**Fixed-Price**- Entry Level ($) - Est. Budget: $65 - Posted

I'm looking for an engineer to develop a set of piecewise equations for computing the stress field around a shaped hole in an infinite plate. The hole shall take the form of compound ellipses, which intersect at a points of equal slope (see attachment).
The analyst will assume that the stress field of each of the compound ellipses will behave independently from one another. Verification of equal stress state at the intersection of the ellipses is required. The assumption will be further validated with finite element modeling in future work. The stress field around the perimeter of the ellipse will be a function of theta and will include the following parameters:
R = Ratio of A-to-B (0<R<inf)
M = curvature at intersection, squareness (-inf<M<0)
The stress field around an elliptical feature can be found from a reference such as Peterson's Stress Concentration Factors, or other locations on the internet (e.g. http://www2.mae.ufl.edu/haftka/adv-elast/lectures/Sections14.1-2.pdf).
The developed equations will be used to optimize the length-to-width ratio and squareness of such a hole in a known biaxial stress field, using stress superposition in a fatigue-critical application.
Applicants should provide proposal with:
1. Estimated cost
2. Estimated number of hours to perform work
3. Soonest possible start date and associated finishing date
>>>DELIVERABLE<<<
The deliverable will be a PDF document with the derivation of a piecewise equation for the stress field around the perimeter of a shaped hole, as described in the attachment.

**Skills:**Calculus Geometry Mechanical Engineering Physics