How to make line pressure linearly vary along length of line element?

StefanH

eg. start 50 kN/m, increase to 100 kN/m over length of 0,5m
how to get length variable x or u into equation?

disla

HI StefanH,

The problem could be solved using some algebra but once applied it is difficult to make it work because line pressure as a function of position is not a follower or doesn’t work to me on Beams.
If you want to try modelling with solids or shell elements, I have found some workarounds. The file contains a variety of varying loads applied to a line. Beam is very limited, but you could apply this method to a solid beam or shells. Temperature is useful to check if formula is right.
The formula comes from building the unit vector between nodes X0 and X1 separated a distance “d” and knowing the values V0 and V1 on those nodes.

cwharpe

Nice work, disla! The method employing direction cosines is the proper general approach for 3D space.

@StefanH:

I see you need to track the X coordinate for your ramp function, which the (Constant) Line Pressure function does not allow (it needs only the element length).

I think there is a way to create a Ramped function for beam (line) elements using Traction Pressure, if you divide the Traction Pressure by the element perimeter. This effectively mimics the Line Pressure function, yet provides access to coordinate variables (i.e ramp functions, etc.)

The algebra of the ramp function could be of a form [a(x-x0)+b], where a=slope, b=initial pressure on first element, x0=coordinate of first node.

Ex: Wide Flange beam beginning @ x=7, 36" PERIMETER, starting press. 20 psi, ramp slope 3. Select your beam "faces" then under the Z pressure field, Enter: -[3*(x-7)+20]/36. Confirm your hand calculations by summing Reaction Forces.

Recommend aligning your model with cardinal x/y/z axis, otherwise you're compensating for vector components, in which case refer to @disla's work. Also, if your beam cross-section varies, you'll have to be careful to adjust the perimeter value in the equation.


Rationale
Consider the following:

• There is an equivalent element force comparing i) Loading a 10" long element with Line Load of 50 lb/in, versus ii) Applying a 50 lb/in^2 Pressure to a strip 1" wide x 10" long.
  

• When selecting the face of a line element (notice in expanded view it won't allow you to pick just one face), the scalar that gets returned is the elements' entire perimetral surface area. That is, Area= perim. x length.
  

• To arrive at that 1" wide strip analogy, the (selected) Area would be divided by its perimeter. Since the Traction function = Pressure x Area = Pressure x perim. x length, it's equivalent to divide the Pressure by perimeter.
  

disla

@cwharpe

It works. Great !!
So we have a generalized method for any load function in any direction and it can be used with the internal solver and all its beam sections.
Really Nice. Thank.

Regarding direction cosines, once you discover quaternions there is no looking back.