Structural Optimization with Uncertainties

Structural Optimization with Uncertainties

Structural optimization is currently attracting considerable attention. Interest in re-
search in optimal design has grown in connection with the rapid development of

aeronautical and space technologies, shipbuilding, and design of precision machin-
ery. A special field 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 as-
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 fluctuations in the environment and to variations in the material


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. We study optimal design with incomplete in-
formation, accounting for the interaction between the structure and its environment,

properties of materials, existence of initial damages and damage accumulation. This

study is devoted to overcoming mathematical difficulties caused by local function-
als. Most of the attention of the book is devoted to the minimax approach using worst

case scenario, i.e. the guaranteed approach. But a probabilistic approach that does
not guarantee the result is also described in the monograph, because it gives more
“optimistic” results. Also, a mixed probabilistic-guaranteed approach is discussed
and applied.


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