# The force distribution along curved surface of contact [closed]

Is it possible to calculate the stress or contact force distribution over a curved contact surface?

I will try to explain the general idea in the figure below. Object $$O$$ (could be assumed to be rigid if it helps) is laying on the curved surface of a rigid body $$B$$ with the contact surface $$S$$ bounded by $$A$$ and $$B$$. Object $$O$$'s weight is negligible. A torque $$T$$ is applied at point $$P$$ on $$O$$. I am interested in calculating/estimating the distribution of force $$f(s)$$ applied along the contact surface $$S$$.

In case it is an indeterminate problem, would it be possible to calculate an approximation of the problem? (Any further assumptions that relax the problem to a calculable level are welcome)

Thanks!

• Maybe others can understand your diagram, but I'm struggling. Can you make things a bit more clear? Jan 17 at 14:40
• @BobaFit , thanks for your comment. I tried providing more details. Please let me know if I should provide any further info. Jan 17 at 15:49
• Is the shape arbitrary? If so it's unlikely you can do anything at all, also the situation for O being rigid or not are completely different from one another. Jan 17 at 16:17
• @Triatticus , thanks for your attention. Let's assume that the surface is parameterized and differentiable along the contact area. Would that help us? And either of the assumptions regarding the rigidity of $O$ is accepted if it concludes to a solution. Jan 17 at 16:27
• What I mean is both situations are different, as in the produce two different solutions. At that point you'd need some sort of model of the materials properties like density, rigidity, various mechanical moduli that can tell you things like shear strength and such. You may need to settle for some very specific situations to get an answer. I would start with simpler shapes first to understand how a distributed load is applied to a surface. Jan 17 at 19:29