Based on the classical elastic-plastic theory,an elastic-plastic finite element program was developed respectively for kinematic hardening material,which had a successful simulation of fatigue crack propagation with a singularity isoparametric element and the criterion of critical intensity factor.

Blow-up for degenerate and singular parabolic systems with nonlocal source;

Creation and application of a new type of three-dimensional isoparametric singular element with 12 nodes

The characteristic of this model is:a new interface edge singular element model is derived based on the numerical fundamental solutions obtained from the finite element eigensolutions method.

The finite element analysis models of linear elastic fracture with 20-nodes substance element and cracking singular element were established.

As an analytical study, a 3D orthotropic FEM model is also adopted to pick up the singularity in the strain and stress at the crack tip, where singular elements are used around the crack tip.

In this paper according to comparing extrapolate method with singularity element method which are the methods of calculating the stress density factor in linear elastic fracture mechanism field,Thus gets corresponding conclusion.

In this paper two methods of calculating stress density factor in linear elastic fracture mechanism field, namely extrapolated methods and singularity element method, are compared.