In the present study, a conservative integral based on the Betti reciprocal principle is extended for calculating the intensities of singularities at a vertex of the interface in three-dimensional piezoelectric bonded joints. Eigenanalysis formulated using a three-dimensional finite element method (FEM) is used to calculate the order of stress singularity, angular variables of mechanical displacements, stresses, electric displacements and electric potential. A model with applied both mechanical and electrical loading conditions are considered. In order to investigate the influence of mesh refinement and integral area on the accuracy of the results, models with various element sizes and integral areas are used. The results are compared with those obtained from conventional FEM, in which using extremely refined meshes near the singular point.

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