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Stiffness method for tripod structure

Stiffness method for tripod structure

Stiffness method for tripod structure

(OP)
I'm trying to create results based on the stiffness method in excel to compare with an ANSYS simulation of a tripod structure with cross member reinforcements (see attached pictures). I'm not creating the entire stiffness matrix for all three legs, because I feel that would be redundant since they have the same dimensions and spacing. Where the legs meet at nodes 2 and 3 I do multiply the stiffness values by 3 in the global matrix to represent the three legs meeting at the point. In the end I get an 18x18 global stiffness matrix. The thing I'm confused about is: how do I represent the frictional contact between the tripod and the floor which it rests on? Also, I'm confused if I'm setting this up right. In examples I've seen using the stiffness method, you set up the global matrix and set the deflections to zero where the structure is constrained, then solve for the u-variables. You then take those results and set up another matrix based on the force/moment values that correspond with the u-variables solved in the previous step, and solve for that with a simple matrix multiplication.

For this structure, the joints are welded and it touches the floor at node 6. Are nodes 2, 3, and 5 considered fixed? Am I on the right track? I'm very interested in FEA methods and would appreciate it if someone experienced could lend a hand.

RE: Stiffness method for tripod structure

Overall questions- can't help there.
At the floor, it looks like you'd have to assume a "fixed" connection, solve for reactions, then check to see if the base plate slides or uplifts with those reactions. If you're solving repeatedly via spreadsheet, you could set up 4 solutions, one for each combination of sliding/not sliding and lifting/not lifting, then see which solution set to use based on checking uplift/sliding criteria.
Also consider that if, in reality, this thing is usually going to be anchored whether it needs it or not, you can assume that to begin with and simplify it.
At nodes 2 and 3, the center member would be assumed restrained against rotation and horizontal movement due to symmetry; at node 5, it wouldn't, and it looks like all three nodes could move vertically under load.
I'm assuming since you're only evaluating one of the diagonals, that your loading is vertical only.

RE: Stiffness method for tripod structure

(OP)
Correct there is one vertical, applied load at the top of the center round tube. So node 6 = fixed, nodes 2 and 3 rotation is fixed and horizontal movement is fixed. Node 5 all DOF's are unrestrained. What about 1 and 4? To me they can only move in the vertical direction, so again rotation and horizontal movement would be fixed.

RE: Stiffness method for tripod structure

i think modelling 1/3 of the structure is needlessly complicating a simple model. how are you applying a symmetric boundary constraint to the central tube ?

another day in paradise, or is paradise one day closer ?

RE: Stiffness method for tripod structure

(OP)
How would I simplify it beyond what I've shown? Initially I tried just analyzing one leg as a plane frame with no center tube, with the angled leg and cross-member considered fixed at the location they would 'attach' to the tube, and the applied forces being the reaction forces at the foot. This yielded different results (higher stresses) than running a simulation on the overall structure with a frictional contact at the feet. Thus I thought I had to go back and somehow include the center tube as part of the analysis. I guess where I'm getting hung up is assigning the proper constraints for the DOF's at the various nodes.

Honestly, I'm not sure how to represent the symmetry of the the legs being evenly spaced in the stiffness matrix.

RE: Stiffness method for tripod structure

exactly ... "simplifying" the tripod to a single leg complicates the problem. It's a simple enough FEM to model the complete tripod.

another day in paradise, or is paradise one day closer ?

RE: Stiffness method for tripod structure

(OP)
Oh right, I see. Sorry I misinterpreted what you meant. Its simple enough to model with software, but calculating it analytically is confusing me. I'm not sure how or at what step in using the stiffness method to represent each leg being evenly spaced 120 degrees apart. The way I'm doing it you wouldn't know, so I must be setting it up incorrectly. I don't have any good reference material on stiffness methods of FEA. Online searches usually comprise of very simple 2D beam/frame structures which don't give any useful insight either.

RE: Stiffness method for tripod structure

310toumad:
Use polar coordinates, with the center at the central round tube.

Edit... Actually I meant to say cylindrical coordinates.

RE: Stiffness method for tripod structure

and the symmetric boundary condition in polar is ?

another day in paradise, or is paradise one day closer ?

RE: Stiffness method for tripod structure

(OP)
Where would I apply the use of polar coordinates? As far I as I know, the creation of stiffness matrices only involves the properties of A, E, I, and L for the members. Then you set up the force/displacement relationship and solve for the displacements for each node using the
u = [K]inv *{f], then you can solve for the internal shear/moments. Maybe the process is different for a 3D frame? I just don't see where you'd include the position of the members relative to a reference point such as the center tube in this instance.

RE: Stiffness method for tripod structure

yes, co-ordinates are not part of the stiffness matrix,
but they are part of determining displacements.

In more complicated models they are used to calculate lengths ... for very simple models like this you can input L directly.

If you're trying to learn this from first principles, first congratulations; second, try a structure with more interesting effects ... like a beam ... a propped cantilever, a double cantilever.

another day in paradise, or is paradise one day closer ?

RE: Stiffness method for tripod structure

(OP)
I suppose the key lies in the transformation matrix, although I can't find any examples where they use polar or cylindrical coordinates. I can't even find a space frame example for a stinkin' tripod.

RE: Stiffness method for tripod structure

yeah, but your "stinkin' tripod" is easy enough to build the stiffness matrix.

I suggest 3 nodes on each leg, three nodes on the central cylinder, 9 nodes in all (3 unique nodes on the central cylinder ... the loading point, the upper tripod leg junction, the lower stub beam junction, possibly a 4th at the base of the cylinder, but I don't think it'll do anything in a simple static analysis; 2 more on each tripod leg ... at the ground contact, and at the stub beam, and you already have to top of each leg on the cylinder). Now how do these connect to one another ... 1-2, 2-3 is the cylinder, 2-4, 4-5 is one tripod leg, 3-4 is one stub beam, etc

another day in paradise, or is paradise one day closer ?

RE: Stiffness method for tripod structure

(OP)
Right, that makes sense. But the legs are not in the same plane since it is a 3D frame. Would I have to use x, y, z, transformations? Sorry for so many questions, I just want to fully understand the method.

RE: Stiffness method for tripod structure

yeah, use x-y-z ( or other co-ord sys like polar) to local the nodes, but then, as you've said the important stiffness thing is distance between nodes ...

another day in paradise, or is paradise one day closer ?

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