Adding material made it worse, and here is what I had missed
A stiffening plate that moved the problem instead of solving it.
Adding material made a chassis worse in this case because bolting a stiff plate across a flexing panel only moves the flex to the boundary of the new plate, and that boundary can end up carrying a sharper, more concentrated version of the exact problem the plate was meant to solve.
An iron-on patch on the knee of a pair of jeans
An iron-on patch on a worn knee of a pair of jeans shows the same failure in a completely different material. The patch itself is stronger than the surrounding denim and it never tears. What tears instead is a new hole that opens right along the patch's own edge a few weeks later. The stiff square no longer bends with the rest of the fabric the way the original denim did, so all of the knee's normal flexing, which used to spread gently across a wide area of cloth, is squeezed into the narrow band where the stiff patch stops and the soft fabric starts again. The problem has been relocated a few millimetres away, and the new location is often weaker than the original ever was, because it is now doing all of the bending that used to be shared across a much larger area.
Where the load goes once the plate is on
A panel that is flexing under load is doing so because it has no efficient path for carrying that load in tension or compression, the way a properly triangulated panel would, and is instead relying on the surrounding structure bending to absorb the movement. Bolting or welding a stiff plate across part of that panel does stop the plate's own footprint from flexing, but the load that used to spread across the whole panel still has to go somewhere, and the path of least resistance is now the narrow band right at the plate's edge, where stiff meets soft.
The arithmetic of that is unkind. Suppose the original panel bent gently over its full width, and the plate now covers four-fifths of it. The same total movement has to happen somewhere, and if the plate's footprint no longer bends at all, the uncovered fifth has to take up all of it, bending roughly five times as sharply as before. Sharper local curvature means higher local stress, so the edge of the plate ends up working harder than any single point of the unmodified panel ever did, and it is there that a fatigue crack tends to start.
Tapering a reinforcement into the structure
Recognising this pattern changes what a fix is checked against before it is trusted. A stiffening plate, gusset or doubler only helps if the load it removes from the original flexing region does not simply reappear as a sharper concentration at the boundary it creates. That means the reinforcement has to taper gradually into the surrounding structure, spreading the transition from stiff to soft over enough distance that no single point is forced to absorb all of the change on its own.
A plate with a hard, straight edge welded or bolted directly onto a flexing panel is the shape most likely to fail this test, since a hard edge is precisely where the stress concentration forms. The same amount of extra material spread out as a gradually thickening taper, or feathered in with a curved edge, is far more likely to solve the problem it was added to fix. On the jeans, the equivalent would be a patch that thins towards its border and blends into the denim, so the fabric can hand its bending over to the patch little by little.
When a plate is the right answer
None of this means reinforcement is a bad idea in general, only that its shape matters as much as its presence. A panel that is genuinely under-triangulated, with no diagonal load path at all, benefits enormously from an added plate or gusset, because the plate is then providing the only load path that exists and has no existing one to compete with. The question to ask is whether the reinforcement is closing a real gap in the structure's load path, or being dropped on top of a load path that already exists and works, only less stiffly than desired.
In the first case the plate does real structural work with nowhere for the load to concentrate unfairly. In the second, the plate has to compete with the surrounding material's own way of carrying load, and unless its edges are shaped to blend into that behaviour, it tends to win the argument locally while losing it for the structure as a whole. A useful habit before adding any doubler is to trace, with a finger on the drawing, where the strain in that panel will have to go once the new material is in place, and to look hard at wherever the finger stops.
My key error with this
I had been taught to think of stiffness as something you buy with material, so when the base plate under the chassis flexed more than I wanted it to, my first instinct was to bolt a thicker, stiffer plate across the area that was moving. The panel itself did stop flexing, exactly as I expected it to, and for about a week I thought the problem was solved. What actually happened is that the flex had nowhere to go except to the edge of the new plate, where the stiff region ended and the original panel resumed, and that boundary began working far harder than any part of the original assembly ever had, until it cracked along a line that traced the outline of my repair almost exactly. The plate had not removed the deflection, it had concentrated it, and I had spent weight and time making one specific region of the structure worse. What replaced the belief is that a structure carries load along a path whether or not I have thought about that path, and that stiffening one region without asking where the strain will move next is not reinforcement at all, it is relocation.