singular stresses at a vertex and along a singular line in three-‎dimensional piezoelectric bonded joints

Singular stress fields in three-dimensional piezoelectric bonded joints are investigated at a vertex and along a free edge (the singular line) of an interface. two perfectly bonded joints, which are different in the side surface shapes, are considered. the joints consist of multi-terms of singularity. two-major terms of singularity are investigated in details. the orders of singularity at the vertex and along the singular line are calculated using three-dimensional finite element eigenanalysis. the intensities of singularity are calculated using the conservative integral. the intensities of singularity at several points located on the singular line are examined. the relationships between the intensities of singularity and the distances from the vertex are plotted to determine how the vertex singularity affects the singularity along the singular line. finally, the relationships between singular stress fields at the vertex and along the singular line are considered.