Geometrically nonlinear higher-order shear deformation FE analysis of thin-walled smart structures

Vu, Duy Thang; Schmidt, Rüdiger (Thesis advisor)

Aachen : Publikationsserver der RWTH Aachen University (2011)
Dissertation / PhD Thesis


In this thesis the influence of geometrical nonlinearity is studied in the finite element analysis of quasi-static and transient dynamic response of shape and vibration control of thin-walled structures with integrated layers or patches of piezoelectric materials. The thesis addresses the kinematic hypotheses on which linear and nonlinear theories of such smart structures are based. Finite plate elements are developed, which employ strain-displacement relations based on either first- or refined third-order transverse shear deformation hypothesis. Using these kinematic models, comparative finite element simulations are performed for the transverse stress distribution analysis, the nonlinear shape control and the time histories of nonlinear vibrations and sensor output voltage due to a step force acting on thin beams and plates, respectively, with a piezoelectric patch bonded to the surface. Furthermore, an experiment reported in literature for vibration control of a clamped beam using a piezoelectric layer bonded to the surface is simulated. The comparative studies are performed based on linear theory, von Kármán-type nonlinear theory, and nonlinear moderate rotation theory.