I would like to bolt a bracket to a steel pipe (1.5 inch diameter), with the nut located inside the pipe. Since the application needs to support a considerable amount of weight, I need some kind of washer or spacer that is flat on one side but spherical (or cylindrical) on the other side, to match the inside surface of the pipe. I'm afraid that a regular washer will buckle and/or crack under the pressure, since the force would not be distributed evenly. What can I use to solve this problem?
Most washers will flex somewhat, so unless it's a really small pipe, or you're installing in really cold temperatures, you shouldn't worry ... but I'd be more concerned with being able to hold the nut still while you're trying to bolt to it in a smaller diameter pipe. (I don't know if the 1.5" is ID or OD, but if it's outer diameter, and it's got any significant wall thickness, it's going to be tight)
If you're really concerned, you should be able to find a rubber gasket to put in there to take up some of the gap; you could also cut down a rubber grommet or bushing to fit in there. You could also use multiple thinner washers which will flex more easily than a single thick one.
Another option would be to take a hole saw that's got a similar inner diameter to the pipe, cut a plug of wood, then slice a chunk off to make the flat-on-one-side-curved-on-the-other piece you're looking for. (and then use a fender washer or similar so the nut doesn't dig into the wood).