On the conventional boundary integral equation formulation for piezoelectric solids with defects or of thin shapes |
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Affiliation: | 1. Luxembourg Institute of Science and Technology, LIST, 5, Avenue des Hauts Fourneaux, L-4362 Esch/Alzette, Luxembourg;2. Laboratoire d’Etude des Microstructures et de Mécanique des Matériaux, LEM3, UMR CNRS 7239, Université de Lorraine, Ile du Saulcy, F-57045 Metz, France;3. Université de Lyon-INSA, Laboratoire de Génie Civil (LGCIE), Batiment Coulomb, F-69100 Villeurbanne, France;1. CeNSCMR, Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Republic of Korea;2. Functional Ceramics Group, Korea Institute of Materials Science (KIMS), 66 Sangnam-Dong, Changwon, Gyeongnam 641-831, Republic of Korea;3. iBULe Photonics Co. Ltd, 7-39 Songdo-dong, Yeonsu-gu, Incheon, Republic of Korea |
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Abstract: | In this paper, the conventional boundary integral equation (BIE) formulation for piezoelectric solids is revisited and the related issues are examined. The key relations employed in deriving the piezoelectric BIE, such as the generalized Green's identity (reciprocal work theorem) and integral identities for the piezoelectric fundamental solution, are established rigorously. A weakly singular form of the piezoelectric BIE is derived for the first time using the identities for the fundamental solution, which eliminates the calculation of any singular integrals in the piezoelectric boundary element method (BEM). The crucial question of whether or not the piezoelectric BIE will degenerate when applied to crack and thin shell-like problems is addressed. It is shown analytically that the conventional BIE for piezoelectricity does degenerate for crack problems, but does not degenerate for thin piezoelectric shells. The latter has significant implications in applications of the piezoelectric BIE to the analysis of thin piezoelectric films used widely as sensors and actuators. Numerical tests to show the degeneracy of the piezoelectric BIE for crack problems are presented and one remedy to this degeneracy by using the multi-domain BEM is also demonstrated. |
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