MODELING AND FINITE ELEMENT SIMULATION OF SMART STRUCTURES

Abstract

In the last two decades, the subject area of smart/intelligent materials and structures has experienced tremendous growth in terms of research and development. Most applications of smart structures comprise piezoelectric materials as integrated actuators/ sensors due to their suitability for shape control and faster response time. It has been experimentally shown that these materials exhibit non-linear behavior even at low electric fields. Few re5earchers1251126] have successfully developed geometrically non-linear models with linear electro-elastic relations. A very few authors considered the material non-linearities considering the rate-independent hysteresis in ferroelectric materials. However, the behavior of piezolaminatecl structures under large electric fields and small strains can he predicted more accurately using non-linear const.itutive equations for which the available literature is very scarce. Nevertheless, all the numerical models available in literature except Kapuria[12], neglect the two-way electromechanical coupling which results in inaccurate solutions. This dissertation work is focused on non-linear modeling and finite element simulation of smart piezoelectric shell structures using nonlinear constitutive relationships of electro-mechanical coupling under large electric fields. The non-linear finite element formulations are derived from the virtual work variational principle using the non-linear electro-elastic relations given by Tiersten[34]. A robust four node shell element refined by applying an enhanced assumed strain method for in-plane bending strains and an assumed natural strain method for transverse shear strains is used. The electric potential is assumed to vary quadratically through the thickness of shell and the outer surfaces are considered equipotential being electroded. The kiiiemnatical relations are based on first order shear deformation hypothesis assuming small strains and small rotations. The non-linear equilibrium equations of statics and dyiiamics are solved using iterative Newton-Raphson approach and Newmark's method in Fortran. The developed numerical method is validated with experimental and analytical results available in literature. Additionally static and dynamic behavior of smart l)iezo-actllated structures under strong a)plie(I electric field is denionstrated by deploying the developed numerical FE- model to some numerical problems.