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Development and Applications of Geometrically Nonlinear Piezoelectric Shell Elements

Wenkai Niu, University of Nebraska - Lincoln


The investigation in this dissertation is concerned with development and applications of geometrically nonlinear triangular shell finite elements for the studies of highly geometrical nonlinear piezoelectric structures. In engineering practice, a nonlinear approach for piezoelectric shell structures is needed. This method is to enable one to (a) reveal the changing of configurations more precisely comparing with linear approach, and (b) deal with practical situations where large mechanical/electrical inputs and, in turn, large deformation phenomena exist. Hybrid strain and mixed formulation-based three node flat triangular shell elements are obtained for linear and nonlinear piezoelectric shell structures analyses. The elements are obtained by combining geometrically nonlinear shell elements with drilling degree-of-freedom and a piezoelectric shell element with assumed electrical field. For the nonlinear analysis the updated Lagrangian formulation and incremental Hellinger-Reissner variational principle are applied, with incremental displacements and strains being independent assumed fields. The hybrid strain and mixed formulation-based elements have features, such as finite strain, director formulation and updating thickness. The actuator and sensor equations as well as control algorithms are also introduced. A collection of geometrically nonlinear piezoelectric structures is treated by using the developed elements. The collection includes bimorph beam, sandwich beam, simply-supported sandwich plate, cylindrical ring, spherical cap, cylindrical panel, energy bender, simply-supported square plate, and cylindrical shell. These structures are analyzed for static and dynamic behaviors with piezoelectric actuating and sensing. Considerations of large deformations and strong electrical fields are emphasized. Computed results are compared with available analytical or numerical results reported in the literature. These numerical results have demonstrated the excellent performance of the geometrically nonlinear piezoelectric shell elements. Recommendations for further investigations are finally included in this dissertation.

Subject Area

Mechanical engineering

Recommended Citation

Niu, Wenkai, "Development and Applications of Geometrically Nonlinear Piezoelectric Shell Elements" (2017). ETD collection for University of Nebraska-Lincoln. AAI10682944.