Lower bounds for the buckling of axially loaded stiffened shells

The buckling problem of unstiffened and stiffened shells exists since about one hundred years. During this time investigators around the world tried both to create new methods of analysis and to receive a good experimental confirmation. In most cases, as is well known, a large difference exists between data following from the theory and tests. In the last years the growth of possibilities of calculating technics and appearance of data banks of initial imperfections in different countries stimulated new theoretical ideas of how to use them in engineering and design. This approach leads to good results, but the question remains of how one can use it in cases of creating new structures. How one can confirm theoretical values if the test data and the field of initial imperfections are absent. The approach suggested here allows one to overcome the mentioned difficulties.