Evaluation of notch singularity orders in piezoelectric materials

A new method is proposed to analyze the stress singularity and the electricity singularity at the piezoelectric notch tip. Based on the assumption that the displacement field at the notch tip was expanded as the power series asymptotic expansion, the governing equations on the notched structure, i.e., the stress equilibrium equations and the Maxwell equation, were turned into the characteristic equations respects to the singularity orders. The mechanic and electric boundary conditions on the notch surfaces were transformed into the combination of the singularity order and the corresponding eigen-functions. The analysis of the piezoelectric notch singularity orders was turned into calculating the eigen-values of the ordinary differential equations under corresponding boundary conditions. The interpolate matrix method was introduced to solving the established differential equations. Numerical results show that all the singularity orders at the piezoelectric notch can be evaluated in the present method. As a special case of the notch, the singularity orders of cracks can also be obtained by the present method.