stress/shear analysis of components

assume in the first part of your question we are measuring the stresses at the moment the ball is about to pass through the hole. Say R1 is the radius of the hole at rest and R2 is when it is expanded to allow for the passage, and we assume no warping of the surface.

$V = F/2pi R_2$

As for he second part the shear stress equation for composite beams is: $$ tau = VQ/It$$ V is the shear from the shear diagram, Q is the first moment of area of the part of the beam above or below the centroid.

All you need is the dimensions and if the platform is made of a different material its E and G, shear modulus of the platform. You need to multiply the platform section area by $E_{platform}/E_{base material}$ to calculate the centroid.

Edit

For the first part you need some basic data like the dimension of the hole and radios of the ball, to verify if the stresses are plastic or elastic. You can model the plate around the hole as many say 60 radial cantilever beams connected to each other by concentric rings.

if the plate is thin enough it will allow bending around the edge of the hole or it will make the whole expand while creating a depressing. Another case that can be modeled in FEM is the bell itself will shrink into a football shape to pass through.