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As I have to design the vertebra bone and its natural boundary conditions I came across a problem.

How can I applied a uniform load if the place where the force is applied is a parabolic curve.

Ok so I get the curve will have this value $$y(x) = -y_1/x_1 \cdot x^2 + y_1$$

So I did the derivative $\frac{dy}{dx}$ to discover the tangent of the curve so it can be possible to calculate the normal force so I can apply the normal force to the surface.

My question is how is it applied to the surface?

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Not enough information to answer. Uniform and normal to the curvature of the spine or uniform parallel to the direction of gravity (i.e. the weight of each vertebra) – Mark Rovetta Jun 6 '13 at 18:49
Welcome to Physics SE! Your question still is not obvious to me. You used a 2D function to discribe your 3D bone. Are you asking for the normal force, which is applied to a 2D bone? – Stefan Bischof Jun 6 '13 at 18:50
I'm using a two dimensional plate and constantly remodelling the bone taking the small values of density till I arrive to the trabecular disposition like in a RX. but now I have to impose the natural boundary conditions and I have some difficulty cuz I don't know how to applied this force. the force is uniform they all have q0 value and they follow the curve (uniform and normal to the curvature of the spine) – Barão António Lopes Jun 6 '13 at 19:08
this picture illustrates the force and how it has to be applied imageshack – Barão António Lopes Jun 6 '13 at 19:48

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