A geometrically nonlinear analysis of interlaminar stresses in unsymmetrically laminated plates subjected to inplane mechanical loading

<title>Shape control of a nonlinear smart plate</title>

“…(9) The Cauchy stress tensor can be computed from TKL by using o.ij = J'X1,KX,LTKL. (10) In order to complete the formulation of the problem, we need to specify initial displacements and initial velocities; we take these to be zero.…”

“…Moderate loads can cause finite deformations of such structures. Norwood et al [9], Kulkarni and Hanagud [10], and Pal et al [11] have accounted for geometric nonlinearities by using nonlinear strain-displacement relations and linear stress-strain relations in modeling piezoelectric materials. Fully nonlinear material models that account for both large deformations and large electric fields have been developed by Maugin et al [12] and Tiersten [13,14].…”

Finite dynamic deformations of smart structures

“…Whereas foregoing studies have considered in®nitesi-mal deformations and hence have used linear material models, Norwood et al (1991), Kulkarni andHanagud (1991), andPai et al (1992) have accounted for material and/or geometric nonlinearities. Crawley and Anderson (1990) experimentally showed that the normal strain vs. electric ®eld relation for the G1195 PZT is highly nonlinear for driving electric ®elds exceeding 100 V/mm.…”