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On the singularities of the thermo-electro-elastic fields near the apex of a piezoelectric bonded wedge. (English) Zbl 1119.74398
Summary: Based on the generalized Lekhnitskii formulation and Mellin transform, the thermo-electro-elastic fields of a piezoelectric bonded wedge are investigated in this paper. From the potential theory in a wedge-shaped region, a general form of the temperature change is proposed as a particular solution in the generalized Lekhnitskii formulation. The emphasis is on the singular behavior near the apex of the piezoelectric bonded wedge, including singularity orders and angular functions, which can be computed numerically. The interface between two materials can be either perfectly bonded, namely type A, so that the continuity of electric displacements holds, or a thin electrode, namely type B, so that the electric potential is grounded. Case studies of PZT-5H/PZT-4 and graphite-epoxy/PZT-4 bonded wedges reveal that, in most cases, the type B continuity condition has more severe singularities than type A due to the mixed boundary point of the electrostatics at the apex of the wedge. The results of this study show that the reduction or disappearance of singularity orders is possible through the appropriate selection of poling/fiber orientations and wedge angles.

MSC:
74G70 Stress concentrations, singularities in solid mechanics
74F05 Thermal effects in solid mechanics
74F15 Electromagnetic effects in solid mechanics
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