Structural Engineering and Mechanics

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Efficient methods for integrating weight function: a comparative analysis

  • Dubey, Gaurav (Department of Mechanical Engineering, Institute of Technology, Guru Ghasidas Vishwavidyalaya) ;
  • Kumar, Shailendra (Department of Civil Engineering, Institute of Technology, Guru Ghasidas Vishwavidyalaya)
  • Received : 2014.05.25
  • Accepted : 2015.07.27
  • Published : 2015.08.25
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Abstract

This paper introduces Romberg-Richardson's method as one of the numerical integration tools for computation of stress intensity factor in a pre-cracked specimen subjected to a complex stress field across the crack faces. Also, the computation of stress intensity factor for various stress fields using existing three methods: average stress over interval method, piecewise linear stress method, piecewise quadratic method are modified by using Richardson extrapolation method. The direct integration method is used as reference for constant and linear stress distribution across the crack faces while Gauss-Chebyshev method is used as reference for nonlinear distribution of stress across the crack faces in order to obtain the stress intensity factor. It is found that modified methods (average stress over intervals-Richardson method, piecewise linear stress-Richardson method, piecewise quadratic-Richardson method) yield more accurate results after a few numbers of iterations than those obtained using these methods in their original form. Romberg-Richardson's method is proven to be more efficient and accurate than Gauss-Chebyshev method for complex stress field.

Keywords

References

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  1. Improvement in the numerical method for integrating weight function of pre-cracked specimen vol.154, 2016, https://doi.org/10.1016/j.engfracmech.2015.12.036
  2. Approximate Stress Intensity Factors for a Semi-Circular Crack in an Arbitrary Structure under Arbitrary Mode I Loading 2018, https://doi.org/10.1016/j.tafmec.2018.01.007