Consider a deformable cylinder without gravity with a uniform spinning angular velocity and the cylinder is not in contact with anything. In theory this cylinder shouldn't change its cross sectional area or volume as it spins with a uniform angular velocity. But in finite element simulation is it possible for the volume or cross section area to change in time as it spins around its own central axis?

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    $\begingroup$ There are many details involved in different time discretization techniques, but I think that, in general, you cannot expect the kinetic energy to be conserved exactly. Some time discretization methods may do it better than the others. $\endgroup$
    – knl
    Apr 14 at 8:20
  • $\begingroup$ the change in the volume or cross section area is so big when time goes big that I'm not sure if it's due to numerics at all $\endgroup$
    – feynman
    Apr 14 at 9:55
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    $\begingroup$ I have no idea why you say the CS area and volume should not change. The cylinder is acted on by a body force due to centripetal acceleration. $\endgroup$ Apr 14 at 17:36
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    $\begingroup$ I think he is meaning that starting from rest, after certain time, an equilibrium is reached after which there is no change in the volume assuming the angular velocity stays constant. $\endgroup$
    – knl
    Apr 14 at 19:31
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    $\begingroup$ Yes, that is case I am assuming, also. There is a closed form solution for this steady-state case that is presented in many theory of elasticity texts. The cylinder expands radially due to the centripetal acceleration. $\endgroup$ Apr 14 at 19:45

1 Answer 1


You can take an analogy of trying to simulate a circular orbit of a single particle in a gravitational potential. If you use the explicit Euler method, for example, your orbit will become larger and larger. If you use the implicit Euler method, the orbit will become smaller and smaller. Of course, we expect the radius to remain constant.

In other words, even for very simply problems, things that we think should be conserved are not conserved by numerical methods. Similar things will be true if you are trying to solve more complex problems.

Of course, in your concrete situation, there is always the possibility that it's a bug.


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