Structural optimization is currently attracting considerable attention.
Interest in - search in optimal design has grown in connection with the
rapid development of aeronautical and space technologies, shipbuilding,
and design of precision mach- ery. A special ?eld in these
investigations is devoted to structural optimization with incomplete
information (incomplete data). The importance of these investigations is
explained as follows. The conventional theory of optimal structural
design - sumes precise knowledge of material parameters, including
damage characteristics and loadings applied to the structure. In
practice such precise knowledge is seldom available. Thus, it is
important to be able to predict the sensitivity of a designed structure
to random ?uctuations in the environment and to variations in the
material properties. To design reliable structures it is necessary to
apply the so-called gu- anteed approach, based on a "worst case
scenario" or a more optimistic probabilistic approach, if we have
additional statistical data. Problems of optimal design with incomplete
information also have consid- able theoretical importance. The
introduction and investigations into new types of mathematical problems
are interesting in themselves. Note that some ga- theoretical
optimization problems arise for which there are no systematic techniques
of investigation. This monograph is devoted to the exposition of new
ways of formulating and solving problems of structural optimization with
incomplete information. We recall some research results concerning the
optimum shape and structural properties of bodies subjected to external
loadings.
