Structural sizing by generalized, multilevel optimization

Developments of a general multilevel optimization capability and results for a three-level structural optimization are described. The latter is considered a major stage in the method development because the addition of more levels beyond three does not introduce any new qualitative elements. Therefore, a three-level implementation is, qualitatively, the equivalent to a multilevel implementation. The method partitions a structure into a number of substructurin g levels where each substructure corresponds to a subsystem. The method is illustrated by a portal framework that decomposes into individual beams. Each beam is a box that can be further decomposed into stiffened plates. Consequently, substructuring for this example spans three levels: the bottom level of finite elements representing the plates, an intermediate level of beams treated as substructures, and the top level for the assembled structure. This example is an extension of a previously presented case that was limited to two levels.