Strange results to thermal loads

[manuele.scipioni]

Hello everybody,

I'm trying to figure out the solution to a problem I'm encountering with thermal loads.

I have a simple rectangular plate with a certain thickness, perfectly symmetrical with respect to the reference frame. It is constrained only by blocking the Y-displacements (direction of the thickness) of its lower face. I apply a certain temperature as "initial condition" and a higher temperature as "body temperature". I would expect to find displacements in the X-Z plane (perpendicular to the thickness) which are symmetrical with respect to its center of mass, wouldn't I?

Instead I find that the plate expands in a strange way and is kind of deformed, losing its original shape and proportions.

I add a picture of the displacements in the Z-direction for the sake of clarity.

Thank you in advance to whoever will try to help me.

Manuele

[John_Holtz]

Hi Manuele,

What analysis type are you using?

How many warnings did you receive? What warning numbers were they?

Based on your description, there are no constraints in the X or Z direction, so the model is probably unstable. This fact by itself could give unreasonable results. Also, if there is no constraints holding the model in X or Z, why would you expect it to expand symmetrically versus all in one direction? Or 3/4 in one direction and 1/4 in the opposite direction? You need to apply X and Z constraints to tell the analysis where you want the zero displacement to be located.

Finally, assuming your plot shows the total displacement, the results almost make sense. If the +X -Z corner is stationary, then the +X +Z corner would expand the least because it is closet to the corner, the -X -Z corner would expand more, and the -X +Z corner would expand the most because it is the farthest. This is the pattern that I see in the plot. It is hard to see from the plot, but it looks like there is some rigid body rotation also because the model is not statically stable.

[manuele.scipioni]

Hi,

It is a linear static analysis with the only load being this change in temperature.

I receive no warnings at all.

I would expect it to expand symmetrically simply because the component is in itself symmetric and the load is uniform, I see no external forces (not even reaction forces from the support) acting in the X-Z plane, so why should the center of mass move in this plane?

I apologize for the low quality of the picture but I don't know how to produce a higher contrast with the background.

The plot shows only the displacements in the Z-direction, and none of the corners remain stationary:

The (+X;+Z) corner goes towards the +Z direction and the (+X;-Z) corner goes towards the -Z direction (behaving as I imagined in my mind), but the (-X;+Z) and the (-X;-Z) both go towards the +Z direction, causing a rigid body rotation and a movement of the center of mass.

Does this mean that I can't perform simulations with thermal loads if the body is not statically stable? How would you then represent the situation of a component simply supported by a table and experiencing a change in the room temperature?

Thank you,

Manuele

[John_Holtz]

Hi,

You asked "Does this mean that I can't perform simulations with thermal loads if the body is not statically stable?"

No, it means that you cannot do a linear static analysis on a model that is not statically stable. It does not matter what the type of load is.

The way a static analysis is solved (in InCAD and most simulation software) can be understood by thinking of the model as a spring. The equation for a spring is F=k*x where F is the load, k is the stiffness, and x is the displacement. The load F is applied and k is known (based in part on material properties and elements), and it solves a system of equations to find x. The stiffness of a linear static model occurs because of the constraints. If the model has no constraint in some direction, the stiffness in that direction would be 0. So in your case with no load, the solver is trying to calculate x=0/0, and the answer to that is anything (or undefined). Since it is a static analysis, the mass of the part has no bearing on the analysis. 

There are lots of ways to restrain the model so that it is statically stable without restricting the "free" displacement. This is one way to do it: