## cantilever beam deflection results

## cantilever beam deflection results

(OP)

Hello everyone,

I am trying to calculate the max deflection U2 of a 3D cantilever beam of square cross-section with a load at the free end. I have completely constrained the fixed end and placed concentrated forces on the top nodes of the free end. To keep the beam from bending along the z-axis, I constrained the element at the free end between the top nodes to deflect only in U1 and U2. However, the deflection results in ABAQUS are over one order of magnitude less than those based on the cantilever beam deflection formula. What is the reason behind this discrepancy?

-Tom

I am trying to calculate the max deflection U2 of a 3D cantilever beam of square cross-section with a load at the free end. I have completely constrained the fixed end and placed concentrated forces on the top nodes of the free end. To keep the beam from bending along the z-axis, I constrained the element at the free end between the top nodes to deflect only in U1 and U2. However, the deflection results in ABAQUS are over one order of magnitude less than those based on the cantilever beam deflection formula. What is the reason behind this discrepancy?

-Tom

## RE: cantilever beam deflection results

corus

## RE: cantilever beam deflection results

greaterthan those based on beam deflection theory (I must have been thinking I needed the ABAQUS results smaller as I was writing that statement).Corus: I don't think applying the force in kg instead of N is the reason for the discrepancy. I used a 1000N force in my theoretical calculations. When I performed the 2D deflection analysis in ABAQUS, I specified a -1000 load in U2 which gave me a result with a relative error of 1.5%. I did the same thing for the concentrated forces in my 3D analysis.

## RE: cantilever beam deflection results

## RE: cantilever beam deflection results

## RE: cantilever beam deflection results

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## RE: cantilever beam deflection results

Dan

## RE: cantilever beam deflection results

Be careful, very careful doing that! Spreading a load out over a number of nodes in this manner is not the same as applying a uniform pressure, regardless of whether you have a uniform mesh on a simple square or rectangular area or not. When available in either the pre-processor of your choice or the input deck itself, always apply a pressure instead.

Why? Because a uniform pressure will correctly honour the shape/displacement functions and geometry of each element face, whilst point loads at each node on the surface will not.

Think of it as the difference between lying on a water bed as opposed to lying on a bed of nails.

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## RE: cantilever beam deflection results

I can see why applying a pressure load would lead to a more accurate analysis than a series of point loads. However, selecting the Pressure load type in ABAQUS only lets me apply it to the surface and not a line of a 3D object. Is there another load type I could use to achieve the desired effect? I tried using a Line load but instead of selecting the top edge of the free end cross-section, ABAQUS selects all the edges in the beam.

## RE: cantilever beam deflection results

You can however partition the surface to leave only a small area in which to apply a pressure load. Bear in mind that the analysis is only accurate if it models accurately the real world situation. Loads are rarely applied as point loads in real life, other than perhaps by contact, and even then that is over a small area.

corus

## RE: cantilever beam deflection results

Thanks.

## RE: cantilever beam deflection results

Trying to apply loads spread over a line in 3D is no better than applying point loads, since the line has no physical width and hence no physical area. Thus rather than applying load at the point of a nail, you have merely transferred it to a knife edge.

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