Numerical Analysis Of The Singular Behavior Of The Interface Side

Based on the singular stress field with multiple singularities, numerical methods to determine the orders of the multiple stress singularities are proposed from the numerical solutions obtained by common numerical procedures. Several models of bonded dissimilar materials with interface edges are calculated.Displacement, electrical potential, singular stress fields and singular electrical displacement fields near a singular point are deduced by the eigenfuntion expansion method based on the general solution of the spatial axisymmetric problem of the transversely isotropic piezoelectric media. A generally axisymmetric interface edge of bimaterials with arbitrary interface angle and joining angle is analyzed theoretically by using this method. Eigenequation about singularity, singular stress fields and electrical displacement fields near the interface edge are obtained under axisymmetric distortion.Finally, a special finite element formulation which is based on the principle of minimum potential energy has been developed for determining the orders of the singularity of the singular stress fields around the singular point (interface edge, interface corner and the interface crack) in the bonded dissimilar anisotropic/anisotropic, piezoelectric/piezoelectric as well as piezoelectric/anisotropic materials. The numerical results show that this method is very convenient and efficient.This thesis has the following three innovations: 1. One numerical method to determine the orders of the multiple stress singularities is proposed from the numerical solutions obtained by common numerical procedures. 2. Eigenequation about singularity, singular stress fields and electrical displacement fields near the axisymmetric interface edge of two bonded dissimilar transversely isotropic materials are obtained under axisymmetric distortion. 3. A special finite element formulation has been developed for determining the orders of the singularity in the bonded dissimilar piezoelectric/ piezoelectric as well as piezoelectric/anisotropic materials.