Balloon deformation - calculating effect on surface points

[ocitalis]

I am befuddled over how to calculate the force acting on a surface point of a deformed balloon (filled with water or air). I have drawn a picture to help illustrate. I have written a small program in c++ that uses the Runge-Kutta algorithm to simulate simple physics systems, like networks of interconnected springs connecting point masses, in 2 dimensions. My simulation does not incorporate gravity.

I want to be able to simulate things like multiple balloons of varying internal pressures packed together in a 2d box. Or a squeezed water balloon that is instantly released and rises back into it's natural circular shape.

1.) Does it even make sense to attempt to simulate an object with internal pressure (balloon) in 2 dimensions, or are 3 dimensions absolutely required?
Assume that I can calculate the internal area of each balloon, the internal pressure, distance from the balloon's center, and all other necessary variables.
2.) How do I calculate the force exerted on the surface points pointed to by red arrows in the picture?
3.) Does the force exerted on the surface points originate from the center of pressure of the balloon? Is this center calculated like calculating the centroid of a solid polygon?

 

[ocitalis]

Does anyone have any input? Is the question unclear? Replies are greatly appreciated.

 

[astrokreng]

1.) It is possible to simulate an object with internal pressure in 2 dimensions, but it may not accurately reflect the behavior of a real balloon in 3 dimensions. In 2 dimensions, the balloon would essentially be a flat surface, whereas in 3 dimensions it would have a spherical shape. However, if your simulation accurately incorporates the internal pressure and other variables, it may still provide useful insights and predictions.

2.) To calculate the force exerted on the surface points, you will need to consider the pressure differential across the surface. This can be calculated using the internal pressure and the surface area of the balloon. The force can then be calculated using the formula F = PA, where P is the pressure and A is the surface area. This force will be directed perpendicular to the surface at each point.

3.) The force exerted on the surface points does originate from the center of pressure of the balloon. This can be calculated using the centroid of the surface area, similar to calculating the centroid of a solid polygon. The center of pressure is the point at which the total force acting on the surface is considered to act. However, in a complex system with multiple balloons and varying internal pressures, the center of pressure may shift and change as the system evolves.