Hi everyone... I've been a longtime lurker but this is my first post on the forum. I'm a mechanical engineering grad student at Pitt with a lot of years (too many?) of Formula SAE experience, mostly focused on chassis design/fabrication.
Anywho, since I already knew the FEA process for a space frame I spent a few hours playing with the Locost frame in the ANSYS student edition. The results are similar to what you'll find elsewhere (i.e. Cymtrik's report), but one advantage is that the screen shots I have show the stress distribution through the frame... so you get an idea of the most critical load paths.
This analysis wasn't intended to be 100% accurate, but rather to give a relative comparison of stiffness and weight changes for the most common modifications. The dimensions aren't perfect, some modifications may interfere with other parts of the vehicle, your mileage may vary, weight loss results not typical, and all the other disclaimers apply.
The analysis details are:
X axis lateral, Y axis vertical, Z axis forward
Left rear shock mount constrained about X-Y-Z displacement
Right rear shock mount constrained about Y displacement
Left front shock mount displaced 0.200in along Y
Right front shock mount displaced -0.200in along Y
Beam elements for square section members, Pipe elements for round section
Since the shock mounts are 23.0in apart, this corresponds with one degree of twist. The program solves for the force (lbs) required at each front shock mount to generate this twist, so averaging the forces and multiplying by 23.0 gives the approximate stiffness in in-lbs/deg. Divide by 12 to get ft-lbs/deg
I'll summarize the results. Note that we want to see tubes "turn green" in the pics; this indicates they are loading up. Blue means they aren't carrying much load and red means they are carrying disproportionately high loads.
First Pic: Basic book frame
Note that the stresses in most of the frame are very low... this is because it takes very little torque to twist one degree! Stiffness is only 663 ft-lbs/deg, weight is 92 lbs as modeled here.
Second Pic: Similar to common "Aussie mods," but with an additional V from shock mounts down to aft crossmember (may interfere with crank pulley!)
The braces shown here are 0.75x0.065 round steel tubing. Stiffness roughly doubles to 1291 ft-lbs/deg for a five pound weight increase to 97 lbs.
Third pic: Engine bay crossmembers
Hre's the tricky part: if you want a stiff frame, you HAVE to find some way to get these tubes in the frame. If you leave these tubes out, improvements to the cockpit area will give little benefit since the engine bay flex will dominate (think softest spring in series). The closer they are to meeting at the center, the stiffer the frame, but obviously that is impossible due to interference with the engine. Note that the lateral crossmember (across the shock mounts) doesn't take any load, so this can be omitted.
Stiffness: 2072 ft-lbs/deg, weight 100 lbs.
Fourth pic: Diagonals in scuttle, floor, and trans tunnel
Since most builders panel in these areas anyway, it is up to you to decide if it is worth adding both the panelling AND the tubes. Attempting to model a bunch bonded and riveted aluminum panels accurately is beyond the scope of this analysis
Regardless, this gives you an idea of the gains from stiffening these areas. Note that the diagonals in the trans tunnel yielded the largest improvement of this set of mods.
Stiffness: 2580 ft-lbs/deg, weight 117 lbs.
Fifth pic: Reinforcing the seat back plane and rear structure, "mirroring" the panhard brace
I recognize that the rear structure isn't modeled accurately here, but again, this gives an idea of the types of gains to expect by stiffening this area... which are suprisingly (at least to me) substantial.
Stiffness: 3462 ft-lbs/deg, weight 122 lbs.
Sixth pic: Adding "hoop style" diagonals under dash, moving engine bay diagonals
The change to the engine bay diagonals here is an attempt to make it more feasilbe to fit them around the engine... the nodes are shifted outboard 3in each and upward 6in. The dash hoops ADDED approx 200 ft-lbs/deg and shifting the engine braces REMOVED slightly more.
Stiffness: 3392 ft-lbs/deg, weight 129 lbs.
Seventh pic: Enlarge the "primary" framerails to 1.5x0.065 square tubing and enlarge the diagonals in the front suspension bay to 7/8 x 0.065 round tubing.
This was a quick way to analyze the sensitivity of increasing the tubing size (and thus bending stiffness) used for the upper and lower framerails.
Stiffnes: 4385 ft-lbs/deg, weight 140 lbs
Eighth pic: Remove the engine bay crossmembers
To illustrate the importance of the engine bay braces, I eliminated them while inluding MOST of the about changes (I sorta did this out of order). If you simply cannot fit these tubes, increasing the size of the primary framerails in the engine bay is a decent crutch fix.
Stiffness: 2852 ft-lbs/deg