The Transition Method of Geometrically Similar Element for Dynamic Crack Problem

摘要

A semi-analytical method is proposed to determine the dynamic stress intensity factor (DSIF) of two-dimensional (2D) crack 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 crack 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. The problem of a rectangular plate with a central crack is calculated.