Principal curvature
Principal curvature
(OP)
Hi
I am trying to understand a theoretical problem involving the contact between two surfaces from Roarks Formulas for Stress and Strain. I have uploaded a screen shot of the formulations of the solution.
I understand most of the solution, except the principal curvatures. I have tried to look up principal curvature, but still not sure how is applied to this problem and how it is used to solve the contact problem.
I would really appreciate any help.
https://dl.dropbox.com/u/47274064/Prin_curve_1.JPG
Thanks.
I am trying to understand a theoretical problem involving the contact between two surfaces from Roarks Formulas for Stress and Strain. I have uploaded a screen shot of the formulations of the solution.
I understand most of the solution, except the principal curvatures. I have tried to look up principal curvature, but still not sure how is applied to this problem and how it is used to solve the contact problem.
I would really appreciate any help.
https://dl.dropbox.com/u/47274064/Prin_curve_1.JPG
Thanks.





RE: Principal curvature
i'd have more questions about the comment of "max and min radius" for the body, then calling out only one radius ... i suspect the critcal combination is the smallest radius for both bodies (so why mention the max radius ?)
RE: Principal curvature
I understood that it is the reciprocal of the radius, but I also don't really understand what the minimum radii of curvature is or how it is established for a contact problem?
The other aspect I am not sure on is how the planes of R1 and R2 are established?
Any ideas anyone?
Thanks.
RE: Principal curvature
i would consider a plane revolving around the line from the contact point to the centre of the body (however sense that makes ?)
so that the plane sections the body and you can see the radius near the contact area.
roark mentions the angle phi between the two planes on the two bodies.
RE: Principal curvature
Or maybe I have been doing it wrong.
Regards,
Cockroach
RE: Principal curvature
RE: Principal curvature
There is a good introduction to this type of contact problem in "Theory of Elasticity" by Timoshenko and Goodier.
All the terms are clearly defined
Andries
RE: Principal curvature
RE: Principal curvature
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