Pre-Tension in a Gridshell

How would you model pre-tension in a gridshell caused by bending members in Solidworks?

Apparently, Solidworks has the capability to model the pre-tension, by essentially replicating the bending process, which allows the user to start with this model;

Gridshell Beam Model

And bend it a prescribed amount, resulting in this:

Bent Gridshell Beam

It is worth noting that, while this beam is correctly matched to the height and length of a gridshell (calculated mathematically in Matlab), it is only constrained via prescribed displacement at the ends, but the capability exists to constrain several points along the beam, ensuring the final shape matches the desired catenary curve.

Now, can this method handle bolted connections?

Turns out Solidworks also does that pretty well. I started the test with a simple cross of two long beams, connected with the standard curved plate and bolt connection used previously. The result (note this one uses several prescribed displacements to ensure a slightly more accurate catenary shape) is shown below:

Basic Bolted Joint Bent

Which also started laid out flat:

Basic Bolted Joint Model

This model involved most of the same process as before:

1. Lay out the members flat
2. Use Assembly mates to achieve the desired position and layout
3. Fix the center of each beam (this leaves both plates able to flex)
4. Sketch lines into the beams to create the edges that will have prescribed deflections
5. Prescribe the deflections, making use of the "Split" option for selecting lines partway down the beam

Now, what if the bolted connection moves?

The next logical step was to see what happens if the bolted connection itself needs to move with the beam; how will Solidworks handle having the bolted connections moving like that? Will everything stay together as it should, or will the bolts do something unrealistic?

To test this, I started making a simple 5-member gridshell, in the shape of a catenary dome, as shown below modeled in Matlab:

Matlab 3-D Plot of 5-Member Catenary Dome

I haven't yet added all the members, but here is the flat assembly so far:

Unfinished Catenary Gridshell Laid Flat

It's hard to see, but each point where beams cross has a full bolted connection (bolted between two curved plates, that might have to change eventually to a more simple shape). The end of each beam was constrained to drop 2m vertically, so that everything ends up at "ground" level. The resulting model doesn't really look like a catenary shape (the next step is to use the Matlab model and constrain each joint to drop by the correct amount), but it shows that the bolted connections managed to hold up, even when the whole joint moves:

Unfinished Catenary Gridshell Bent

The next step is to add more complexity to this model to make it actually resemble the Matlab plot. In order to make the model match the plot, a few things must be added:

1. Add the other cross-beams, with 6 more bolted plate connections
2. Constrain each connection to displace its correct amount
3. If that still doesn't accurately resemble a catenary dome, then move on to prescribing the displacement of each beam at a few intermediate points

Working with Simulation in Solidworks

How do you make sure a bolted connection will model correctly in Solidworks?

Here are a few realizations I had about making sure a simulation of a bolted connection will run correctly:

1. Friction - Solidworks Help page says that friction is added automatically based on the materials chosen, but it isn't (note there is nowhere in material properties to add a coefficient of friction; it's based on both materials contacting, not just one). This means that every component contact must have a coefficient of friction set; if this varies, then multiple component contacts will be needed to fully define the model
2. Solver - The Solver matters; different solvers are better at different things. Most notably, the Direct Sparse Solver, while being potentially less accurate than the Iterative Solver, can better make use of powerful multi-threaded CPU's (such as the 32-thread Xeon in the Watkins Hall computer lab)

Solving With 'FFEPlus' Iterative Solver - Note 3% overall usage and one core used

Solving with 'Intel Direct Sparse' - Note 39% overall usage and most cores used

3. Washers on Bolted Connections - Washers are commonly used on bolted connections to avoid preload loss at the head or nut of a bolt due to deformation when the contact stress deforms the material where the head/nut presses. However, after reading about their use in bolted connections in Solidworks, I don't think it is necessary to add washers in the simulation, and it has the tendency to make the simulation not actually solve. It seems best, then, to leave washers out (maybe adjust the radius of the head and/or nut, I'm not sure how that works, I'm going to check that out next).

Update: Bolt head size does work in Solidworks Simulation

After testing the same model with a larger bolt head, it would seem Solidworks does in fact model the size of the bolt head (why would they let the user define the bolt head/nut size if they didn't?). This means that the user can use a larger bolt head to model a washer of the same size. Proof shown below:

Joint Model with 12mm Bolt Head - Note the lighter sections (more stress) around the bolt 

Identical Joint Model with 20mm Bolt Head - Note the area around the bolt is now light blue - lower contact stress

Bolted Connections In Solidworks - Gridshell Joint Exercise

Can Solidworks easily handle a bolted connection?

Or: Practice Working on a Gridshell Joint

Gridshells are generally laid out on the ground, then propped into their final shape by scaffolding (or other means, as will be the subject of next year's capstone project). This means that a gridshell joint needs to be attached on the ground while still allowing rotational and longitudinal freedom of its members, and then locked into place when the final form is attained.

The most common way this is achieved today is through the use of clamped plates that sandwich the gridshell members. They are initially applied loosely to allow the members to flex and slide during the erection of the gridshell, and then clamped more tightly later to lock the gridshell into the correct form.

Modeling this joint in Solidworks is a hurdle this research will eventually have to face, due to the potential effect the joints will have on the structure that cannot be modeled by a simple rigid connection. But doing this in Solidworks requires using a bolted connection, which the author was not sure if Solidworks actually had the capability to handle natively. It turns out Solidworks does have this ability, and it really isn't too terribly hard.

In a Solidworks Simulation (in this case a static simulation set to study the stresses on the clamping plates due to rotating force in the members), the user simply needs to select the drop-down menu under 'Connections Advisor' and select 'Bolt' and follow the setup to select the cylindrical cuts the bolt will go through, and the ends where the head and nut will be. This selection even allows for a set preload, a crucial part of any bolted connection (a preload applies the clamping force and prevents joint separation, allowing the joint to be treated as one rigid member).

Approximation of a Gridshell Joint, Showing Bolted Connections

A real clamped connection on a Gridshell would have additional complexity, such as plate shapes that are more visually appealing, and washers (and even some disk springs) on the bolted connection, that are not modeled here. These can be added later to this model or a new model if this ends up being too far from reality.

With that disclaimer in mind, it was possible to run this model, which yielded the following stress visualization:

Approximation of a Gridshell Joint, Under a Twisting Force on the 'Gridshell Members'

This shows almost no load on the members themselves, and almost all of the load on the plates. While this may or may not resemble a realistic connection (ideally the members should only be transmitting compression forces, as shown in the last post), it does show that the bolts are transmitting load through the clamping force they exert.

I also found out that Solidworks does in fact have a way to treat a member as a beam (including selecting joints), so the next step will be to check that out, and see if it is feasible for use in this project.

Testing Catenary Arch and Catenary Dome

How do you verify that a shape is a catenary?

A catenary shape is defined as the shape a hanging chain makes, resulting in pure tension. When flipped, the resulting catenary arch should, under equal and opposite gravitational load, be in a state of pure compression.

To verify the catenary shapes that I made in Solidworks, I turned them into a catenary arch and a catenary dome, using the following procedure:

1. Create a sketch of the center of each 'node' in the hanging chain model
2. Copy the sketch into a new Solidworks part file
3. Spline the points together
4. Sweep a cross section along the spline
5. Fix the ends of the arch/corners of the dome
6. Apply gravitational load
7. View results, if the compression load is close to equal throughout the part, then it can be considered a catenary arch/dome

Using the spline took to create a continuous curve and sweeping the cross section along the curve yielded the following parts:

Catenary Arch

Catenary Dome

With the ends of the arch and corners of the dome fixed and gravitational load applied, the stress visualization showed that the parts are indeed approximately catenary shapes (Note that it was easier to flip the gravitational force than it would have been to flip the part):

Catenary Arch Under Graviational Load

Catenary Dome Under Graviational Load

The side view shows that the shapes (except for near the fixtures, especially on the arch) have a consistent stress throughout the part, further proving that they are roughly catenary shapes:

Catenary Arch Under Gravitational Load, Side View

Catenary Dome Under Gravitational Load, Side View

This means that using Solidworks to model a hanging chain could, indeed, be used as a tool for generating catenary curves to be used in gridshell design. Another option I have been pursuing is using Matlab to create a catenary equation for a given size and shape (input desired height and width, and the script solves for the necessary curvature, and outputs the list of points for the desired shape/form)

Hanging Grid of Spring Chains

Can Solidworks Handle a Matrix of Hanging Spring Chains?

Yes, with similar procedure as the catenary shape of the chain of springs, only this time there is a grid (or matrix) or springs, making a 'catenary dome' that could eventually be used to make a gridshell. The result ends up looking as expected:

Spring Chain Matrix, Hanging

Just as with a single spring chain, starting from a flat position ensures that the hanging is repeatable, and the curvature of the form (basically how far down the chains actually hang) can be manipulated by adjusting the spring constant of the springs, either individually or together.

Spring Chain Matrix Starting Position (disregard the red springs)

Adjusting the springs individually will change the shape from a standard catenary shape, however, and would only make sense when the flipped catenary dome will be under uneven loading.

Both the single spring chain and the spring chain matrix were able to yield sketches representing the position of each 'node,' which means the next step moving forward is to turn those sketches into an actual catenary arch (and eventually a catenary dome) and test them under even graviational loading to see if they are at or near pure compression.