Transition Method of Geometrically Similar Element for Dynamic V-Notch Problem

A semi-analytical method is proposed to determine the dynamic stress intensity factor of two-dimensional V-notch problems. A group of geometrically similar elements is automatically generated layer by layer around the point of singularity. The large number of degrees of freedom around the V-notch tip are transformed to a small set of generalized coordinates by means of the series expansion formulas of the displacement field. By taking advantage of the same stiffness and similar mass of 2D similarly shaped elements, a single transformation of the stiffness and mass for the first two layers of mesh is enough for all. As an example, the three points bending specimen with V-notch is analyzed.