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Keywords: piezoelectric, finite element method, inverse problem, genetic algorithms, medial axis, transfinite interpolation, stretching function.

Summary

The presence of defects in piezoelectric ceramics prevents the material from executing the function for which was designed. In this work, a model-based inverse problem to find defects in a piezoelectric PZT-4 quadrilateral plate has been developed combining the finite element method (FEM) and genetic algorithms. The model-based inverse problem can be stated as a minimization problem where each solution is generated by computing a cost functional for which one forward problem is evaluated using the FEM. For this approach there are two problems: i) the genetic algorithm used to solve the optimization problem implies a large number of evaluations. However, the use of gradient-based algorithms is limited to local optimization, while the genetic algorithm permits a global optimization to be attained. On the other hand, ii) strong concentrations of the electric field and stresses around the defect arise for piezoelectric materials with a defect, as it has been reported in the literature. Note that, these concentrations are greater than for elastic materials without coupling.

Therefore, the main goal of this work is draw quality meshes to solve the forward problem using the FEM. To this end, a fully automatic algorithm has been developed to construct multi-block structured meshes in two dimensions that provide good results in a reduced CPU time. The algorithm follows three steps: i) to subdivide the domain into simple blocks, using the medial axis transform, ii) to mesh each block, by a simple transfinite interpolation, and iii) to concentrate elements next to the defect, using an special stretching function to determine strain, electrical and stress concentrations around the defect in piezoelectric ceramics.

Finally, some results of the model-based IP solution are shown, concluding that it is possible to characterize the defect with an error of less than 5 times the error in the measurements when a mechanical load transversal to the poling direction is applied.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 88 PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping and M. Papadrakakis Paper 36 Mesh Generation for Cavity Damage Identification in Piezoelectrics R. Palma¹, G. Rus¹, J.L. Pérez-Aparicio² and R. Gallego¹ ¹Structural Mechanics & Hydraulic Engineering, University of Granada, Spain ²Structural and Continuum Mechanics, Polytechnic University of Valencia, Spain doi:10.4203/ccp.88.36 purchase the full-text of this paper Full Bibliographic Reference for this paper , "Mesh Generation for Cavity Damage Identification in Piezoelectrics", in B.H.V. Topping, M. Papadrakakis, (Editors), "Proceedings of the Ninth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 36, 2008. doi:10.4203/ccp.88.36 Keywords: piezoelectric, finite element method, inverse problem, genetic algorithms, medial axis, transfinite interpolation, stretching function. Summary The presence of defects in piezoelectric ceramics prevents the material from executing the function for which was designed. In this work, a model-based inverse problem to find defects in a piezoelectric PZT-4 quadrilateral plate has been developed combining the finite element method (FEM) and genetic algorithms. The model-based inverse problem can be stated as a minimization problem where each solution is generated by computing a cost functional for which one forward problem is evaluated using the FEM. For this approach there are two problems: i) the genetic algorithm used to solve the optimization problem implies a large number of evaluations. However, the use of gradient-based algorithms is limited to local optimization, while the genetic algorithm permits a global optimization to be attained. On the other hand, ii) strong concentrations of the electric field and stresses around the defect arise for piezoelectric materials with a defect, as it has been reported in the literature. Note that, these concentrations are greater than for elastic materials without coupling. Therefore, the main goal of this work is draw quality meshes to solve the forward problem using the FEM. To this end, a fully automatic algorithm has been developed to construct multi-block structured meshes in two dimensions that provide good results in a reduced CPU time. The algorithm follows three steps: i) to subdivide the domain into simple blocks, using the medial axis transform, ii) to mesh each block, by a simple transfinite interpolation, and iii) to concentrate elements next to the defect, using an special stretching function to determine strain, electrical and stress concentrations around the defect in piezoelectric ceramics. Finally, some results of the model-based IP solution are shown, concluding that it is possible to characterize the defect with an error of less than 5 times the error in the measurements when a mechanical load transversal to the poling direction is applied. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £145 +P&P)
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