Hybrid finite element formulation for wave propagation in piezoelectric materials

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University of New Brunswick
The equations of piezoelectricity are sufficiently complex to limit closed form solution for all but the simplest cases. This is unfortunate, since the piezoelectric effect plays an important role in the fields of crystal physics and electromechanical transducer technology. Even though numerical and computational analysis has provided significant advances in the field, the successful study of piezoelectric transducers is affected greatly by accurate material parameters, optimal device design/geometry and reliable modeling of wave propagation phenomena. This thesis is concerned with the latter, as it proposed and assessed a finite element formulation with mixed polynomial/trigonometric interpolation functions for wave motion analysis in linear piezoelectric media. This mixed formulation promises a reduction in computation time due to a decrease in the number of required elements. A code written in FORTRAN is used as the main simulation tool, and the transient study utilized an explicit time integration. Displacement and velocity field responses were obtained for three distinct case studies, each subjected to different boundary conditions and loads. The numerical accuracy and efficiency of the method were established as a function of the number of elements per wavelength in the model, as well as the degree of enrichment in the shape functions. These were compared to conventional FEA shape functions built in the FORTRAN code and using a calibrated solution modeled in Comsol Multiphysics™ as the reference value. The hybrid formulation produced encouraging results, with good improvements in simulation times for 2-D analysis, while maintaining the accuracy of the solution and showing potential for significant savings in model size and memory requirements. The computational cost change in the 1-D analysis was minor in comparison. Lastly, the computational time savings obtained with the hybrid interpolation functions could be more significant if applied to 3-D models. These are commonly used in applica-tions involving structures with built in piezoelectric transducers for structural health mon-itoring, as well as composite materials in medical imaging, among others. However, further refinement of the FE code, numerical integration techniques and addition of new element types are still necessary before tackling these challenges.