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Structural Engineering and Mechanics
  Volume 43, Number 3, August10 2012 , pages 321-336

A new numerical modelling for evaluating the stress intensity factors in 3-D fracture analysis
Zongjie Cao and Yongyu Liu

    As an improvement on the isoparametric element method, the derivation presented in this paper is close to that done by Wang (1990) for the 2-D finite element. We extend this idea to solve 3-D crack problems in this paper. A new displacement modelling is constructed with local solutions of threedimensional cracks and a quasi-compatible isoparametric element for three-dimensional fracture mechanics analysis is presented. The stress intensity factors can be solved directly by means of the present method without any post-processing. A new method for calculating the stress intensity factors of three-dimensional cracks with complex geometries and loads is obtained. Numerical examples are given to demonstrate the validity of the present method. The accuracy of the results obtained by the proposed element is demonstrated by solving several crack problems. The results illustrate that this method not only saves much calculating time but also increases the accuracy of solutions. Because this quasi-compatible finite element of 3-D cracks contains any singularities and easily meets the requirement of compatibility, it can be easily implemented and incorporated into existing finite element codes.
Key Words
    crack; stress intensity factor; singular element; finite element method
Zongjie Cao and Yongyu Liu: Department of Aviation Mechanical Engineering, Aviation University of Air Force,
Changchun, 130022, China

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