Finite Geometrically Similar Element Method for Dynamic Problem of a Cracked Specimen

Abstract

A group of geometrically similar elements is automatically generated layer by layer around the tip of crack. By taking advantage of the same stiffness and similar mass of similarly shaped elements, the combined stiffness matrix and combined inertia matrix in area can be expressed by the displacement row matrix of outer polygon. The global stiffness matrix will be obtained if the combined stiffness matrix and combined inertia matrix of area are assembled to those of another elements according to corresponding nodes. The small set of generalized coordinates can be obtained through solving the equation, and then the dynamic stress intensity factor of crack will be obtained. The three points bending with single crack and shearing model with double cracks in explosive loading were calculated with finite geometrically similar element method.