Application of the internal and external Williams functions to plane elasticity problem for A Mode I crack


  • E. Yakovleva Інститут проблем міцності імені Г.С. Писаренка НАН України, Ukraine
  • A. Oryniak Інститут проблем міцності імені Г.С. Писаренка НАН України, Ukraine
  • І. Orynyak Інститут проблем міцності імені Г.С. Писаренка НАН України, Ukraine



Crack, stress intensity factor, inner and outer Williams function, convergence, Eri functions, static plane body


The main idea of this research is in applying Williams functions to calculate stress intensity factors (SIF) in case of 2D elastic bodies with cracks. Firstly, we employ the concept of Williams functions converging on infinity which can be used along with
traditional functions to analyse infinite bodies and to study partially loaded crack boundaries. We show the convergence of SIF for the case of a strip and for the bodies with circular boundary depending on the number of Williams functions and on the number of
intervals on the boundary in case of numerical integration. Secondly, we complement the standard set of equations with the global equilibrium conditions of the elastic body to improve the accuracy of the calculation. We compared the computed stress with the one
defined on the boundary.


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How to Cite

E. Yakovleva, A. Oryniak, and Orynyak І., “Application of the internal and external Williams functions to plane elasticity problem for A Mode I crack”, Mech. Adv. Technol., no. 2(83), pp. 31–41, Oct. 2018.



Original study