Finite Geometrically Similar Element Method for Dynamic Fracture Problem
A finite geometrically similar element method is proposed to determine the dynamic stress intensity factor. 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 tip of singularity is 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 similarly shaped elements, the combined stiffness matrix of super-element is obtained directly. The small set of generalized coordinates can be obtained through solving the equation, and then the dynamic stress intensity factor of V-notch (crack) will be obtained. There are some advantages for this method such as good adaptability, high precision and good convenience.
S.W. Nam, Y.W. Chang, S.B. Lee and N.J. Kim
Y. T. Li and P. Ma, "Finite Geometrically Similar Element Method for Dynamic Fracture Problem", Key Engineering Materials, Vols. 345-346, pp. 441-444, 2007