Evaluation of stress intensity factors of notched plate by an over-deterministic method basing on the boundary element method

Abstract

The singular stress field near the vertex of a notched plate will affect the safety of structure.It is necessary to evaluate the strength of a notched plate.The singular characteristic equation of the notch in a plate is firstly established,basing on the elastic governing equation of a plate and the asymptotic expansion theory near the notch tip.The interpolating matrix method is then introduced to solve it for getting the singularity orders,characteristic angle functions and their derivatives of the notch.The boundary element method is thereafter applied to determine the displacements of the inner points on the arc around the notch tip. The displacement values are substituted into the asymptotic expansion to form a set of non-positive definite equations,which are solved by the over-deterministic method to obtain the amplitude coefficients in the asymptotic expansion. The stress intensity factors are further given out basing on the amplitude coefficients. The stress intensity factors of the notched plate under the symmetrical load,anti-symmetric load and mixed-mode load are respectively investigated.