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| Hyper-singular equation method for radial crack in elastic plane with a circular inclusion |
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| DOI：10.7511/jslx20084102 |
| KeyWord:circular inclusion,radial crack,hyper-singular integral equation,stress intensity factor |
| DU Yun-hai YUE Jin-chao LV Cun-jing ZHANG Di |
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| Abstract: |
| A radial crack in an elastic plane with a circular inclusion is investigated by use of a hyper-singular integral equation method.Based on the fundamental solution of a plane with a circular inclusion under a polar co-ordinate,and using Betti's reciprocal theorem and the finite-part integral concepts,two independent hyper-singular integral equations for the crack problems of model I and model II are derived,in which the unknown functions is displacement discontinuities on the crack surface.Then,a numerical method for the solution of the hyper-singular integral equations are proposed,and the crack displacement discontinuities are approximated by products of a series of the second type of Chebyshev's polynomials and a basic density function,which exactly express the singularities of stress near the crack tips.The numerical solutions for the stress intensity factors of some examples are given.From the numerical results,it is shown that the stress intensity factors of a crack are greatly varied with the radius of a circular inclusion,the position of crack and the shear elastic module of a circular inclusion. |
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