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I have to implement the following figure in a programme I am writing but I actually don’t know if there exists an analytical equation describing it. Before I had my problem propagation like a rectangular box, but this might give a better approximation. For your information I am writing a programme to describe fracture propagations in oil reservoirs at work. Do some of you guys know if it can be obtained and if yes  what it is? If no, why not? Generally assume that radius R1, R2, R3 and R4 are all different from each other. I was thinking about separating it into four sub problems and use the fact that I am looking for a function that has to be perpendicular to each radius, but I don’t want to spend a lot of time on this if there is a generally known formula.
Thx,
Peter.
PS: Note that the outer elliptical line is wrong but just there to illustrate the problem!
Thx,
Peter.
PS: Note that the outer elliptical line is wrong but just there to illustrate the problem!
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