# 2D Thermal Expansion Without Rigid Body Motion

I am doing a thermal expansion simulation on a simple 2D rectangle. I want to the rectangle to be fixed in space (no rigid body motion) but still be able to deform in all directions. I have found that using a fixed support boundary condition locks that edge from deforming at all. Is there another type of boundary condition that can allow for thermal expansion without rigid body motion?

• To have free expansion, only a single point can have no motion, all other points will all move relative to that point.

The way you achieve this is to put a Displacement boundary condition on the left edge of X = 0 and a Displacement boundary conditon on the bottom edge of Y = 0. The bottom left point will therefore have X and Y = 0 and every other point will be free to expand.

A Fixed Support along an edge will prevent both X and Y motion, which is not free expansion.

• Thank you for the reply, that worked! Is it possible to have a stationary point in the middle of the geometry so it can expand in all directions (+/- x and +/-y)?

• Yes. Go back to CAD and slice the body using two planes running through the center. Use Shared Topology to connect the four pieces. That means use the Share button on the Workbench tab in SpaceClaim or "Form New Part" in DesignModeler. Now you have a vertex at the center and a vertex on each edge. Apply a Displacement of X=0 and Y=0 at the center vertex, and a Displacement of Y=0 at the vertex on the left edge. That works in a 2D analysis. You need to do three points for a 3D analysis

• That makes sense, thank you so much!

• Hi @peteroznewman, I am performing a similar simulation except the body is a symmetric cylinder with a hollow cylindrical void at the center (see reference image). I want the cylinder to expand or contract without external constraints but still avoid the rigid-body motion.

Could you please suggest boundary conditions for the above analysis?

Thank you.

• The geometry is axisymmetric, and if you use a uniform temperature change to expand the part, you could draw a rectangular surface in the XY plane with the axis of rotation along the Y axis. Then you can set the bottom edge to have Y = 0. This will let the part freely expand with no strain.

In 3D, select the end face in a Remote Displacement, but make sure the behavior is Deformable and not Rigid. Set all the constraints to zero. This will let the part freely expand with no strain.