Evaluation of the singularity exponents and characteristic angular functions for piezoelectric V-notches under in plane and out of plane conditions

• The singularity orders for piezoelectric notches are evaluated.
• The variation behavior of singularity orders with polarization directions is investigated.
• The conventional transcendental equations for determining singularity orders are avoided.

Based on the assumption that the physical fields close to the V-notch vertex are expressed by the series asymptotic expansions, the evaluation of singularity exponents for piezoelectric V-notches is turned into solving the characteristic values of ordinary differential equations under given boundary conditions, which are a set of equations with variable coefficients and solved by the interpolating matrix method developed by part of the authors before. The singularity analysis for V-notches under in plane and out of plane conditions is taken into account. Numerical results show that all the singularity exponents and the characteristic angular functions can be evaluated synchronously without the need of solving the transcendental equations iteratively. The present method is not only suitable for the singularity analysis of V-notches, but also for cracks and interface ends, without encountering the problem of ill-posed equations when the complex potential function method for the singularity analysis of V-notches is degenerated to analyze the singularity of cracks.