مدل سازي اجزاء محدود تير با وصله هاي پيزوالكتريك با مدل غير خطي فون كارمن

چكيده انگليسي :

Finite Element Modeling of the Piezolaminated Beam Using Von Karman Nonlinear Strain Displacement Relation Ahmad Ali Tahmasebi Moradi aa tahmasebimoradi@me iut ac ir aatahmasebi@yahoo com March 15 2010 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 IranDegree M Sc Language FarsiSupervisors Ziaie Rad Saeed Professor Email szrad@cc iut ac ir Behbahani Saeed Assistant Professor Email behbahani@cc iut ac irAbstract Piezoelectric actuators sensors have been widely used for the design of smart structures over the last twodecades leading to high performance and light weight solutions They can be either surface mounted orembedded into a host structure Surface mounted actuators sensors are normally poled in the thickness direction so that they act as extension actuators sensors while embedded actuators sensors are normally poled in thelongitudinal direction therefore they act as shear actuators sensors In view of their wide application the modeling of these structures is a major concern for many engineers Itoften requires a coupled modeling between the host structure and the piezoelectric sensors and actuators Due tothe complexity of the system different theoretical assumptions have been considered in dealing with couplingbetween mechanical and electrical fields Hence many researches have been conducted on the modeling ofpiezolaminated structures In first glance it seems that all aspects of the finite element modeling of a piezolaminated beam have beenalready presented in the literatures However it has to be noted that in all the finite element models of apiezolaminated beam the small deformation theory was assumed It can be shown that an electromechanicaleffect for the extensional piezoelectric layers is overlooked due to this assumption This is the main drawback ofavailable approaches in the literatures which is taken into account in the present work This effect changes theface stiffness of the beam By considering this effect the higher applied voltage to the extensional piezoelectriclayers leads to more change in the face stiffness even for small deformation domain Although this effect wasconsidered in some other models In these models it was shown that it could be a very useful and importanteffect to change the face stiffness of the beam However those were not finite element models and weresuffering from a poor electromechanical coupling In addition these models were not easy to handle for use invarious control algorithms In this work an electromechanically coupled finite element model for a piezolaminated beam was presented For the mechanical model classical sandwich theory CST was considered where the core was modeledaccording to the third order shear deformation theory TSDT On the contrary the face sub layers weremodeled with the Euler Bernoulli hypothesis By means of the Von Karman s theory the displacements strainsrelations were developed For complete satisfaction of the electrostatic equilibrium equation for both shear andextensional piezoelectric layers the longitudinal and transverse electrical fields were considered In the nextstep a variational formulation was written using the Hamilton s principle with extension to the piezoelectricmedia Then using the aforementioned assumptions a finite element FE model was developed Electrically constant electric difference of potentials for core and face piezoelectric layers were assumed Also quadraticshape functions for the third order variable of electric potential were considered for the core piezoelectric layers For the mechanical variable interpolations linear Lagrange quadratic and cubic shape functions wereconsidered for the axial displacement bending rotation of the core and transverse displacement respectively For obtaining a faster and more reliable solution and also for preventing the ill conditioning problem theelectrical and elemental variables were condensed out statically Finally by examining the governing equationfor the sa

طهماسبي مرادي، احمدعلي

مدل سازي اجزاء محدود تير با وصله هاي پيزوالكتريك با مدل غير خطي فون كارمن

اصل گسترش يافته , هميلتون , تئوري مرتبه سوم برشي , تئوري ون كارمن , روش المان محدود