Abstract: Based on asymptotic extension of displacement field at a composite notch tip, equilibrium equation for a notch subjected to anti-plane loading is transformed into a characteristic differential equation respects to notch singularity orders. A transformation is applied to convert the equation into a set of characteristic linear ordinary differential equations. Interpolate matrix method is introduced to solve the equations for getting notch singularity orders. A single material notch, a bi-material notch and a notch terminated at bimaterial interface are studied successively. Examples indicate that the method provides all stress singularity orders synchronously. Though singular stress state is not shown with regard to non-singular orders, non-singular stress orders are indispensable parameters as evaluating complete stress field at notch tip region.

Key words: composite, notch under anti-plane loading, singularity analysis, asymptotic extension