Beam deflection - Hand calculations vs Code_Aster vs Midas MeshFree vs Experiment

Few weeks ago I participated in Midas MeshFree software demonstration. It isn't another classic FEM tool, but something fresh on simulation market. This software doesn't require creating mesh on CAD file. Sounds interesting, isn't it?

I decided to check it by making some comparison with classic FEM tool Code_Aster and by making some experiment.

At home conditions I created a test stand. I used things, which you can find in garage or buy in DIY store: an old book shelf, a vice, an electronic scale, PA38 alu flat bars, a roman screw and a caliper as below.

Figure 1. Hand test

The roman screw worked as a tensioner. I applied ~0.7kG of force:

Figure 2. Load ~0.7kG of force – applied by adjusting roman screw

Next I had to measure the deflection:

Figure 3. Measurement of the deflection f = 3.74mm

Vertical deflection amounted to around f = 3.74mm. Each alu bar had 175mm length, 20mm width and 3mm height.

Hand calculation of the deflection

I used linear approach and classic beam solution, which assumes low max deflection ( about beam thickness )

Figure 4. Hand calculations  of the deflection f = 3.091mm

Hand calculation gave vertical deflection f = 3.091mm

Code_Aster vs MIDAS MeshFree solution

One edge was fixed (ux=uy=uz=rotx=roty=rotz=0). Horizontal and vertical force was applied to a single node on opposite edge. Linear approach. In MIDAS MeshFree I set similar conditions. Below you can find both solutions:

Code_Aster solution ( vertical displacement ) below:

Figure 5. Code_Aster solution of the deflection f = 3.056mm

Analysis with Code_Aster gave results f = 3.056mm

MIDAS MeshFree ( vertical displacement ) below:

Figure 5. Midas MeshFree solution of the deflection f = 3.049mm

Analysis with Midas MeshFree gave results f = 3.049mm.

I received 4 different values of deflection:

• experiment f=3.74mm
• hand calculation f=3.091mm
• Code_Aster f=3.056mm
• MIDAS MeshFree f=3.049mm

Not bad results for home conditions. The biggest unknown was material property. I had to trust tables. I could calculate Young modulus from the deflection, but I wanted to check it without correlation.

After this study I decided to spend more time in the future with this topic and get more detailed comparison. Especially solver settings and mesh adjustment. What is curious MIDAS has mesh, but volumetric not associated with geometry. It is numerical method borrowed from CFD solutions

Next article with detailed comparison will appear soon.

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Michał Szulewski

CAE Engineer

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