Simulating inter-connected springs/beams

[Alkatran]

I've been writing a simple program to simulate what is essentially a bunch of springs connected together at nodes. However, I'm having trouble.

Currently I just calculate instantaneous force for every spring/node, step ahead a fixed amount, and repeat. The problem is this tends to overestimate and I end up with a the whole system gaining a ton of energy unless I dampen the springs by a large factor.

What is the next step up for this type of thing?

 

[out of whack]

It sounds like stepwise recalculations (possibly coupled with rounding errors on floating point numbers) are causing the problem. One kludge is to add up the total energy after each iteration and, if it has increased from the previous total, do a second pass to reduce all forces proportionately. This will solve the problem of creeping energy increase directly.

Of course the main problem is the stepwise approach used in the simulation. The errors introduced by these approximations will cause total energy to change and they will also cause the model's behavior to deviate from an actual device's. The simplest solution is to reduce the size of each step to minimize the "staircase approximation" of the curves that are being modeled. Another solution is to find a better, more accurate midpoint value at each iteration, but this is not a programmatic problem, it takes some analysis of your model to find out what is best.

 

[ravenprp]

One potential solution to your problem could be to incorporate a damping factor into your simulation. Damping is a force that opposes the motion of the springs, and it can help to reduce the amount of energy that is gained in the system. You can also try adjusting the stiffness of the springs to see if that helps with the overestimation issue.

Another approach could be to use a more advanced simulation method, such as a numerical integration technique like Runge-Kutta or Verlet, which can be more accurate and stable for simulating interconnected systems. These methods take into account the acceleration and velocity of each spring/node, rather than just calculating instantaneous force.

Additionally, you may want to consider adding constraints to your simulation to mimic real-world conditions. For example, if your springs are connected to a fixed point, you can use a fixed constraint to prevent them from gaining excessive energy.

Overall, it may take some trial and error to find the best approach for your specific simulation, but incorporating damping, using a more advanced simulation method, and adding constraints can all help to improve the accuracy and stability of your simulation.