# Can we simulate rigid body motion using finite element analysis?

I was wondering if we could model rigid body motion of bodies using finite element models. Particularly I'm interested to know if we can model motion of objects with no constraints or with some degrees of freedom (such as only rotation). Though I've used word 'rigid body' to convey the situations closest to what I'm considering, In reality there will be stress, considering non-uniform application of force on surface/body or because of rotation they undergo, and these are not small enough to ignore.

• Rigid bodies - by definition - have no strain and stress. What are the equations you would like to solve with “no constraints”? Mar 21, 2018 at 9:05
• Thanks. This is about equations of motion - F = m*dx^2/dt^2., and its rotational counter part. Though I've used word 'rigid body' to convey the situations closest to what I'm considering, In reality there will be stress, considering non-uniform application of force on surface/body or because of rotation they undergo, and these are not small enough to ignore. Mar 21, 2018 at 10:54
• Can you give us an example of what you want to model? Mar 21, 2018 at 11:06
• Suppose you've a rotating solid sphere, which is has magnetic dipole in it. It's subjected to an external magnetic field. The sphere also has linear motion. Mar 21, 2018 at 11:09
• Finite element codes that have a nonlinear formulation (i.e. nonlinear strain-displacement relations) are designed to handle arbitrarily large displacements and rotations. Most commercial structural finite element codes have this capability and there are many open source codes that do as well. Mar 21, 2018 at 11:42

Finite element method is used to change the boundary value problem, with an infinite number of unknowns, into a system of algebraic equations with a finite number of degrees of freedom (DOFs).

For example, the response of the deformable body, which conveniently is described by partial diffrenetial equation (PDE), using finite element method is transformed into a system of algebraic equations with the finite number of DOFs.

If you write equations for rigid body or system of rigid bodies, you do not have PDE; you have immediately a system of algebraic equations. Thus no need for finite element method.

The problem with the system only rigid bodies is that is very often over-constrained, since only you have equations of equilibrium to work with. However, this is another story.

• If we write equations of motion in differential equations format, we may not get systems of algebraic equations directly. Do we? Mar 25, 2018 at 16:57
• Correct, I made shortcut here; finite element method is applied to discretise problem in space, not in time. You can think that you apply the first discretisation in time, and then in space or vice versa. Mar 25, 2018 at 17:00