Got some math working (I think) to compare different Gantry cross sections. Would appreciate any criticisms or comments on my methodology.

I have gotten my static FEA capabilities up and running and will attempt to analyze some different gantry configurations with it. My FEA refuses to deal with complicated aluminum extrusion CAD so I will simplify the extrusions as a hollow rectangular beams with internal cavity adjusted so that the hollow beam and the 80/20 extrusions have the same moments of inertia. Not looking for absolute displacement numbers, only comparisons between configurations.

First image is my starting CAD design for the gantry. Called Gantry_0
Second image is the FEA geometry used.
Third image is the loadcase used. I am fixing the beams ends in space and applying a line load of 500N at the bottom of the Z axis block.
Fourth image is the result. About 0.125mm. Means nothing except as a comparison to results from other configurations.

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Next is my first configuration change where I box the beams with a plate underneath the rails. Gantry_1. Again the images are Geometry, Loadcase, and results. This time the displacement is about 0.086mm compared to the original of 0.125. So the plate helped some.

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My next configuration (Gantry_2) is to box the other side of the gantry and see what I get.

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Image progression is the same as above. Resulting displacement is 0.056mm for further improvement in the stiffness of the beam. Hard to see in the results image but the majority of the flex is in the lower beam at the Z axis attachment. See below.

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So I will add a half size beam along the lower beam to form an "L" shape to the gantry. Just like the sticky above recommends, haha. More to come.

John C