Meshing hole with concentric pattern

Hi all, 

 

Can someone explain to me how you can get a mesh that looks like the ones in the picture below? Basically, a series of concentric rectangles around the hole. The pic is from an Altair ebook. It suggests to split the surface along the diagonals and use the bias option along the diagonal (to get the different density), I tried but I can't get the nice regular rectangular pattern, but rather something like in the second pic below. 

 

I think there must be an automated way to obtain such a mesh, rather than manually splitting the surface with trim lines... 

 

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Thank you!!