Same Design - Different Materials

I'm not an aeronautical engineer, but I think about airplane design all the time. I look at designs and admire their forms and the functions that they produce.

Is there any significant history of experimental builders taking a successful design, be it wood, metal, rag and tube or composite construction, and building the same aerodynamic package in a different material?

If one considered overall weight, weight distribution, center of gravity, strength of materials, strength of assemblies, deflection and maybe a few other variables, could you still get into trouble?

I'm a long way from ever trying something like this, but I'm curious what some of the very knowledgable designers will have to say.

Thanks.