Hi,
I have a very simple case. Thermal expansion of a solid cylinder of 176,5 mm. Material aluminium with thermal coeff of 2.4*10^-5/K. Calculated by hand this makes it expand 2,13 mm diametrical. I also did this in Abaqus where I only simulated 0.1 angle of a cylinder. I got the same result.
However, when I model a full cylinder, I get completely different results, and the thermal expansion varies greatly with varying length of the cylinder. How does that make sense?
Sincerely
David
David Forrestad Swensen, the difference in thermal expansion between a partial cylinder and a full cylinder can be attributed to the boundary conditions imposed on the two models. When simulating only a 0.1 angle of the cylinder, the boundary conditions are effectively applied only to a small portion of the cylinder's surface. This allows the rest of the cylinder to expand more freely, resulting in a larger overall expansion. In contrast, when simulating a full cylinder, the boundary conditions are applied to the entire cylinder surface. This restricts the cylinder's expansion, leading to a smaller overall expansion compared to the partial cylinder model. Additionally, the variation in thermal expansion with varying cylinder length can be explained by the different aspect ratios of the cylinders. Longer cylinders have a smaller surface area relative to their volume compared to shorter cylinders. This means that longer cylinders have less material exposed to the surrounding environment, which can affect their thermal expansion behavior. To accurately predict the thermal expansion of a full cylinder, it is essential to use a full-cylinder model and consider the effects of boundary conditions and aspect ratio. If only a partial cylinder model is available, it is important to be aware of the limitations of the model and interpret the results accordingly.
Engr. Tufail Thanks for your thorough answer. When I simulated the small sector its boundary conditions are set axially and tangentially, such that it can move only radially. That would make it very fixed to move only radially, wouldn't it? The full cylinder was fixed only axially at both end surfaces. However, the small sector is more consistent with the hand calculations. Would you say that the the formula: "deltaD = Diameter*ThermalCoeff*TempChange" is not valid for a full cylinder? You mention that a longer cylinder has a smaller surface relative to its volume that makes it less exposed to surrounding environment, but why would that be relevant in a simulation? The Model should have the same temperature all over.
Nils Wagner Sure! The small section model is not constrained in the axial direction, only tangentially which makes it more equal to the hand calculations. The full cylinder is constrained axially at both end surfaces. Temperature change is now set to 230. The requested .inp files are attached for both models.
David Forrestad Swensen
The length of the cylinder is 200mm, whereas the radius is 82.75 mm.
You will have 3 rigid body modes, i.e. rotation about x-axis and translation along y- and z-axis. You might use an Inertia Relief analysis.
What is the reference temperature?
David Forrestad Swensen The formula 'deltaD = Diameter * ThermalCoeff * TempChange' is generally valid for radial expansion, but the differences in simulation results between a small sector and a full cylinder may arise from variations in boundary conditions. The restrictive conditions on the small sector, allowing only radial movement, may differ significantly from the axial constraints applied to the full cylinder. Additionally, the length-dependent thermal behavior observed could be influenced by the surface-to-volume ratio impacting heat exchange.
Nils Wagner Thanks for your quick reply! The initial temperature is 20 degree Celsius and target temperature it 250 degree Celsius, so a deltaT of 230 degree Celsius.
Ah, sounds interesting. I have never done an inertia relief analysis myself.
David Forrestad Swensen Please find enclosed the solution using the free education edition of PERMAS. https://www.intes.de/edu
Please note that the formula is correct if the Poisson ratio is equal to 0.
Nils Wagner Thanks a lot Nils! I tried to recreate the model in Abaqus the way you did it. I got basically the same output, 0.457 mm displacement.
What do you mean with "the formula is correct if the poisson ratio is 0"? what formula?
Do you think this approach with inertia relief analysis is a good approach to predict the thermal expansion for this cylinder? It looks logical to me.
Nils Wagner here is a picture just to show the results from abaqus
David Forrestad Swensen
https://physicstasks.eu/1809/diameter-increase-of-cylinder-when-being-heated
You have suppressed the displacements in x-direction, solely.
Therefore, a static analysis is not possible due to 3 rigid body modes.
BTW, I have added your example to the permas4edu GitHub repository.
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