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help for determination of crack initiation location with analytical methods

  There are three elliptical holes in the given plate, but make different angle with the direction of stress applied on the plate. I wonder if I can gain the solution listed below using analytical methods?(1) crack initiation will happen in which ellipse firstly, (2)the exaxt crack initiation location around the ellipse? And how?

 

thanks a lot!

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liuliping's picture

This seems to be an interesting problem. I am also curious if the elastic problem invoving multiple elliptic cracks has been solved analytically. It may be hard, but still doable. Of course, one may always turn to numerics.....

The answer is 'no'. Analytical solutions are known either for a single crack or ellipse in infinite plate or for several specially located cracks (infinitely thin cuts) or for a crack at the centre of a strip (in special orientations).

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