Calculating tension and compression forces

[Bilbert]

I have been playing around with a simple physics engine, which i developed with the help of these boards, and an interesting idea came to mind as I was trying to solve another physics related problem. I thought I would post here and get some comments on the idea, either being feasible or already done. Here goes: the basic problem is to calculate the net compression or tension on rigid bodies connected by joints.

A simple example is the double pendulum. Lets say the top joint is anchored and two bodies swing in series below. Gravity being the only external force, then the weight of the lower body would put tension on the upper body. I'm looking for a method to calculate the tension force on the upper body from gravity and the pull of the lower body. Now, i know how to do this when the example is so simple, but when you add more bodies into series the problem becomes much more complicated. Add in more complicated body configurations and its even more complicated.

My first solution was to handle the problem like impulses. All the bodies i put into a graph to define the relationship between them then in steps I would let the forces move from body to body. When two forces were applied to a body from opposite sides, the net of the two would be the compression force and so on. I think it works but seems kinda clumsy. Its not that I really want any amount of accuracy, I just think there must be a better way.

After developing my LCP solver for constraints, I thought I could solve this in the same manner. Setup a matrix with the relationship of each body to every other body and solve the series of equations with respect to the external force. I'm fairly certain this must have been done before. My math isn't good enough for me to develop the relationship matrix myself but it seems feasible. I don't know. Any thoughts?

Bilbert

[Dirk Gregorius]

You can look at the Featherstone or at Baraff's linear time solver. Both analytically compute the constraint forces of tree like joint structures in linear time.

[Bilbert]

Actually, i did implement a Baraff solver. I developed it using 2001 sigraph notes and with help from here. My understanding, though I am not certain, is that solving constraints does not answer my problem. It would only indicate how much force is needed to balance the equation. For example, if a body was being equally compressed from two opposite sides, the absolute movement would be zero. Since its automatically balanced, the solver would not correct any force. But, the body is being compressed and I'm looking for that value. I would like to find the amount of force on the top link of chain hanging from the ceiling or the stress on a steel beam at the bottom floor of a building.

[Dirk Gregorius]

I am constructional engineer and usually you use FEM programs for these kind of computation. Still, once you have the constraint forces you should be able to also find the stress and strain of each body.