrate the interlaminar stresses, respectively, Von-misses, sxy andMax in-plane stress. Once again, to reduce the interlayer stresses, particulary at the criticalpoint, {10N force is applied by the piezoelectric actuator. It is observed that applying thisprocedure moves the interlaminar stresses to the safe side, and consequently, improve thein{service performance as shown in Fig. 15. Morphing composite usually expose to dynamicloading, requiring a reliable failure control strategy for dynamic loading as well.

Fig. 12. Distributing interlaminar stresses of Von-Misses through thickness between layers.

Fig. 11. Distributing interlaminar stresses sxx through thickness between layers.


Figure 16 shows the axial stress sxx subjected to a sinusoidal dynamic forces: 70 sin (5t) and{10 sin (5t). The harmonic force {10 is applied by PZT auctor as a failure controller. One maynote that almost 17% of stresses decrease in peak stresses when using PZT actuator, to move thestresses to the safe side.

Fig. 14. Distributing interlaminar stresses Max in-plane stress through thickness between layers.

Fig. 13. Distributing of sxy stress along thickness.


4. CONCLUSION

A nonlinear finite element model by using layerwise displacement theory is used to simulatethe snap-through phenomena in smart composite morphing tail. The interlaminar stresses dueto buckling in snap-through mechanism is computed.

Fig. 16. Stress sxx of critcal point on effect of dynamic force.

Fig. 15. Comparing sxx, Von-misses, sxy and Max in-plane stress with and without failurecontroller.


An on/off strategy is designed to control the shape of composite structure in{service bypiezoelectric actuator.

Respectively, PZT actuator apply load in opposite direction to prevent failure specifically, indelamination surface.

Using a PZT actuator, an electrical load is applied at the plate to reduce the interlaminarstresses and move the loading condition to a safe side.

It is observed that the present control technique may significantly reduce the risk ofunpredicted failure in the smart morphing composite plate. In particular, apply a small amountof electrical force using the piezoelectric actuator reduced the interlaminar stresses by 17 %,thus, improving the performance and safely issues in the structure.

5. ACKNOWLEDGEMENTS

The authors wish to thank the support provided by Sharif University of Technology,International Campus on Kish Island.

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